Users participate in multiple social networks for different services. User identity linkage aims to predict whether users across different social networks refer to the same person, and it has received significant attention for downstream tasks such as recommendation and user profiling. Recently, researchers proposed measuring the relevance of user-generated content to predict identity linkages of users. However, there are two challenging problems with existing content-based methods: first, barely considering the word similarities of texts is insufficient where the semantical correlations of named entities in the texts are ignored; second, most methods use time discretization technology, where the texts are divided into different time slices, resulting in failure of relevance modeling. To address these issues, we propose a user identity linkage model with the enhancement of a knowledge graph and continuous time decay functions that are designed for mitigating the influence of time discretization. Apart from modeling the correlations of the words, we extract the named entities in the texts and link them into the knowledge graph to capture the correlations of named entities. The semantics of texts are enhanced through the external knowledge of the named entities in the knowledge graph, and the similarity discrimination of the texts is also improved. Furthermore, we propose continuous time decay functions to capture the closeness of the posting time of texts instead of time discretization to avoid the matching error of texts. We conduct experiments on two real public datasets, and the experimental results show that the proposed method outperforms state-of-the-art methods. As illustrated in With the development of social networks, users usually own multiple social network accounts for different purposes. In particular, a report , where the continuous time decay function is designed to capture the closeness of posting time. Apart from modeling the similarities of words in texts, we capture the similarities of named entities in the knowledge graph to enhance the semantical similarities of the texts. In addition, we introduce the continuous time decay functions to circumvent the failure of matching caused by time discretization. With the time decay function, the similarities of words or named entities are reweighted based on the posting time to capture the closeness of time.We propose a user identity linkage model with the In detail, we first extract the named entities in the texts and link them to the knowledge graph. To model the correlations of the semantics of texts, we construct the word and named entity similarity matrix and reweight the word and named entity similarity matrix based on the posting time through time decay functions. We then leverage the convolutional neural networks to learn similarity signals. Finally, an attention mechanism is applied to aggregate the word and named entity similarity signals to predict the user identity linkage. We evaluate the effectiveness of the proposed method on two real public datasets, namely, Foursquare–Twitter and Flickr–Yelp.We propose a novel user identity linkage method based on user-generated content, in which the semantics of texts posted by users are enhanced by introducing the additional correlations of named entities in a knowledge graph. To the best of our knowledge, this is the first time that named entities of a knowledge graph are considered in the user identity linkage task.We propose continuous time decay functions to capture closeness of posting time to circumvent the problem that similar content may fall into different time slices caused by time discretization.We conduct experiments on two real public datasets to demonstrate the effectiveness of our proposed method. Furthermore, we show the detailed ablation study to prove that named entity similarity modeling and the time decay functions significantly contribute to the results.Our main contributions can be summarized as follows:The rest of the paper is organized as follows: User identity linkage can be divided into three categories based on user information sources: profile-based methods ,8,9,10, The basic assumption of the profile-based methods is that users may fill in similar registration information on different social networks. The main goal of these methods is to capture the similarities of the profiles of users. For example, Zafarani et al.  claimed Another category of predicting user identity linkage is to leverage the network structure of users to capture the similarities of users ,12,13,22generated contents are modeled for predicting identity linkages of users. Feng et al. [In recent years, the behavior-based methods have been widely studied ,6,18,24,g et al.  divided g et al.  proposedA and social network B, respectively. More platforms can be expanded through pairwise prediction of two social networks. For a user A and a user B, the content they post is denoted as F is the binary classification function to be learned to predict the identity linkages of users. The output of F is 1 if the users’ identities from different social networks are consistent, and 0 otherwise.Without loss of generality, we assume that user identity linkages are predicted on two social networks, denoted as social network EKG), which is composed of three modules: word and named entity representation, word matching