The outdoor images captured in sand dust weather often suffer from poor contrast and color distortion, which seriously interfere with the performance of intelligent information processing systems. To solve the issues, a novel enhancement algorithm based on fusion strategy is proposed in this paper. It includes two components in sequence: sand removal via the improved Gaussian model-based color correction algorithm and dust elimination using the residual-based convolutional neural network (CNN). Theoretical analysis and experimental results show that compared with the prior sand dust image enhancement methods, the proposed fusion strategy can effectively correct the overall yellowing hue and remove the dust haze disturbance, which provides a constructive idea for the future development of sand dust image enhancement. In sandstorm weather, the images captured by imaging equipment always have such issues as color distortion, low contrast, and low recognizability. Affected by Mie scattering, the blue–violet light is absorbed by sand dust particles much more quickly compared with red and orange light, which plays an adverse role in various remote-based computer vision tasks and seriously interferes with the performance of intelligent information processing systems. Therefore, the image quality enhancement technology for sand dust images is an important research topic in the field of image processing and computer vision.4. However, such a fusion strategy on image enhancement in bad weather mainly focuses on image dehazing8, image deraining10, and image desnowing12. To our best knowledge, there is no well-known reported work related to sand dust removal for outdoor scene images up till now, which highlights the value of our research. The current image sand dust removal algorithms can be roughly divided into image restoration17 and image enhancement22 two mainstream categories.At present, fusion algorithms have a wide range of applications in image processing24. These algorithms employ the prior knowledge25 to estimate the intermediate parameters, which are then substituted into the atmospheric scattering model to recover the clear images. Image enhancement algorithms improve the clarity of sand dust degraded images via the prior image processing theory. Such as balancing the histogram equalization21, guided filtering26, and Retinex-based filtering27.Image restoration methods mainly rely on the atmospheric scattering modelThere are still some issues that cannot be ignored. For the physical model-based methods, inaccurate intermediate parameters may lead to dark tones and artifacts in the output images. For image enhancement algorithms, these methods are only suitable for a certain sandstorm scene. Many sand dust enhancement algorithms will fail if the distribution of sand dust images is too complex.12, which all benefited from the public datasets32. However, the absence of available sandstorm datasets hinders the development of CNN-based sand dust image enhancement algorithms.Recent years have witnessed the great success of CNN, which has attracted widespread attention from the field of image processing. Numerous researchers designed the enhancement algorithms based on CNN to handle the degraded images in complex environmentsTo bridge the gaps, we proposed a fusion strategy that includes both color correction and image reconstruction. The improved color correction algorithm based on the Gaussian model is used to remove the visual distraction of sand. We then transform the dust removal task into a haze removal task to further improve the clarity of the input images. The CNN based on the residual structure is designed to eliminate the dust nonlinearly, and we provide a comparison result on the real-world sand dust image, as shown in Fig. We proposed a simple but effective fusion strategy for combining the conventional image processing algorithm with CNN to improve the clarity of the sand dust images. The proposed fusion algorithm provides a novel way for future research on sand dust image enhancement.A color correction algorithm based on the Gaussian model is improved in our method to balance the hue of degraded sand dust images.We designed a novel CNN built on an autoencoder-like structure, which can effectively improve the local area brightness and reduce the loss of detail information in the training process.The remainder of this paper is organized as follows. The existing sand dust removal algorithms are introduced in “The main contributions of this work are summarized as follows:I(x) is haze image; J(x) denotes corresponding haze-free image; A is the global atmosphere light of the haze image; t(x) is the transmission. The sand dust image can be treated as a haze image with color distortion. Therefore, we described the degradation model as the following:D(x) is the color degradation model. To restore a clear image, the sand dust image degradation model can be transformed into the following:25. Finally, they substituted the parameters into the degradation model to restore the dust-free images. Dhara et al.16 proposed a dehazing algorithm using weighted least squares filtering on dark channel prior and color correction that involves automatic detection of color cast images. Peng et al.14 proposed a new approach to estimating ambient light which is needed by the DCP restoration methods and added adaptive color correction into the degradation model to stretch the contrast of the image while solving the issue of color distortion. Considering the attenuation of the blue channel may cause the DCP method to fail, Gao et al.17 proposed a sand dust image restoration method based on reversing the blue channel prior (RBCP). Shi et al.15 proposed an algorithm based on halo-reduced DCP dehazing for sand dust image enhancement, they corrected color in the LAB color space based on gray world theory, removed the dust using a halo-reduced DCP dehazing method, and contrasted stretching in the LAB color space using a Gamma function.There are two categories in current sand dust removal algorithms, including image restoration and image enhancement. The sand dust image restoration algorithms were designed based on the atmospheric scattering model, which is widely used to describe the imaging process in haze weather. Mathematically, the structure of the physical model can be expressed as:18 proposed a retinex-based enhancing approach, they adopted an effective alternating direction optimization strategy to solve the proposed model. Cheng et al.22 compensated the loss value in the blue channel, and enhanced the image contrast and edge information through guided image filtering. Shi et al.19 proposed a normalized gamma transformation-based contrast-limited adaptive histogram equalization (CLAHE) with color correction in Lab color space for sand-dust image enhancement. Wang et al.21 proposed a fast color balance method followed by a fusion model to enhance the sandstorm-degraded images.The other mainstream method is the image enhancement algorithm. Many researchers enhance the sand dust image quality by balancing the histogram and adjusting the contrast of the degraded image. Fu et al.Sand dust images have narrow histogram distribution. The current enhancement methods adopted image processing theory to balance the color and contrast of the images can only improve the clarity of the images to a certain extent, and the balanced images are still hazy in vision. Moreover, the manually designed prior knowledge based on specific observations may not always suit the inherent properties of the degraded sandstorm images.Currently, the mainstream methods of sand dust removal are based on traditional algorithms, most of them may corrupt the image textures and over smooth the detail information. To the best of our knowledge, there is no excellent reported fusion method related to sand dust removal for outdoor scene images. In view of the shortcomings of the conventional sand dust removal algorithms, we proposed a novel fusion algorithm to combine color correction algorithm with deep learning, which can further improve the visibility of sand dust degraded images. The framework of the proposed method is shown in Fig. Experimental results show that direct processing of degraded sand dust images using CNN does not yield satisfactory results. There is still a certain degree of color deviation in the output, and more detail will be discussed in the ablation study.33 proposed an image color correction algorithm based on the Gaussian model. The algorithm only uses the G component as the benchmark to calculate the extension coefficient. However, there are some disadvantages in the strategy of using only a single channel distribution as a reference. The corrected results are susceptible to the G component, if the G component with wide or polarization histogram distribution, the original method will suppress the contrast of the image, which may cause the pixel values to overflow or underflow, resulting in local information being lost and color degraded.Therefore, it is still necessary to preprocess the sand dust degraded images. According to the prior characteristics of the sand dust image, Zhi et al.To solve the above-mentioned issues, we reprogrammed the adaptive color adjustment strategy with the pixel difference in each channel of RGB as a reference to adjust the pixel values for each channel separately. Meanwhile, for the characteristics of low luminance and low contrast of sand dust images, we enhanced the images whose luminance mean value is less than the reference luminance to highlight the original local details of the images. The flow chart of the Gaussian model-based improved color correction algorithm is shown in Fig. Step 1 Normalizing R, G, B components pixel values of input Step 2 Calculating the extension coefficient C, respectively. We adopted the maximum value of pixel difference in R, G, and B components as a reference to calculate Step 3 Updating RGB channels pixel values of the color-biased images by the following:I is the sand dust image; G is the color correction model; Y is the output of G. The improved color deviation correction algorithm based on the Gaussian model can be simplified as:Assuming After being processed by the color correction algorithm, the distribution of the outputs is similar to the hazy images. Thus, to further improve the image visibility and the universality of the algorithm, we designed a simple yet effective end-to-end network.The unit in the network includes a convolution layer, a normalization layer, and an activation layer. The skip connections in the model can retain more information flow in the training process. The residual block in the deep feature fusion module can effectively solve the issue of gradient diffusion and improve the robustness of the network.N residual groups, each group contains m residual blocks for the deep features fusion of the image. Assuming n is the dimension of the feature vector and ith residual block