and named entity matching, and prediction. In the representation module, we first extract the named entities through named entity recognition and link them into the knowledge graph to capture the semantics. To capture the interactions of words and named entities individually, we first initialize the representations of words and named entities and construct the matching matrices of words and named entities, where the similarities of semantics on the word and named entity level are obtained in the matrices. Users with the identity linkage are likely to post similar content in a close time period. Therefore, we introduce time decay functions to reweight the similarity matrices to capture the closeness of posting time. We apply the convolutional neural network to learn the similarity signals in the reweighted word and named entity matching matrices. Finally, the prediction module aggregates the learned word and entity similarity signals to predict whether the users from different social networks have the identity linkage. We will introduce the details of the modules in the following sections. M is the total number of words posted by the user N is the total number of words posted by the user To capture the semantic information hidden behind text words, we initialize word representations with unsupervised word representation learning algorithms. Word embedding learning algorithms, such as Word2Vec , GloVe , and BERP and Q are the numbers of the entities posted by user Apart from the words in texts, capturing the correlations of named entities hidden in the texts enhances the semantics of user-generated content, which provides discriminative evidence for predicting the identity linkage of users. We extract named entities in the content and map them to the corresponding entities in the knowledge graph for introducing external knowledge. We denote the mapped entities in the knowledge graph of user e TransE  to initiThe basic assumption is that users with the same identities from two social networks behave similarly. In other words, users are prone to posting similar contents in close time periods if their identities are the same. Thus, the key goal is to capture the correlations of semantics hidden in the texts and the closeness of posting time. We construct the word and named entity similarity matrices based on the interactions of words and named entities, where the relevance of the semantics is captured in the matrices. To measure the closeness of posting time, we introduce time decay functions to reweight the matrices based on the posting time. When semantics are relevant and the posting time is close, a higher value is obtained, which indicates the similar behaviors of users, and users are more likely to have identity linkage. Finally, we learn the matching signals of the word and named entity similarity matrices through convolutional neural networks.mth row and nth column in word similarity matrix mth word in the content posted by the user nth word in the content posted by user r are discarded, i.e., set as 0 in our scenario.We first construct the word similarity matrix mth row and nth column in time difference matrix x is less than x) is 0. The step decay function assumes that the word similarities remain consistent until reaching the threshold To capture the closeness of posting time, we propose to attenuate the word similarity matrix by the continuous time decay functions instead of time discretization, where the similarities of words with a larger time gap are penalized. Specifically, for the word sets  follows:d1(x)=sigThe key idea behind the time decay function is to reweight the word similarity matrix based on the difference of the posting time of the words. The larger time gap indicates less importance of the word similarities for predicting the identity linkage of users. We penalize the word similarity matrix pth row and qth column in named entity similarity matrix pth named entity of user qth named entity of user r. We reweight the named entity similarity matrix Similarly, we now measure the similarities of named entities in users’ posts. We first introduce the named entity similarity matrix. For the representations of named entities quations –6); Tpi; TpiHi={k-layer convolution networks, Inspired by the field of computer vision where the convolutional neural network (CNN) extracts pixels, edges, and patterns features of images, we apply CNN on reweighted word and named entity similarity matrix ere ReLU  is adoptf is the sigmoid function, which normalizes the predicted results, and o is the final output of the model. We employ cross entropy loss to train the model, i.e.,N is the number of the samples, and ith sample, respectively.To predict user identity linkage, we aggregate word and named entity matching signals. It is straightforward to concatenate or add the word and entity matching signals Algorithm 1: Overall procedures of proposed model (EKG)Input: Content r;Output: The prediction result o;1Preprocess the content 2// Calculate the word and named entity similarity matrices Initialize the representations of word and named entity;345r;// Calculate the word and named entity time differences matrices Filtering 67 // Reweight word and named entity similarity matrices based on posting time;8910Extract word and named entity matching signals Equation ;11Aggregate the word and named entity matching signals through an attention mechanism based on Equations –14);;14);12o that the user identities are consistent based on Equation ,,Mw and Mquations  and 9),,Mw and Mquations  and 10)Mw and Mequations . Finallyhttps://github.com/goleey/EKG (accessed on 3 October 2022).In this section, we describe our experiment settings and results. We released our code publicly Dataset: To demonstrate the effectiveness of our proposed model, we conduct experiments on two real public datasets, namely, Foursquare–Twitter [–Twitter ,31 and F–Twitter . The staFoursquare–Twitter: Foursquare is a location-based social network where users post their comments on the place that they visit. Twitter is a microblogging social network where users communicate with each other. As described in the literature [terature , they fiFlickr–Yelp: Flickr is a photo-sharing platform where users share photos with descriptions. Yelp is a location-based social network where users comment on check-in places. As the literature [terature  states, Text Preprocessing: The content posted by users on social networks are noisy due to colloquialization, symbols, emojis, etc. We first preprocess the texts by removing the above symbols and stop words via the rules. In detail, the symbols such as comma, period, ellipsis are removed, and stop words are removed by regex matching by the stop words list, which are collected by the NLTK (https://github.com/nltk/nltk).(accessed on 3 October 2022) In addition, the words have different morphologies, and the words with different forms may refer to the same semantics. To avoid the inconsistent morphology problem, we normalize the words by lemmatization. The lemmatization is implemented based on WrodNet (https://wordnet.princeton.edu/) (accessed on 3 October 2022) which is a database that contains the relationships of words. After lemmatization, the words with different forms are transferred to the same original forms. For example, the word “ate” is transferred to the word “eat”.Named Entity Recognition and Linking: Apart from capturing the word relevance in texts, the correlations of named entities hidden in the texts enhance the semantics of texts posted by users across different social networks, which provides discriminative evidence for predicting the identity linkages of users. We start with extracting entities from the content of users, which is formulated as a named entity recognition task (NER). NER aims to seek the entities existing in texts and classify them into categories, including organization, location, quantity, etc. We adopt the transition-based chunking model proposed by Lample [https://www.wikipedia.org/) (accessed on 3 October 2022) to retrieve the corresponding entities for disambiguation.y Lample , which uy Lample  to labely Lample ,36,37,38y Lample , we submTo compare the performance of the proposed method, we implement the following baselines that capture user behaviors to predict the user identity linkage, where content or check-in of the users across social networks are modeled. Four categories of baseline methods are used, including feature-based methods, topic-based methods, semantic-based methods, and check-in-based methods. In addition, we ensure that the text preprocessing in baselines is the same as our proposed methods for a fair comparison.Feature-based methods:WAI [Words Are Important: A Textual Content Based Identity Resolution Scheme Across Multiple Online Social Networks”) extracts the part-of-speech, symbols, expressions, and high-frequency words of users’ content and then trains classifiers to predict user identities. Furthermore, WAI analyzes the importance of different features.WAI   extracts not only text features of users, but also network features. The text features include the number of texts posted by users, topics, writing styles, etc. For a fair comparison, we only adopt the textual features of this work.LSIF   proposes to learn the topics of contents through author topic model and dynamic topic model. The assumption is that user’s topics are similar if their identities are the same. Finally, Hellinger distance and residual sum of squares are applied to measure the similarities of the topics to predict user identity linkages.UBL  (Short fDCIM [Dynamic Core Interests”) predicts user identities by modeling their temporal topic distribution of the contents. DCIM first divides the text into different slices in chronological order and then uses LDA to learn the core topic distribution of the text within the slices. Finally, user pairs with similar topics are classified as the same identities.DCIM  (Short fSemantic-based method:UGCLink [UGCLink: User Identity Linkage by Modeling User Generated Contents with Knowledge Distillation”) is the closest work to our proposed model. UGCLink proposes to discretize text by time and use convolutional neural networks to model word, phrase, and sentence-level similarity signals within each time slice. In addition, the model uses knowledge distillation to make the semantic representations of the learned words have geographic location information. Finally, a binary classification model is used to predict user identity.UGCLink   learns the trajectory representations of users, and users with similar representations might have the same identity. Specifically, Dplink designs an encoding model where spatio-temporal information of users is mapped