and the output is f(x) represents the output of the residual block; l in ith block respectively; r represents the instance normalization layer. The deep feature fusion module is composed of N residual groups, and each residual group contains m residual blocks. Therefore, the output Nth residual group can be deduced from Eq.  loss. L1 loss is widely used to minimize the difference between the output and the reference image, which can be written as:x respectively; x and y; SSIM is commonly used to evaluate the similarity of two images. In our network, we took SSIM loss as a sub-constrain, which can be written as follows:We integrated the above loss functions and assumed that 28, NH-Haze29 and RESIDE30.Datasets can affect network performance to a great extent. However, it is difficult to collect a large number of paired sand dust samples in reality for training the network. At present, the mainstream dehazing methods based on deep learning train the network through synthetic haze images. The common dehazing dataset including NYU-Depth15. Moreover, we adopted RESIDE OTS30 to train our dust removal network. Then, we synthesized the sand dust images based on RESIDE30 to evaluate the performance of the proposed fusion algorithms.In this paper, the real-world sand dust images in the experiments all come from the dataset constructed by Shi et al.In the experiments, all the parameters in the network are initialized with Gaussian random variables; For training the network, the images are cropped to 30 to calculate the full-reference metrics. Considering the characteristics of low brightness and contrast of dust degraded image, we randomly select Due to the specific nature of the sand dust images, there is no publicly available dataset for evaluating the algorithms. So, we synthesized the sand dust images based on RESIDE SOTS16, NGT19, FBE34, HRDCP15 and TTFIO23. For the fairness of comparison, all the code of the comparison algorithms is from the website of their authors. The comparative results of the qualitative analysis on the synthetic dataset are shown in Fig. 16 cannot eliminate the influence of color deviation, it over-enhanced the blue channel component, resulting in an overall blue-violet tint to the images and the results still have obvious color distortion. Furthermore, it seems that the results of NGT19 and HRDCP15 are grayed out, the contrast of the processed images is too low and the details are not prominent, there are no significant visual improvements in both of their results. FBE34 can solve the color distortion issue very well, and the images are visually improved. Nevertheless, the algorithm only removes the sand, there is still a certain sense of haziness in vision. TTFIO23 can correct the color of the degraded image and remove dust to some extent, but the outputs appear visually unnatural due to the brighter sky area. The comprehensive comparison shows that the proposed method can effectively improve the clarity of the sand dust images. The residual structure of the network plays a positive role in balancing the brightness and the contrast of the images, making the outputs closer to the reference images.We compared the proposed method with the prior sand dust removal algorithms including CIDCTo quantitatively evaluate the performance of the comparison algorithms, we adopted Peak Signal to Noise Ratio (PSNR), Structural Dissimilarity (DSSIM), CIEDE2000, and CIE94 as the metrics. PSNR and DSSIM are widely used to measure the image quality, while CIEDE2000 and CIE94 are commonly adopted to evaluate the image tones. The higher metrics of PSNR and the lower DSSIM, CIEDE2000, and CIE94 denote the better performance of the algorithm. The comparison metrics are listed in Table 16 and TTFIO23 can remove the dust and improve the clarity of the image, but the images processed by the algorithms still have obvious color distortion. Although NGT19 and HRDCP15 can balance the hue and brightness of the images the contrast of the results is too low and the results are still hazy in vision. The outputs of FBE34 are better than other comparison algorithms, however, the brightness in the local area is too dark. Visually, the proposed color correction algorithm can effectively correct the tone of the images. By combining the correction algorithm with CNN, the clarity of the degraded images can be further improved. Please zoom in for a better illustration, the proposed algorithm can remove the haze more thoroughly and generate more natural results with less color distortion. As shown in Fig. In sandstorm weather, the concentration of sand dust images is not evenly distributed, which leads to a larger color deviation range of the real-world degraded images than the synthetic images. The difficulty of sand dust removal in real scene images is significantly higher than in synthetic images. To further evaluate the performance of the algorithms, it is necessary to conduct comparisons on real-world sand dust images. We provide several comparative examples of real-world degraded images with different visibility levels, as shown in Fig. 35, Spatial-Spectral Entropy-based Quality (SSEQ)36 and Blind Image Quality Indices (BIQI)37 to objectively evaluate the performance of the algorithm on real-world sand dust images. As shown in Table We adopted the non-reference evaluation metrics including Natural Image Quality Evaluator (NIQE)There is a doubt that why do we need to first correct the color distorted channel and then improve the visibility using CNN rather than direct optimization for sand dust image with CNN? In this section, we will further analyze and discuss the effect of the fusion strategy. Specifically, there are three different ways: (1) Color correction; (2) End-to-end CNN; (3) Fusion strategy (Proposed method). We synthesized the training dataset for the training network using the method mentioned in “The qualitative comparisons for the ablation study on the synthetic dataset are shown in Fig. In addition, we also made comparisons on real-world sand dust images. As shown in Fig. For the above experimental results, we conclude that, on the one hand, the proposed end-to-end CNN may not be compatible with this sand dust removal task. On the other hand, as we all know, CNN has a strong ability to fit the training data, but the generalization ability of CNN is often limited by the dataset. Even though we synthesized the sand dust images visually close to the real image, the synthetic dataset is not representative of all real-world sandstorm scenes due to the complex distribution of sand dust.The imaging mechanism of sand dust images should be deeply studied based on atmospheric scattering models, and the distribution of more sand dust degradation scenarios should be taken into account.The traditional algorithm is used to preprocess the image, and the CNN is employed to process the complex nonlinear mapping, which can improve the robustness of the algorithm and reduce the learning pressure of the neural network. This fusion strategy provides a novel way to solve such challenging image enhancement tasks.The appropriate prior theory may play a positive role in training CNN. We advocate a combination of appropriate priors and learning algorithms to make their advantages complementary.In this paper, we proposed a novel fusion strategy for single image sand dust removal task. The proposed method can effectively solve the issues of color distortion and local information loss widely existing in the prior sand dust removal algorithms. The residual network can suppress the noise, adaptively adjust the brightness and stretch the contrast of the images. The comprehensive experiments show that, compared with the prior algorithms, the proposed method can effectively improve the clarity of sand dust degraded image. The local details of the images are more prominent, and the overall tone is more in line with the visual characteristics of human eyes. However, the implementation of end-to-end neural networks is remain hampered by the fact that there is no publicly available sandstorm dataset, and we are still exploring a more theoretical synthesis method to promote future research on sand dust image enhancement. Based on our evaluation and analysis, several overarching observations and empirical findings are summarized as:


Management research is allocating energies to seek ways to improve organizational performance. Branding has become a significant phenomenon that academicians and scholars have studied. Improving the brand’s overall equity requires strategies that the brand managers must implement. Based on Marx’s theory, the present study attempts to determine the role of product perceived value on customer-based brand equity, brand resonance and customer affective commitment, respectively. Moreover, this study also tries to determine the mediating roles of brand resonance and customer affective commitment in the relationship between product perceived value and customer-based brand equity, respectively. For this purpose, the data were gathered from 310 customers of branding products in China. The present study applied partial least square structural equation modeling for empirical analyses using Smart PLS software. The present study’s findings acknowledge that product perceived value did not directly influence customer-based brand equity. However, results confirmed that product perceived value positively influences brand resonance and customer affective commitment. Furthermore, the outcomes of the present study also concluded that both brand resonance and affective commitment played a mediating role between product perceived value and customer-based brand equity, respectively. Theoretically, the study contributed to the literature by examining the influence of product perceived value on customer-based brand equity. The study also enriched the literature by providing key findings related to the mediating roles of brand resonance and customer affective commitment. Practically, the study is beneficial for the brands and they can enhance product perceived value by improving product design, effectively communicating product benefits, and executing effective promotional strategies. Brands have played a significant role during the frenzy of acquisitions and mergers since the late 1980s. In the recent decade, brand valuation has shifted from developed economies to emerging economies which has changed the branding question considerably . In the Recently, studies in the discipline of customer-based brand equity have suggested a shift from measuring and conceptualizing the construct to examining the relationship with other concepts in the marketing domain . Brand eBrand equity is measured by three factors i.e., uniqueness, perceived quality/perceived value, and willingness of the customers to pay the high price . This suBrand resonance is referred to as the relationship between the brand and its customers including the willingness of the customers to buy and recommend