into the latent space.Dplink   curve. A higher AUC score indicates that the probability of ranking a randomly chosen positive sample is higher than a random negative one.To compare the effectiveness of baselines and our proposed method, we apply various evaluation metrics, including precision, recall, F1 score, and AUC score. Precision, recall, and F1 score are defined asAll the experiments are performed on a Linux machine with 2.7 GHz Intel cores and 128G RAM. We implemented the model by PyTorch 1.1. The model is optimized with the Adam optimizer. In addition, the batch size is 32, and the embedding dimensions of words and entities are both set to 50. We set the layers of convolution networks as 2, where the sizes of kernels are 3 × 3 × 5 and 5 × 5 × 5, respectively. All the parameters are initialized by the Xavier Initialization  method. Our proposed method EKG outperforms all the baseline models. In addition, the methods of modeling semantic information  are more effective than the methods of trivial feature extraction . The feature extraction methods are trained by extracting features such as expressions and parts of speech from the texts. However, these features are often noisy due to users’ posting habits, leading to the misclassification of user identity linkage.Compared with topic-based methods , which learn the topics of the user’s text to capture the user’s similarity, our proposed method models the interactions of the representations of words and named entities individually. The topic-based methods fail to explore the correlations of the semantics of texts. The users are predicted with the identity linkage only if the topic distributions are similar. However, users on different social networks may not post words that are exactly the same.The recall of DCIM is higher than our proposed model in Foursquare–Twitter dataset, whereas the precision of DCIM is much worse. We further analyze the core topics extracted by DCIM in Twitter, and we found that the topics mostly include the oral words that are often used by most users. Thus the recall score is high; however, the precision score is low.We notice that the precision and recall score differ in the two datasets for all methods. The precision score is relatively higher than recall in Foursquare–Twitter, whereas the opposite results are reported in Flickr–Yelp. The reason is that the distributions are different in these two datasets, and the styles of content on Twitter are different from that in Flickr.UGCLink is a semantic-based model which discretizes the content of users by time and fails to explore the entity similarity existing in the text. Compared to UGCLink, our proposed method explicitly introduces the time decay function and entity correlation modeling, which is proven to be effective via the experiment results. Specifically, our proposed method additionally constructs the named entity similarity matrix to enhance the semantics relevance of texts, which is beneficial for exploring similar behaviors of users across different social networks.Dplink is a check-in-based model that predicts user identity based solely on the user’s check-in information. However, the check-in data on Twitter are sparse, and most tweets are not associated with locations. Thus, it is hard to apply Dplink when social networks are not location-based. Our proposed method discards the check-in information. Instead, we propose to learn the correlations of words and named entities in texts to explore the behaviors of users to predict their identity linkages.Our proposed method produces superior results compared to baselines, due to achieving two key goals in content-based user identity linkage, i.e., external knowledge introduced from a knowledge graph and the continuous time decay functions. We will discuss the effectiveness of these two improvements in what follows.To demonstrate the effectiveness of the time decay function, word matching module, and named entity matching module, we conduct an ablation study experiment by removing or replacing each part of our model on two datasets, as shown in It can be observed that either removing or replacing the modules degrades the performance compared with our proposed model. Compared to EKG, we remove the entity similarity modeling in EKG-W, which degrades AUC by 5% on the Foursquare–Twitter dataset. The reason is that extracted named entities  enhance the semantics of texts, where the similarities of texts are more discriminative when predicting user identity linkages. Capturing the similarity of named entities promotes the user identity linkage task.On the basis of EKG-W, we design EKG-D, where the time decay function is replaced with the discretization of texts by posting time. We can observe that the performance drops. When dividing the texts into slices by time, the texts with similar semantics may fall into different slices. Thus the similarities of these texts are not modeled, leading to the failure of user identity linkage.Moreover, to demonstrate the effectiveness of word similarity modeling, we remove the word similarity modeling module, while only keeping the named entity similarity modeling. It is observed that the performance of EKG-E drops the most. The reason is that not all the texts in social networks consist of named entities. It is not sufficient to predict user identity linkage only based on the named