the band to others . It is aCustomer affective commitment is developed as a result of the passionate connection of the customers with the brand that demonstrates personal identifications . Both muBased on the gap found in the literature, the present study postulated some objectives which are: to examine the impact of product perceived value on customer-based brand equity, to analyze the effect of product perception on brand resonance, and to determine the impact of product perceive value on customer affective commitment. The study has two mediating variables i.e., brand resonance and customer affective commitment, so the study has formulated the objective based on these constructs. The objectives are: (1) to investigate the mediating role of brand resonance in the relationship between product perceive value and customer-based brand equity and (2) to analyze the mediating role of customer affective commitment in the relationship between product perceive value and customer-based brand equity.The current study also posited the research questions which have been addressed. The research questions are: what is the impact of product perceived value on customer-based brand equity? What is the effect of the product perceived on brand resonance? And what is the impact of product perceived value on customer affective commitment? The study has two mediating variables i.e., brand resonance and customer affective commitment, so the study has formulated the questions on the basis of these constructs. The research questions are: does brand resonance mediate the relationship between product perceived value and customer-based brand equity and does customer affective commitment mediate the relationship between product perceived value and customer-based brand equity?The study was conducted in China and the data was acquired from the customers who purchase branded products. This research intends to analyze the role of product perceived value and customer-based brand equity with the mediations of brand resonance and customer affective commitment. To address the objectives of the study, the study established the hypotheses which are based on the following theory.Marx’s theory was developed by Marx in 1954 as a critique of the school of human relations. According to this perspective, organizations are not the rational system to perform work efficiently, rather organizational systems are power systems designed for the maximization of profits and control. Marx’s value-based perspective consists of two dimensions i.e., the sphere of production and the sphere of circulation. These spheres focus on the process of capital accumulation. According to Marx, there are three core values in the organizational context, i.e., use value, exchange value, and value. Use value is defined as the physical or other characteristics of a product that induce the demand for that product. It is the product utility. Exchange value highlights the monetary value given by the individuals in exchange for the product. It is the money from value. Value is referred to as the labor time embodied in the product. According to Marx’s perspective, value is socially necessary for provoking benefits for the organization .Considering the framework of the study, product perceived value impacts customer-based brand equity, brand resonance, and customer affective commitment with the mediations of brand resonance and customer affective commitment. The relationship between the variables has been borrowed from Marx’s theory which points out that value are a significant facet of building an organization. The value-based perspective highlights the importance of value provided by the organization either use value, exchange value, or value. This theory is deeply rooted in the framework of the study see .Perceived value is the key facet and is regarded as an important factor of most customer-based brand equity frameworks . ProductPerceived value plays a significant role in building brand equity because customers need high value from the products. Customer-based brand equity consists of five major determinants, i.e., value, commitment, trust, social image, and performance. These determinants contribute greatly to developing customer-based brand equity. For example, Few studies have been conducted to understand how perceived value impacts customer-based brand equity. For example, H1.Product Perceived Value has a positive association with Customer-Based Brand Equity. explainePerceived value influences customer satisfaction such that when the customers receive high value from the product, they get satisfied. This satisfaction then leads to brand resonance. In this regard,  claimed The value offered to the customer builds brand image and reputation which consequently impacts brand resonance . The cusH2.Product Perceived Value has a positive impact on Brand Resonance.Customers make a purchase decision on the basis of their evaluation in terms of how good their experience was with the brand . For exaHigh product perceived value tends to contribute to the future commitment of the customers to the brands . ProductH3.Product Perceived Value has a positive impact on Customer Affective Commitment.Brand resonance is referred to as the relationship between the brand and the customer that includes the willingness of the customer to purchase or recommend the brand to others. The perception of the customers about the brand is built through their experiences and learning about the brand and what value they offer to the customers . TherefoOne of the core dimensions of brand equity is brand loyalty, and brand loyalty is built when the customer can relate to or resonate with the brand . This reThe mediating role of brand resonance has been explored in a few studies only. For instance, H4.Brand Resonance positively mediates the relationship between Product Perceived Value and Customer-Based Brand Equity.In the marketing literature, customer affective commitment plays a key role as it is a major determinant of influencing the brands . ScholarMore recently, scholars recognize affective commitment as a significant factor for the brands as it induces customer desire to recommend the brand to peers . The preAmong the scant literature available relating to customer affective commitment as a mediator, H5.Customer Affective Commitment positively mediates the relationship between Product Perceived Value and Customer-Based Brand Equity.Based on the above discussion and the literature, the authors developed the following conceptual framework see :This study aims to identify the effect of product perceived value on customer-based brand equity through the mediating role of brand resources and customer affective commitment. Hence, the present study data was gathered from consumers of various branded products in China. In this regard, the authors visited different brand outlets to seek permission for data collection from the customer. For this aim, they met with outlet managers, conveyed the complete data collection objective, and assured them that data would be collected only for educational purposes. The authors also guided the managers regarding the importance of the practical implication of the study for whom data would be collected. So, they also assured them that the practical implication would be shared upon their request. Hence, managers showed a positive response and were permitted to collect data.The authors developed self-administrated questionnaires based on a cover letter for data collection. This cover letter conveyed the whole objective of data collection to the participants as this study helps the organizations ensure better services and products based on customers’ views. Moreover, through the cover letter, it was also conveyed that no answers are right and wrong as their true answers would help in generating natural outcomes for this study. Hence, this step boosts the confidence of the customers to get as natural as possible responses. The questionnaire was first developed in English and then translated into Chinese as English was not common in China for speaking and reading. Hence, the authors developed dual-language questionnaires to ease the customers’ understanding. Translation of questionnaires was completed under the guidance of senior researchers. As per their guidance, the author also collected sample base data from students on dual language questionnaires for language proficiency examination. In this way, all errors and corrections were made, and the senior researchers approved finalized questionnaire.The authors adopted a convenient sampling technique for data collection from customers. They took two weeks for data collection and personally visited different brand outlets and gave approximately 8 h a day to collect data. They also requested all the visitors and customers of different outlets for questionnaire filling and offers soft drinks to customers to fill out the questionnaires. In this way, the authors targeted 350 customers and got back 350 questionnaires. After confirming their completeness and validness, they finalized 310 responses for data analysis. Hence, this study’s empirical analyses are based on a 310 sample size.The present study participants’ responses were measured based on five points Likert scale. This scale has five numbers where 1 represents “strongly disagree,” 2 represents “disagree,” 3 represents “neutral,” 4 represents “agree,” and 5 represents “strongly agree.” This study assessed data from previously validated items. The construct perceived product value was measured with five items scale adapted from p values.The present study applied the variance-based partial least squares structural equation modeling (PLS-SEM) technique instead of other co-variance-based techniques such as AMOS. The basic purpose behind this selection is the effectiveness of PLS-SEM for both types of studies (confirmatory and exploratory) . StructuThe results of model measurement consist of two parts: model reliability and validity. The present study considered the values of “Cronbach’s alpha, roh-A, composite reliability, and average variance extract (AVE)” to approve the model’s reliability , and all2 values are measured to describe the model’s strength, such as the values of latent variables exceeding or near 0.5, which indicates moderate strength of the model, and the values near 0.25 show weak model strength  are 0.479, 0.293, and 0.402, respectively, which shows moderate model strength (2) values of the model are considered significant if they are larger than zero  ratios, are used to evaluate the discriminant validity of the current study . The Fort” values and “p” values of statistics for the acceptance or rejection of the hypotheses. The current study hypothesis results are shown in t = 0.350, p = 0.726) depicted product perceived value does not positively impact customer-based brand equity. Hence, the first hypothesis of this study is rejected. The outcomes  of hypothesis 2 confirmed that the product’s perceived value positively impacts brand resonance, which means the second hypothesis of the present study is accepted. In addition, the beta value of hypothesis 2 revealed that one unit change in the independent variable  would result in 0.692 changes in the dependent variable (Brand Resonance). According to the results  of the third hypothesis, product perceived value positively impacts customer affective commitment, confirming that the second assumption of the present study is accepted. In addition, the beta value of H3 showed that one unit change in the independent variable  would result in 0.541 changes in the dependent variable (Customer Affective Commitment).The empirical investigation of the current study was accompanied by using a bootstrapping approach through 5000 samples with replacements to measure the significance level. The direct, indirect, and total paths are presented in The present study also considered the mediating role of brand resonance and customer affective commitment between product perceived value and customer-based brand equity, respectively . For theIn this turbulent era of competition, organizations seek ways to enhance performance and be more competitive in markets. The outcomes of the present study depicted that hypothesis 1  is not accepted, which means that the product perceived value does not have a positive association with customer-based brand equity online. However, these results are not consistent with prior studies , as thesThe findings of hypothesis 4 revealed that brand resonance positively mediates the relationship between product perceived value and customer-based brand equity. The findings of hypothesis 5 confirmed that customer affective commitment positively mediates the relationship between product perceived value and customer-based brand equity. This research study contributes in the body of literature in several significant ways. Existing research depicts that there are limited literature exists which explore the predictors of consumer-based brand equity . MoreoveMoreover, analyzed the influence of customer satisfaction on repurchase intention with the mediation of affective commitment. The researchers argued that affective commitment must be studied with other variables related to new branded products. Therefore, the current study incorporated customer affective commitment as a mediator in the relationship between product perceived value and customer-based brand equity on branded products.The results of this study also yield some important practical implications. It becomes imperative for the branding and marketing managers of various brands to undertake efforts and implement strategies to enhance the perceived value of their product offerings. The enhancement of perceived value will lead to the development of positive behavioral outcomes such as an increase in customer-brand-based equity. Some of the ways in which product perceived value can be enhanced include: improving product design, effectively communicating product benefits, and executing effective promotional strategies. Moreover, the marketing managers and organizations should also focus on enhancing brand resonance and affective commitment of the customers toward the brand. To achieve this, the organization should focus on establishing brand awareness and developing strong relationships between the organization and its customer base. This can be achieved by providing exceptional customer service and by implementing high values of transparency and customer-centricity.Like other studies of social sciences, the current study also has some limitations, which may motivate scholars to conduct the research in the future. The sample size of this study was small and hence the results may not be generalizable; future studies may enlarge the sample size to enhance the reliability of the results. This study is conducted on Chinese customers only; future studies may expand the scope to other regions to enhance the reliability of the results. Moreover, a cross-sectional design was adopted by the present study. Future researchers should adopt a longitudinal design by acquiring data over multiple time intervals to enhance the credibility of the results. This study analyzed the impact of product perceived value on customer-based brand equity through the mediating mechanisms of brand resonance and affective commitment. Future studies should introduce other mediating variables such as perceived brand image, customer engagement, and brand awareness to broaden the understanding of the various antecedents and predictors of customer-based brand equity.In this era of competition, firms are seeking ways to enhance performance and be more competitive in markets. Customer-based brand equity is a phenomenon that has become the point of attention for various researchers and scholars worldwide. Studies have been initiated to investigate how customer-based brand equity can be developed and enhanced. However, there is a dearth of knowledge concerning the various antecedents and predictors of brand-based equity. Based on Marx’s theory, the present study attempts to determine the role of product perceived value on customer-based brand equity, brand resonance and customer affective commitment, respectively. Moreover, this study also tries to determine the mediating roles of brand resonance and customer affective commitment in the relationship between product perceived value and customer-based brand equity, respectively. The present study’s findings acknowledge that product perceived value did not directly influence customer-based brand equity. However, results confirmed that product perceived value positively influences brand resonance and customer affective commitment. Furthermore, the outcomes of the present study also concluded that both brand resonance and affective commitment played a mediating role between product perceived value and customer-based brand equity, respectively.The original contributions presented in this study are included in the article/supplementary material, further inquiries can be directed to the corresponding author/s.The studies involving human participants were reviewed and approved by Harbin Normal University, China. The patients/participants provided their written informed consent to participate in this study. The study was conducted in accordance with the Declaration of Helsinki.GX conceived and designed the concept. XY collected the data. YQ wrote the manuscript. All authors contributed to the article and approved the submitted version.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Atrial cycle length (CL) is an important feature for the analysis of electrogram (EGM) characteristics acquired during catheter ablation (CA) of atrial fibrillation (AF), the commonest cardiac arrhythmia. Nevertheless, a robust ACL estimator requires the precise detection of local activation waves (LAWs), which still remains a challenge. This work aims to compare the performance in (CL) estimation, especially under fractionated EGMs, of three different LAW detection methods relying on different operation strategies. The methods are based on the hyperbolic tangent (HT) function, an adaptive amplitude threshold (AAT) and a (CL) iteration (ACLI), respectively. For each method, LAW detection has been assessed with respect to manual annotations made by two experts and performance has been estimated by confusion matrix and mean and individual (CL) error calculation by EGM types of fractionation. The influence of EGM length on the individual (CL) error has been additionally considered. For the HT method, accuracy, sensitivity and precision were 92.77–100%, while for the AAT and ACLI methods they were 78.89–99.91% for all EGM types. The CL error on the HT method was lower than AAT and ACLI methods (up to 12 ms versus up to 20 ms), with the difference being more prominent in complex EGMs. The HT method also showed the lowest dependency on EGM length, presenting the lowest and least variable error values. Therefore, the HT method achieves higher performance in (CL) estimation in comparison with previous LAW detection techniques. The high robustness and precision demonstrated by this method suggest its implementation on CA mapping devices for a more successful location of ablation targets and improved results during CA procedures. Being the most common cardiac arrhythmia in clinical practice, atrial fibrillation (AF) affects more than 43 million people worldwide . The risSo far, catheter ablation (CA) is considered the star AF treatment due to its high effectiveness and safety ,4,5. TheFor many of the aforementioned techniques, the detection of local activation waves (LAWs) is an elemental step. In low fractionated EGMs, LAWs can be easily detected, hence facilitating the analysis . HoweverOne of the first and most cited works employed an adaptive amplitude-based threshold which varied according to the last detected peaks, showing low error values for regular or low fractionated EGMs but increased rates for fractionated signals . The CL-Given the advantage of bipolar over unipolar EGMs in being insensitive to ventricular activity and the high use of the former in AF studies, the appropriate strategy choice for works that may need to implement LAWs detection in their analysis can be quite confusing yet inevitable. Despite the results shown in the aforementioned studies, each one of them has used a different database. Hence, a direct comparison would be unfair or would not be directly performed. The main objective of the present work is to perform a straightforward comparison between the three most robust aforementioned LAW detectors, the adaptive amplitude threshold (AAT) , the atrThe manuscript is organized as follows. The dataset employed in this study consisted of 119 EGMs of 10 s in length, recorded by a Labsystem™ PRO EP recording system  after obtaining the written consent of 22 patients undergoing CA procedures. EGMs were sampled at 1 kHz and filtered by an adaptive notch filter to reduce powerline interference together with a 0.5–500 Hz band-pass filter to limit high-frequency noise. The dataset was manually annotated and classified by EGM types by two expert physicians according to Wells’ classification . Type I The methodology of each of the studied LAW detection strategies is presented briefly in the next subsections, followed by a comparative example of the preprocessing method adopted by each strategy.The first method implemented was the AAT algorithm . This telsewhere .The ACLI method  is basedThe HT method  also modThe preprocessing of this method also used a novel technique, the HT function, aiming to reduce high amplitude variability observed in CFAEs in order to facilitate the detection process that follows next. For this purpose, each recording is segmented into 7-second intervals with lsewhere .A comparative example of these three different preprocessing strategies applied over the same EGM is shown in Accuracy, Sensitivity and