entities due to the sparseness.We analyze three main hyperparameters in our model on two datasets, e.g., different time decay functions, the threshold of filtering the word and named entity similarity matrix, and the decay factor in an exponential time decay function.We propose three time decay functions to penalize the word and named entity similarity matrix. It can be seen that the exponential decay function achieves the best AUC score, followed by step decay, and finally linear decay. Compared with the other two decay functions, the gradient of the exponential decay function is large at first and tends to decrease as the time gap becomes larger. The exponential decay function smoothly captures the similarity of users’ interests over a long period of time, which is suitable for describing the dynamics of users’ posting content. The step function assumes that the similarity of texts exceeding a certain time threshold is 0 to focus the similarity matrix on the scores that are in a close time period. In addition, the linear function assumes that the similarity scores decrease in a linear way. Compared to the exponential decay function, the gradient is invariable as the time gap grows. However, as the time gap becomes larger, the score of the linear function is still higher than that of the exponential function, which may introduce noise to the similarity matrix. In general, we finally adopt the exponential decay function as the weighting function for the word and named entity similarity matrix.r to discard the small scores to avoid the cumulative effect of small scores. For simplicity, the filter threshold is set to be the same value for the word and named entity similarity matrix. After obtaining the similarity matrices of the word and named entity, we apply a threshold When the threshold is low, most dissimilar words or named entities are kept in the similarity matrices, and the matching signals are accumulated as a high score, which misleads user identity linkage. As the threshold increases, the performance of classification improves, which indicates the effectiveness of our proposed filtering method. However, when the threshold reaches 1.0, that is, only the same words or named entities are retained, the performance drops. The reason is that it ignores the semantic similarities of words or named entities and classifies user identities strictly according to whether the words or entities are consistent. However, users seldom publish the exact same words on different social networks.To explore the effectiveness of different Equation ), we furAs The method in this study proposes to enhance the semantical similarities of texts with the knowledge graph, and continuous time decay functions are designed to avoid the failure of matching introduced by time discretization. We observe that the method achieves better performance compared to baselines. However, there are still some limitations of the study.First, some users may not post similar texts across different social networks. The existing literature, including ours, which captures the similarity of texts posted by users, may fail in this scenario. To mitigate the above problem, future study should be undertaken to explore the additional information of users, such as attributes or check-ins, to model the correlations of users across different social networks.Second, the ratio of the sampling negative users is set as 1:1 in our experiment. However, the number of negative users is more than 1 in practice. As a result, introducing more negative users will lead to imbalance classes, which makes it hard to train the model. Thus, a future direction can be learning the classifier under the imbalance settings of samples to improve the effectiveness of the user identity linkage task.Third, the parameters of time decay functions are set to the same value for all users. However, different users may have different habits when they post the texts. For example, some users post texts after a long time gap across different social networks, while some users post texts on one social network once they post them on the other social network. An improvement could be learning the different parameters of time decay functions for different users based on their habits.It is anticipated that introducing the additional information, sampling more negative users, or learning different parameters of time decay functions for different users will promote the results and achieve more accurate prediction results. We will further investigate these problems in future studies.This study proposes a user identity linkage model with the enhancement of the knowledge graph, where a continuous time decay function is designed for capturing the closeness of posting time. Two main problems are proposed in this study. The first problem is that modeling the semantics of words is not sufficient for predicting user identity linkage. Moreover, dividing the texts into different time slices will lead to the failure of relevance modeling. To solve the above problems, apart from word similarity modeling, the proposed model extracts the named entities in the content and links them into a knowledge graph for enhancing the semantic relevance of texts. Furthermore, to solve the problem that similar words or entities may fall into different time slices after time discretization, continuous time decay functions are designed to reweight the word and named entity similarity matrix. Finally, the proposed model achieves more accurate results on the real public dataset compared to state-of-the-art baselines.We limit our study to the users who post similar texts with close posting time. However, some users may not post similar texts across different social networks. Consequently, future work is directed to exploring the texts together with the check-in data to jointly capture the similarity of user behaviors to further improve the accuracy of user identity linkage.


We define a new Financial Environmental Kuznets Curve (FEKC) by introducing the square term of financial development on the environment-finance relationship. Empirical results prove the existence of non-linear relationships between the composite index of financial development and environmental degradation for the group of advanced economies. In the case of methane, we validate the presence of an inverted-U shape association in line with the FEKC hypothesis, while for greenhouse gas and CO2 the link follows a U-shaped pattern. The impact of financial development on environmental sustainability is monotonically positive and statistically significant while the ecological footprint is not statistically linked with the level of financial development within G7 countries. Economic growth, human capital, population density and primary energy consumption appear as significant drivers of environmental quality and sustainability.This paper analyses the impact of financial development on the environmental quality and sustainability for the group of G7 countries over the period 1990–2019 based on static panel data-fixed effect models. The objective is to explore if there exists a non-linear relationship between the whole financial system development and a wide array of measures of environmental sustainability and degradation, namely adjusted net savings, greenhouse gas, CO Over the last decade increasing concerns have been arising in the fight against climate change, global warming and biosystems’ degradation. Since the approval of the Kyoto Protocol different commitments have been assumed by countries worldwide and nowadays environmental protection is at the core of policymakers’ agenda.A decisive step from an international point of view is the commitment of well-developed countries to the achievement of Sustainable Development Goals (SDG). This initiative requires important financial support from public authorities and private financial systems because the transition process would not be possible if enough financing is not available for changing the prevailing economic model and promoting the more pollutant sectors to evolve towards a neutral carbon economy by 2050.The specialized literature apprehends much attention to the negative externalities associated with environmental damage and climate change, and it has involved diverse disciplines like ecology, economy, and law, just to cite few .In particular, the role of the financial system has been widely analyzed in the literature from different perspectives, like its impact on the level of economic growth, technological progress, and income inequality . The priHowever, until recent days prosperity has only been measured in socioeconomic terms, but with no reference to the natural environment. Quite recently for the sake of measuring prosperity new metrics aligned with ESG criteria  are being used. However, our current economic model focused on a linear approach and based on increasing industrialization and commercialization demands high energy that results in high emissions and a serious threat to human beings . The effHaving emphasized the importance of the financial system as facilitating the transition towards a carbon neutral economy and a sustainable development model, this study sheds new light on the linear and non-linear impact of financial development in terms of environmental degradation and sustainability. In this paper we define a new Financial Environmental Kuznets Curve hypothesis (FEKC) as the existence of an inverted U-shaped relationship between levels of financial system development and levels of environmental degradation.We will analyze the group of G7 countries that are financially developed and well positioned to guide developing countries within the path towards sustainability because if developed countries do not take decisive steps in these years, global goals of planet sustainability would not be achieved.  argued tIn particular, the article will explore if there is a threshold after which the level of financial development exerts a positive impact on the environment, either by reducing polluting emissions or increasing levels of environmental sustainability. When countries financially evolve and adopt greener technologies, switch to a more intensive use of renewable energies or invest more heavily in research and development activities, this could result in diminishing polluting emissions. This seems an interesting topic that deserves to be further empirically examined if we are aimed at simultaneously achieving an effective environmental protection and ambitious sustainability standards in the medium term.(1)To assess which are the drivers of environmental burden and sustainability for the specific group of developed countries.