Precision were calculated. True positive (Confusion matrix and CL error metrics were employed in order to evaluate the performance. Regarding the confusion matrix, Details on CL error calculation are provided next. The effect of EGMs duration as well as fractionation has also been considered.The number of LAWs successfully detected at each method was calculated by comparing the annotations made by the algorithm with the manual annotations made by the experts, allowing a threshold of 40 ms. Performance was evaluated in terms of Accuracy, Sensitivity and Precision, providing an overall perspective on performance, including the undersensing and oversensing rates of each algorithm.The error in estimating the average CL at any of the three methods was measured as the absolute difference between the mean CL of the manual and algorithm’s annotations, as can be seen from As previously stated, this metric was introduced in order to reliably calculate the CL error for each algorithm, without any bias inserted from possible under- or oversensing tendencies. In this case, the error at each CL is defined by the absolute difference between the manual annotations, called reference annotations, and the algorithm’s annotations. The individual CL error is finally calculated by the sum of errors found at each CL divided by the number of reference intervals. The formula for the calculation of the individual CL error is given in the right column of For the undersensing case, as the given CL was longer for the algorithm than for the manual annotations case, the corresponding error is calculated by subtracting the reference CL from the algorithm’s CL. However, in that case, the next interval under comparison will involve the following reference segment, while the algorithm’s segment will remain the same as before, considered to be starting from the reference segment’s initiation point so that a double counting on error will be avoided. An example of this process can be seen in Another aspect analyzed in this study was the influence of the EGMs duration on the individual CL error of each method. For each type of EGM, the three methods were applied progressively from 1 to 10 s of duration over the dataset, computing the individual CL error as a measure of the CL estimation precision.An example of the three AF-type EGMs along with LAWs annotations from experts and the compared techniques can be seen in The results for type III EGMs, also shown in Regarding CL results, The results for type II EGMs are presented in Finally, The results of the application of each method over the dataset for different EGM lengths are presented in Due to the high importance of precise AF substrate mapping, several methods for LAW detection have been developed ,24,25,26The present study has performed a direct comparison of three of the aforementioned methods, the AAT, the ACLI and the HT method. The reason why the DF method was not included in the comparison is the lack of individual CL estimation of the DF method, which is one of the main evaluation parameters of the present study. In addition, the DF method failed to provide satisfactory results under aperiodic signals, which is the most typical situation in highly fractionated EGMs.The results indicate that HT is the most robust and reliable method, showing higher accuracy and precision and lower CL errors, suggesting its recruitment for both future studies and CA devices.The high performance of the HT method can be assigned to the alternative preprocessing strategy and the recruitment of the HT function, which prevented the detector from missing low amplitude LAWs in CFAEs. What is more, this method also adopted a segmentation strategy that allowed the adaptation to various signal lengths, while the combination of an adaptive amplitude threshold with CL correction allowed the detection of LAWs in segments with high amplitude variability . FinallyEGM fractionation plays a significant role in the performance of each method. Normally, in low fractionation environments, performance is high and only a few errors are observed. Thus, low performance in low fractionation EGMs implies a lack of reliability. As EGMs become more fractionated, with indiscernible activations, the LAW detector’s accuracy tends to drop. However, since CFAEs, which are highly fractionated EGMs, are the main challenge of any LAW detector, the performance of each method on that kind of recording is crucial and serves as an index to evaluate reliability and robustness.This study has utilized the Wells’ classification for types of EGMs, with ascending levels of fractionation from type I to type III EGMs. In this way, insufficient results in type I EGMs indicate a less reliable method, while competent results on type III EGMs affirm the reliability of another method. The final assessment is a trade-off among the performance of each EGM type, with special weight to type III EGMs, which are the distinguishing parameter.The HT method showed the highest results in terms of a confusion matrix for all EGM types, being considered this way the most reliable method, achieving high performance. On the contrary, the AAT method showed relatively low results in AF type I EGMs, due to the high amplitude variability present in this EGM type of the current database.The main implementation of LAWs detection in real-time mapping devices is related to CL estimation. Consequently, the error in CL estimation was included in the evaluation procedure. As it was shown, mean CL error can be affected by under- or oversensing incidence, and hence, its employment is not recommended. Contrarily, individual CL estimation is an impartial method. Individual CL error was the lowest in the HT method for all EGMs, implying again the high reliability and performance of this technique, while the AAT and ACLI methods have shown poor results, especially for type III EGMs.Adaptability and proper function regardless of external factors are keys to optimized performance. As signal length varies from study to study, the ability of an algorithm to perform optimally under any length should be taken into consideration for the evaluation of its performance. Additionally, signal length could affect the conclusions of the conducted comparison. For the aforementioned reasons, the individual CL error on each method was assessed over various EGM lengths.The robustness of the HT algorithm was proved not only by the fact that the error was minimal for any EGM type and length but also because it was not significantly affected by the signal length. This means that this method can perform regardless of the duration of the database used, providing flexibility both to prospective studies and to CA devices. On the other side, the AAT method showed the highest individual error for all EGM types, especially high for EGM type I. Moreover, this algorithm showed unusually high dependence on EGM length for types I and II EGMs, possibly due to high discrepancies between amplitude values in various segments of the same recording.The HT method is an optimal LAW detector, showing higher performance than the AAT and ACLI techniques in every aspect under investigation. The high accuracy and robustness of the HT method contribute to precise CL length estimation, regardless of the signal length or the EGM fractionation. The high adaptability of this method suggests its implementation on real-time mapping devices aiming to localize CA targets or its adoption by future studies, providing reliable LAW detection results and precise CL estimation.


Global navigation satellite system (GNSS) plays a crucial role in many fields, such as aerospace and transportation. Integrity is the measure of trust used in GNSS positioning especially in safety-critical applications. Advanced receiver autonomous integrity monitoring (ARAIM), taking full advantage of multi-constellation GNSS, shows huge potential to provide vertical navigation in civil aviation en route navigation and terminal approaches. However, the multi-constellation ARAIM also greatly exposes computational complexity and potential performance hazards in fault modes determination and fault-tolerant positioning. From the perspective of integrity risk control, rather than the pursuit of better positioning accuracy blindly for safety-critical applications, the concept of constellation dynamic selection is proposed and implemented in ARAIM and the performance analysis is discussed in this paper. Only the best two constellations which have the best vertical geometry performance are involved in ARAIM calculation anytime anywhere. The proposed method shows superiority in both integrity availability and computational complexity in both simulations and actual GNSS signal experiments. While the computational complexity is less than 10% of that using four constellations, 100% availability under LPV-200 criteria can be achieved in worldwide coverage experiment. The proposed method also overcomes the shortcomings of ARAIM with two fixed constellations and shows good robustness under depleted scenarios. Furthermore, the statistics results from observation stations proved the applicability and generality of the proposed method under current developing GNSS constellations. Global navigation satellite system (GNSS) is one important positioning and navigation system widely used in aerial vehicles and ground transportations ,2. IntegThe ARAIM user algorithm is implemented based on multi-constellation and dual-frequency GNSS, where the spatial geometry will be improved greatly and the ionosphere error can be corrected easily through dual-frequency observations combination ,15. ARAIARAIM uses multi-constellation observations to improve the satellite geometry and increase redundant measurements. However, a core question is that whether more constellations are better for receiver integrity monitoring. On the one hand, the recent simulation research has shown that based on two constellations, ARAIM can cover about 90% of the world with a 99.5% availability, where the 99.5% availability herein means that the ARAIM is available during 99.5% of the time at the test point . The facRegarding the explosive growth of monitored fault subset, many studies have recognized this problem and proposed many methods to reduce the number of monitored fault subset ,23. HoweWhat cannot be ignored is that the robustness of ARAIM with two constellations is not enough. The hidden trouble is that the single constellation fault will result in a similar performance of conventional RAIM (single constellation). Then, the fault-tolerant positioning result of the single constellation subset will depend on the performance of the corresponding constellation only . The worTo evade the performance uncertainty and the computational complexity of ARAIM with three or four constellations and improve the robustness of ARAIM with two constellations, the concept of constellation dynamic selection is proposed and implemented for ARAIM user