(2)To analyze to what extent developed financial systems are well positioned to protect the environment and help reducing polluting emissions.(3)To assess the existing nexus between financial development and different proxies of environmental degradation at different stages of development, and explore if there is a U-shaped relationship .(4)To give some recommendations for polluting emissions’ abatement strategies based on the empirical findings of this study.Specifically, this paper set the following research objectives:2), methane and nitrous oxide emissions, ecological footprint and a proxy of environmental sustainability.In this paper we adopt a panel data-fixed effect analysis that explains time-invariant country-specific features that may create omitted-variable bias. We also include a wide range of environmental damage variables because there is evidence that they are driven by different forces, to a different extent and in different directions . We will2 emissions, this study also includes varied environmental variables like the ecological footprint, the three main GHG  and also the environmental sustainability measured by the adjusted net savings. Fourth, new variables like the expenditure on research and development activities and a human capital index will be also appraised in this setting. Finally, this article extends previous studies by using more recent data so our findings contribute to the open debate and results can be contrasted with past studies. The data base and the open-source code required to replicate all analyses in this article  are available in [The uniqueness of the paper lies on analyzing the non-linear relationship between financial system development and the natural environment within the EKC framework, assuming that this link is non-permanent, and it depends on the country’s phase of financial development. To the best of our knowledge no previous articles have particularly tested the non-linear impact of financial system development for the specific group of advanced economies and include into the analysis so diverse measures of environmental quality and sustainability as this study. Secondly, to assess the importance of the financial system we use a composite index of financial development that captures both the intermediation activity of banking institutions and the capitalization process carried out through capital markets, which gives a wider perspective of the financialization process than previous studies that are only focused on the credit provision channel . Third, lable in .The remainder of this paper article is organized as follows. The next section reviews the literature on the topic and summarizes the main results achieved by previous studies so far. The section of data and empirical model describes the sample and the econometric technique applied. The fourth section presents the main empirical results, and the implications of the findings are discussed in the fifth section. The article ends with some concluding remarks that outline some recommendations for policymakers and regulators.The existing nexus between the process of financialization and economic growth has been extensively analyzed in the literature. The origin of this line of research dates back to the study of  that def2 emissions and has a positive effect on environmental quality.The link between the environment and economic growth has been hypothesized in the Environmental Kuznets Curve (EKC) framework. The EKC phenomenon was first established in the pioneering work of , which p2 emissions. From a theoretical point of view [Other line of research focuses on the link between growth, financial development and CO of view  have ide2 emissions.Empirical studies carried out reveal that results are sensible to the choice of methodology, the sample of countries, the set of explanatory variables and the period of analysis considered ,16. Thus2 emissions per capita, while the financial liberalization effect will ultimately depend on the strength of the institutional framework in force. In addition, these studies support that financial sector appears to be providing financial services for eco-friendly programs at a lower cost and are specialized intermediaries in financing these types of programs. Ref. [2 emissions. Ref. [2 emissions related to a level of income inequality that should not be exceeded in order to maintain this effect. Ref. [From the literature reviewed in this study we distinguish four groups of studies. Within the first group, some authors like  encountems. Ref.  explore ns. Ref.  reveal tns. Ref.  analyzesct. Ref.  explore 2 emissions, while [2 levels for the group of G8 countries, although this effect is even more pronounced for the group of D8 countries.Within the second group of studies, ref.  analysess, while  find a dA third group of papers is characterized by mixed results when analyzing an extensive panel of countries ,32,33 frFinally, a fourth group of studies do not encounter a significant relationship between financial development and environmental quality like ,35,36,37However, the empirical debate goes beyond the linear association of income, financial development and the environment, and some authors have explored this link within the Environmental Kuznets Curve (EKC) framework based on the work of  that ana2 while ignoring degradation in soil stock, forestry stock, mining stock or oil stock, among others.Within the EKC framework a great body