algorithm. Only the two constellations with the best geometry will be used for ARAIM estimation. The proposed method can get an encouraging high worldwide availability with a low computation burden. Facing satellite outage or even constellation outage, the method also shows superiority in robustness. Most importantly, the flourishing development of multi-constellation provides solid foundation for constellation dynamic selection. The worldwide coverage experiment, depleted scenarios test and observation station statistics fully verified the effectiveness of the proposed method.The rest of the paper is organized as follows: In the milestone reports of ARAIM TSG, the roadmap of ARAIM development is divide into two steps: Horizontal ARAIM and Vertical ARAIM. The Horizontal ARAIM can be considered as the solution of transitional stage from traditional RAIM to ARAIM, which aims at providing horizontal navigation for en route and terminal approach. The Vertical ARAIM aims at providing LPV-200 for worldwide aircraft landing navigation. The LPV-200 is the last period in the non-precision approach and after that is the precision approach Category I. As the Vertical ARAIM can be considered as the ultimate goal of ARAIM application, we will only consider Vertical ARAIM in this paper (hereinafter referred to as ARAIM) and the ARAIM availability criteria is seen as LPV-200.The baseline ARAIM user algorithm is based on snapshot multiple hypothesis solution separation (MHSS). Multiple hypothesis determines the fault modes that need to be monitored to meet the integrity risk with the assist of integrity support message (ISM). Solution separation tests the consistency between the present all-in-view position solution and the fault-tolerant position corresponding to the fault modes determined in multiple hypothesis and test the differences to prompt whether a fault exists. Finally, the LPV-200 criteria, including horizontal protection level (HPL), vertical protection level (VPL), EMT, and vertical accuracy, will be used to evaluate the ARAIM performance.satPi, and constPj, represent the ith satellite and jth constellation in ARAIM, respectively, and satN is the number of satellites in the positioning calculation.The number of subsets and corresponding fault modes probabilities are calculated within the satellite prior fault probability and constellation prior fault probability which is provided by the ISM. However, ISM does not specify which fault modes need to be monitored. This determination must be made by the receiver based on the contents of ISM and the positioning resolution. Different from the traditional RAIM, which can only monitor a single satellite fault, the constellation faults and multiple simultaneous satellite fault can be detected with the assist of ISM. In ARAIM, the constellation faults and satellite faults are independent events in fault modes determination as described in:faultmodep can be calculated as:idx refers to the set of fault events.A satellite fault is a signal in space fault state which may be caused by erroneous satellite navigation data or anomalous satellite payload events. The constellation fault is a common cause which may originate at the constellation service provides (CSPs) ground segment. They are independent events in terms of prior fault probability in the content of ISM. A fault mode is a combination of events. With the prior fault probability received from the ISM, the probability of different fault modes THRESP as the threshold for the integrity risk coming from unmonitored faults. One fault mode corresponds to one fault subset. The ARAIM can work into the step of fault-tolerant positioning after the probability of unmonitored fault modes is less than THRESP.Not all fault modes need to be monitored. ARAIM introduces faultPactual, and the required monitored fault probabilities faultPreq, is calculated as:faultpk, refers to the probability of kth fault mode. THRESP is the threshold for the integrity risk coming from unmonitored faults. faultmodesN is the total number of fault modes. no_faultp is the probability of all-in-view subset, which means no fault exists:satN + constN) represents the total number of fault events.The number of fault subsets should satisfy that the actual monitored fault probabilities are not lower than the required monitored fault probability. The relationship can be given as the following inequality:no_faultp will get smaller as more fault events are involved. It will result in a bigger faultPreq, according to Equation (5). Meanwhile, on the other side of inequality (3), the probability of original kth fault mode gets smaller simultaneously. THRESP, constPj, and satPi, are set as 8 × 10−8, 1 × 10−4, and 1 × 10−5, respectively.According to Equation (6), it is easy to understand that with more constellations involved in ARAIM, the value of One satellite fault is the basic fault mode in ARAIM. As shown in The recent studies unexceptionally verified the exponential increase in fault subsets. The total number that need to be monitored can be hundreds and thousands. When the number of simultaneous faults exceeds two, another core question refers to whether it needs to categorize the multiple satellites fault to the constellation fault. This is outside the scope of this article. We do not consider the specific number, but inevitably the explosive fault modes are significant computational burdens for the airborne receiver.−5, 10−4, and 10−3 are all considered , it can effectively control the expansion of threshold.The relationship between EMTP . It is computed as follows:kT,3 is the solution separation threshold in the up component, and it is the product of faK,3 and faK,3 becomes larger with the increase of fault modes. The EMT at the current epoch will get larger and directly threaten the availability of ARAIM.At the same time, the multi-constellation will affect the ARAIM availability further. EMT is one of the criteria for vertical positioning performance described by the SARPs (Standards and Recommended Practices) and accepted by the ARAIM as one of LPV-200 requirements on the vertical position. It is based on operational trials that showed that an additional requirement was needed beyond the normal requirements of vertical accuracy and integrity . The EMTThe computational complexity and performance uncertainty have been analyzed in the above section. Instead, ARAIM with two constellations is easy to implementation. However, its robustness is not good enough because the availability is seriously affected by constellation difference and satellite outages . In thisThe feasibility of constellation dynamic selection can be talked about from three aspects. The first is the ARAIM algorithm feasibility. The baseline ARAIM algorithm is based on snapshot principle, which means the integrity evaluation only uses the data of present epoch. There is no correlation between neighbored epochs. It provides an opportunity to select observations from different constellations to assess the integrity. The receiver will process the multi-constellation signals as usual but only the constellations selected will be transited to ARAIM evaluation.The second aspect is the number of constellations. The satellite navigation has stepped into a new generation. All the four GNSS systems: GPS, GLONASS, Galileo, and BDS, have been providing global open service. The number of GNSS constellations supports the solution to select particular constellations to pursue high integrity while guaranteeing the positioning accuracy. In other words, it provides new ways to control the integrity risk rather than blindly pursuing the better positioning accuracy for safety-critical applications.The third aspect of feasibility is the fact that there is performance difference among above four GNSS constellations. This difference can come from space. GPS is the only constellations which has six orbits. The orbit inclination of GLONASS is far greater than those of the other constellations. BDS accepts the mixed constellation which includes GEO, IGSO, and MEO. The above differences will result in performance differences in different places. Even in the same place, the performance difference is dynamic with the period of satellites, the satellite outages or the number of backup satellites. This difference will be aggravated by the ground characteristics when GNSS is applied to ground applications, typically the GNSS application in urban canyon. Additionally, the satellite or constellation faults will affect the performance of GNSS apparently. So, it is feasible and necessary for a receiver to select better constellations based on observations at the present moment.The detailed implementation is given in The next step is to find the criterion for constellation dynamic selection. As the basis of ARAIM user algorithm is the improved geometry from multi-constellation, the criterion should evaluate the geometry scientifically and reasonably. Furthermore, the criterion should focus on the geometry consistency at vertical component as the ARAIM focuses on providing vertical guidance. The vertical protect performance is also the biggest challenge for ARAIM application, especially the EMT requirement in LPV-200, which is also for evaluating the vertical positioning performance. Based on the research work in , we alsoAfter the signal baseband processing, the geometry matrix, also known as the Jacobian matrix has been calculated with the weighted least square calculation. The Jacobian matrix separation is given as follows.m constellations involved, the Jacobian matrix G can be rewritten as:Gj is the line of sight (LOS) vector part of jth constellation and jT is the corresponding receiver clock offset part as followsith satellite and n represents the total number of satellites in jth constellation. jT is a n × m matrix and all elements are 0 except the jth column, whose elements are 1.For an epoch with jth constellation is given as:Then the separated Jacobian matrix of For the best constellation combination selection, two selection rules are experimented and evaluated in this paper. Rule 1: the two constellations with the minimum VDOPs. Rule 2: the dual-constellation combination with the minimum VDOP. Corresponding to Rule 1, the constellations will be sorted by VDOP of single constellation from small to large. The top two constellations are the choices into ARAIM calculation. Then under the circumstance of Rule 2, the constellations will be combined to dual-constellation combination, only the one with the minimum VDOP is the target of constellation dynamic selection. The following part is the particular implementation of two rules in receiver algorithm.Under Rule 1, as shown in Equation (14), it is a standard format of geometry matrix of single constellation. Then the two constellations are chosen using the following equationk.jn and kn represent the number of satellites in constellation j and k.Under Rule 2, the Jacobian matrices of different constellations need be recombined into dual-constellation form as followsThe number of combinations is Gnew will replace the original G and is sent to the ARAIM part to determine the fault subsets and calculate the positioning, with the assist of ARAIM ISM information. The fault-tolerant positioning solutions Wk) is considered. The outputs for LPV-200, number of fault modes and the worldwide distribution of constellation dynamic selection are shown and talked in this section.Last is the distribution of constellation dynamic selection in the whole world. As mentioned in the section of introduction, the robustness of ARAIM with two constellations is not enough as the depleted scenarios like satellite outages would hurt the ARAIM availability seriously. To evaluate the robustness of the proposed constellation selection method. The availability under depleted scenario is tested in this section further. A GPS satellite is removed from the constellation to simulate the scenario that one GPS satellite is in maintenance or excluded due to fault. The availability under three above ARAIM modes is tested. The results are shown in As one GPS satellite is removed, in the first two groups, the ARAIM worldwide availability reduces to only about 50% and it is a heavy hit to ARAIM application. The last three groups show good robustness under this circumstance, which are all about 100%. However, the principles to defend one satellite outage are not the same. The ARAIM with four constellation uses the advantage of more visible satellites while the proposed method chooses the best two constellations in spatial vertical performance. The robustness of the proposed ARAIM is no less than that of the ARAIM with four constellations.To further prove the superiority of the proposed method, actual fixed-point GNSS signals are collected in this subsection to evaluate the ARAIM availability. The actual GNSS signals are got from the open access high-quality GNSS data with the support of International GNSS Service (IGS) network, including observation files from different stations around the world and the combined multi-GNSS broadcast ephemeris file. Considering the latitudes and continents, observations from 12 stations are chosen for statistical analysis and every station can track GPS, GLONASS, Galileo and BDS. Distribution of the stations chosen are show in Four ARAIM groups are considered in this test: ‘GPS + Galileo’, ‘GPS + BDS’, four constellations, and constellation dynamic selection. The statistical results are shown in It should be noted that the current GNSS constellations are not all in their nominal configurations. The number of Galileo and BDS MEO satellites have not reach those of their nominal configurations. On the other side, GPS deploys more spare satellites than the need of nominal configuration. It resulted in the availability time varied from about 60% to nearly 100% when fixed dual-constellation is adopted. The ARAIM availability is not evenly spread and rare to reach 99% under the current GNSS constellations. The mean availability results of ‘GPS + Galileo’ and ‘GPS + BDS’ are only 85.76% and 93.00%. However, the availability results under ARAIM with four constellations and ARAIM with constellation dynamic selection are much better than those of ARAIM with two fixed constellations. All values in these two modes exceeded 99% and the results of the latter mode are much close to those of the former one. The mean values are as high as 99.81% and 99.62%, respectively. The proposed constellation dynamic selection method shows strong applicability and generality under the current dynamic developing GNSS constellations. Besides the aerospace application, it is of great help to promote the application of ARAIM in autonomous vehicles and intelligent transportation system.From the perspective of integrity risk control of potential hazards uncertainty and user algorithm implementation complexity, the concept of constellation dynamic selection is proposed in this paper. The stable and healthy development of four GNSS constellations and the baseline ARAIM user algorithm based on snapshot principle provide the feasibility to dynamically select different constellations to evaluate the GNSS integrity in different locations and different epochs.A practical and computationally effective ARAIM method based on constellation dynamic selection is implemented. Two alternative rules are given to select the targeted two constellations with the best vertical geometry performance. Only the two constellations with the minimum VDOP are selected and replaced the other constellations for integrity monitoring. The test results show that the ARAIM worldwide availability can reach 100% under LPV-200 criteria with less than 10% of the computational complexity of ARAIM with four constellations. The proposed method also shows robustness under depleted configurations like satellite outages. Furthermore, the statistics results based on observation stations validated the superiority of the proposed method under current GNSS constellations. A tradeoff is achieved between the high availability and robustness of ARAIM with three or four constellations and the practicability and accessibility of ARAIM with two constellations.The proposed method is especially suitable for expanding the application of ARAIM technology in harsh environment. We also noticed the criterions for constellation selection can be improved significantly, just as the increasing research for satellite selection. With the further study of satellite/constellation prior fault probability and performance in space, the ISM details of different constellations will definitely be different. How to improve the dynamic selection criterion with the ISM to guarantee the best integrity is the next work.


The impact of coronary artery disease (CAD) on all-cause mortality and overall disabilities is well-established. Percutaneous and/or surgical coronary revascularization procedures dramatically reduced the occurrence of adverse cardiovascular events in patients suffering from atherosclerosis. Specifically, guidelines from the European Society of Cardiology on the management of myocardial revascularization promoted coronary artery by-pass graft (CABG) intervention in patients with specific alterations in the coronary tree due to the higher beneficial effects of this procedure as compared to the percutaneous one. The left internal mammary artery (LIMA) is one of the best-performing vessels in CABG procedures due to its location and its own structural characteristics. Nevertheless, the non-invasive assessment of its patency is challenging. Doppler ultrasonography (DU) might perform as a reliable technique for the non-invasive evaluation of the patency of LIMA. Data from the literature revealed that DU may detect severe (>70%) stenosis of the LIMA graft. In this case, pulsed-wave Doppler might show peak diastolic velocity/peak systolic velocity < 0.5 and diastolic fraction < 50%. A stress test might also be adopted for the evaluation of patency of LIMA through DU. The aim of this narrative review is to evaluate the impact of DU on the evaluation of the patency of LIMA graft in patients who undergo follow-up after CABG intervention. Coronary heart disease (CHD) is one of the most common causes of death and disability in developed countries . More thCoronary angiography (CA) is the gold standard technique for detecting coronary atherosclerotic plaques, which are responsible for the occurrence of acute coronary syndromes (ACS) or stable angina. The results from CA imaging led physicians to choose between percutaneous or surgical revascularization for saving myocardial viability and preventing CHD comorbidities and mortality.ESC guidelines on myocardial revascularization  provide The left internal mammary artery (LIMA) is the graft of choice for revascularization of the left anterior descending coronary artery (LAD) ,8,9 becaThe functional evaluation of the coronary graft is crucial for risk stratification of patients who underwent CABG. Despite the reduced rate of occlusion, the probability of a progressive narrowing process due to atherosclerosis progression remains high enough to require a comprehensive diagnostic evaluation of CABG patency. The conventional and current gold standard investigation for the assessment of conduit stenosis is CA, but its invasiveness includes many risks such as vascular trauma, arrhythmias, stroke, myocardial infarction, and arterial dissection.Different methods that directly and non-invasively analyze the patency of the graft have been recently developed. Multidetector computed tomography (CT) showed good sensitivity and specificity , but it Doppler ultrasonography (DU) can be considered as a further non-invasive tool for detecting LIMA patency after CABG as firstly reported by Fusejima et al. . DU has The aim of this review is to evaluate the role of DU in assessing LIMA graft patency during the follow up of patients with CHD treated with CABG.LIMA arises from the subclavian artery opposite to the thyreocervical trunk and descends behind the cartilages of the upper six ribs at a distance of about 1.5 cm from the margin of the sternum. Two mammary veins whose length vary from 15.1 to 26.0 cm run parallel to LIMA .Other arterial conduits can be adopted for myocardial revascularization purposes: right internal mammary artery (RIMA); radial artery; right gastroepiploic artery; and, rarely, ulnar artery and/or inferior epigastric artery .All of these are medium-calibre arterial vessels (diameter 2.5–5 mm). The large amount in elastic components, the internal and external elastic membranes, and the endothelial layer—which is able to act as a paracrine and autocrine organ—are all suitable features for their use in CABG. Due to their structural and functional characteristics, they are able to actively modify their lumen, regulate the amount of blood flowing to organs and tissues, and preserve their own structure from damages deriving from manipulation during the procedure .LIMA is the best vessel to choice for the revascularization of occluded coronary arteries—LAD in particular—due to its location and structural characteristics.Despite the possible use of RIMA, the most widely used graft is the left counterpart: the position of the LIMA in mediastinum, its route and proximity to the heart, and the possibility for an easy surgical anastomosis of the LIMA—as compared to RIMA—to the coronary artery are the most important reasons for routinely adopting LIMA rather than RIMA .LIMA is recognized by cardiothoracic surgeons as the most effective and reliable conduit due to its structural characteristics, lower incidence of adverse events, and greater long-term patency rate ,21,22,23LIMA presents histo-morphological characteristics of an elastic artery as it is possible to recognize the intima, the media, and the adventitia ,27. NeveDuring the intervention, if not performed off-pump, the patient’s aorta and heart are centrally cannulated, and attached to the cardiopulmonary bypass (CPB) circuit. Then, after placing an occlusive cross-clamp on the ascending aorta, the heart is arrested using a high-potassium concentration cardioplegic solution. Then, the surgeon can anastomize the harvested conduit to the coronary artery distal to the zone where the flow is blocked. Then, the cross-clamp is removed and the cardioplegia washed out, the heart begins to contract, and the surgeon can check the grafts for both blood flow and competence as well as possible bleeding from the anastomosis site.Therefore, the resistance of vessels to manipulations should be really high in order to prevent early and late stenosis of the graft. The morphological and ultrastructural characteristics of the vessels account for this resistance. Such resistance is higher than saphenous grafts, whose manipulation can easily lead to their early occlusion soon after CABG intervention .The echo-color Doppler technique represents one of the most attractive instruments for the evaluation of coronary grafts. Despite some limitations related to the reproducibility of the technique, its performance by experts constitutes one of the best methods for the non-invasive assessment of graft patency.The non-invasive approach to the evaluation of LIMA based on echo-color Doppler is complex and challenging.Linear probes are the first line instrument in the evaluation of these vessels, followed by the pencil beam, which allows for a continuous-wave Doppler signal that is able to provide useful information about the hemodynamics. Specifically, pencil probes are able to recognize blood flow by means of a transducer—the Pedoff’s transducer—whose shape is like a pencil and is formed by two separated elements: one that is able to transmit the signal, and the one that is able to receive the backward signal.The linear probe is a 2–4 MHz transducer directly placed on the skin after application of commercial ultrasonic gel. The LIMA graft can be visualized either from the left supraclavicular fossa  or from The left supraclavicular fossa approach is the preferred one. To detect the LIMA flow, the initial velocity range of the color Doppler should be set at approximately 21 cm/s and then adjusted to optimize the visualization of color signals in the bypass graft . The proThe possibility for detecting LIMA flow is lower when the parasternal approach is adopted . Indeed,Preoperative supraclavicular and transthoracic ultrasound of the LIMA shows higher systolic and lower diastolic velocity patterns as in peripheral arteries. Normal LIMA arterial Doppler is usually characterized by a biphasic or triphasic signal . The firThe CABG intervention changes the Doppler profile of the LIMA: the flow in proximal LIMA becomes biphasic (systolic and diastolic). It occurs as a sort of “diastolization” of LIMA blood flow: the Doppler shift frequency drops during the systolic phase and appears more prominent during the diastolic phase ,36. The The prognosis of CABG patients depends on the demonstration of the aorto-coronary by-pass graft functionality. Routine postoperative CA could not be performed in relation to its intrinsic risks.Doppler ultrasound (DU) was developed as an alternative to CA, but it is rarely used due to its suboptimal sensitivity and specificity. Improvements in technological resources and technique have been obtained over the years.Anastomosis evaluation is challenging because blood flows from both the native LAD and LIMA to the anastomotic site, thus causing competitive flow .Difficulties in blood flow detection are also related to the evaluation of the stenosis degree. Elevated flow velocity at DU represents true stenosis; nevertheless, moderate-to-severe stenosis (50–70%) of the LIMA graft is hardly detected by means of DU as flow does not significantly differ from data coming from less-occluded grafts .The pulsed wave (PW) Doppler is the best DU method for the non-invasive assessment of coronary graft stenosis. The first characteristic to be considered is the morphology of the Doppler spectrum profile. Proximal occlusion of the LIMA graft usually makes the flow monophasic, thus showing the loss of the diastolic component; distal stenosis can determine the decrease in diastolic flow pattern, although the biphasic pattern is preserved. Graft failure could be suspected when no flow or a systolic dominant pattern with reduction in diastolic component is detected .Nevertheless, further parameters should be considered when using PW Doppler in order to better identify severe (>75%) stenosis of the LIMA graft. In particular, the physicians’ attention should be concentrated on the following parameters :The peak of the systolic velocity (PSV): a predominant PSV at baseline is considered as a marker of LIMA graft dysfunction .The peak of diastolic velocity (PDV): the higher the baseline values of PDV, the lower the risk for graft stenosis.PDV/PSV ratio: due to its independence from the angle of incidence of the ultrasound beam, it is a reliable parameter to be considered for the evaluation of the LIMA graft. Bach et al.  observedDiastolic fraction (DF): it expresses the impact of the diastolic flow on the composite velocity time integral  of both systolic and diastolic flow. The diastolic VTI fraction is obtained by dividing the diastolic VTI (DVTI) by the sum of the systolic (SVIT) and DVTI according to the following formula ,43:DF = p < 0.01), as well as other single Doppler parameters  [The DF better performs than DVTI as it seems to overcome the intrinsic limitation of the latter. Specifically, reduced inter- and intraobserver variability can be obtained by dividing DVTI to the sum of DVTI plus SVTI. Leitão et al.  found go < 0.01) .Beyond the Doppler parameters at rest, pharmacological tests can be further adopted to evaluate the LIMA graft patency and corroborate the data at rest. The changes in flow velocity after the administration of coronary vasodilator drugs such as dipyridamole (which acts on resistance vessels) or nytroglicerin  can provide useful, dynamic information regarding the evaluation of the LIMA graft. Both of them are able to increase PDV without influencing PSV. In particular, dipyridamole infusion promotes stable blood pressure while increasing heart rate; therefore, the diameter of the LIMA-graft tends to increase, while flow velocity remains stable, thus providing an increase in vessels capacity. NTG administration causes the increase in PDV in LIMA, with no modifications in systolic peak velocity and diameter. Generally, the increase in oxygen demand during DU stress test will cause an increase in the velocity of the flow into the graft: this will confirm the patency of the graft itself ,46.The continuous-wave (CW) Doppler evaluation of the blood flow velocity in the LIMA graft is a further, easy, and reproducible technique for evaluating human coronary flow ,48.Pencil probes using 8 MHz frequency are the instruments to be considered for the recording of the CW Doppler images of the LIMA graft.After positioning the patient supine on the bed in a quiet, temperature-controlled room, the sonographer could stand behind his/her head in a comfortable resting position, with the elbow preferentially put stable on the bed in order to maintain a stable position.The probe should be positioned at the left supraclavicular fossa with an angle manually maintained at 75 to 80 degrees: slow movements should be attained by changing the incidence angle of the probe in order to correctly identify the LIMA graft blood flow.The normal, not-anastomized LIMA typically shows a CW pattern characterized by higher systolic and minimal diastolic waves .The reason is related to the physiology of the vascular cycle: peripheral vascular beds are normally perfused during the systole, thus accounting for the higher peak of systolic Doppler profile as compared to diastolic one in vessels still not-anastomized to the coronary arteries. After the by-pass intervention, the situation of perfusion changes. The coronary artery is usually perfused during diastole. Therefore, the LIMA can show a new, double situation after its connection to the LAD : it can This technique is safe and reproducible above all when used for the evaluation of coronary graft anastomized to LAD, as already demonstrated in the literature ,49,50,51Nevertheless, the influence of different conditions on graft flow should be taken into account in order to have a complete overview of the patency avoiding confounding factors. Ciccone et al.  analyzedThe use of Doppler ultrasound evaluation of LIMA patency represents a reliable opportunity for clinicians for the identification of patients at risk for occlusion of the graft.Although far from being considered as a definite recommendation, we would like to suggest a dedicated flow chart for the application of the ultrasound evaluation of the LIMA in daily clinical practice. Specifically, the link between ultrasound data  and the clinical characteristics of patients  will promote better comprehension of the patients’ needs and the management of them.Nevertheless, limitations should be considered when applying Doppler ultrasound to the evaluation of LIMA. Firstly, the need for the performance of the examination by an expert might limit the widespread use of the procedure. Secondly, inter- and intraobserver variabilities should be always taken into account when dealing with ultrasound techniques. Thirdly, the reproducibility of this technique should be compared with standard-of-care in dedicated clinical trials. Specifically, there is no study dealing with the comparison between duplex ultrasound and CT angiography for the evaluation of the patency of LIMA or RIMA in patients who had undergone CABG: dedicated clinical evaluations should be finalized for this purpose.Finally, multimodality imaging techniques should represent the best approach to patients with cardiovascular diseases—and those who underwent CABG in particular—rather than a single technique approach as this will allow for the correct identification of alteration in patients.LIMA is the conduit of choice for bypass graft in the revascularization of damaged cardiac muscle after myocardial infarction due to coronary atherosclerosis. Its functional evaluation is crucial during the follow-up of patients who underwent CABG intervention. The gold standard investigation for the assessment of conduit stenosis remains CA, but this is an invasive technique and it entails many risks.Different non-invasive methods had been recently developed for coronary graft evaluation. Nevertheless, CT and MRI still show limitations. DU seems to be the best non-invasive tool to assess LIMA patency after CABG both immediately and/or late from the intervention. Its good reproducibility, ease of use, and significant correlation with angiographic results make DU the best technique to be adopted in clinical ambulatory practice in order to follow-up with patients who underwent CABG.