of specialized literature has analyzed the level of carbon emissions ,43,44,45If we specifically analyze the evidence of EKC on developed countries ,53 find 2 emissions. Ref. [Another line of research tries to identify a potential N-shape relationship between the environment and economic growth by including a square and cubic term into the equation. For instance, ref.  separatens. Ref.  confirm ns. Ref.  reveal tns. Ref.  support ns. Ref.  find a cHowever, up to this point, there is a gap in the existing literature because the non-linear impact of financial development has not been considered within the EKC framework for the group of advances economies. Indeed, we find just few studies that deal with this issue, like  at a proIn the light of this mixed and inconclusive evidence we argue that there remains room for exploring the non-linear impact of financial development on environmental quality and sustainability in advanced economies. In this paper we define the Financial Environmental Kuznets Curve hypothesis (FEKC) as the existence of an inverted U-shaped connection between levels of financial development and environmental degradation, so as long as the financial system develops after a threshold the natural environment will benefit from technological progress, greener technologies, move to renewable sources of energy and the implementation of initiatives that help reducing existing levels of polluting emissions. This hypothesis should follow a U pattern in the case of environmental sustainability.This section analyses the data and the econometric strategy applied in this research.This study covers annual time series data from 1990 to 2019 for the group of G7 countries .These countries have been selected because their levels of economic growth are the highest worldwide, so it can be expected that their financial systems are also well-developed. The aim of this study is to capture the effect of financialization at a second stage of development to see if non-linear patterns appear in this relationship.2, Methane (MET) and Nitrous oxide (NIT) . Other important drivers of this relationship that should be controlled in advanced economies are Population Density (POP), Expenditure on Research and Development (RD), Primary Energy Consumption (PE) and Human Capital (HC). Each of these variables play an important role in advanced economies and exert a direct impact in environmental damage and environmental sustainability as argued in the literature review section.The definition and data sources from official statistics of selected variables are shown in This section outlines the econometric instrument deployed in the study. In order to empirically explore the impact of financial development on the environmental degradation and sustainability econometric model panel data regression with fixed effects is used for the baseline model. The term “fixed effects” is due to the fact that, although the intercept may differ across individuals (the 7 countries), each individual’s intercept is time invariant ,63.Ref.  suggest To overcome this issue  employed2, MET, NIT and EF. Additionally, we include the variable ANS as a proxy of environmental sustainability [This study considers five important proxies of environmental quality (ENV): GHG, COnability .In this paper we use as the proxy of financial development the composite index of financial institutions and financial markets development in terms of depth, access and efficiency. For alleviating omitted variable bias, we sequentially added several control variables that are possibly connected with variation in environmental quality and sustainability. In the selection of control variables, after referring to the existing literature, we decided to control four variables, including Population Density (POP), Expenditure on Research and Development (RD), Primary Energy Consumption (PE) and Human Capital (HC).Therefore, we can express the association of ENV with economic growth, financial development, population density, expenditure on research and development, primary energy consumption and human capital as follows:i denotes the country , and t indicates the time period (1990–2019). Log ENV appraises environmental variables. The All variables in Equation (1) are transformed into their natural logarithms to eliminate the effect of variable dimension as well as to reduce dispersion in the data and to minimize issues related to potential multicollinearity and heteroscedasticity in the data. The loglinear transformation data also produce more efficient and consistent results than the simple linear form . The logBased on previous studies that found a non-linear relationship between GDP and environmental quality , this study goes further by analyzing the non-linear nexus between ENV  and FD to investigate the long-run relationship. We test if there is an inverted U-shaped association indicating that at the early stage of financial development the natural environment deteriorates as the financial system evolve, but when achieving a particular threshold of financialization the level of environmental degradation begins to fall. To test this hypothesis, we add the FD- squared value to test the validity of the so-called Financial Environmental Kuznets Curve (FEKC) hypothesis. In regressions we also account for the fact that financial development is correlated with economic growth, and so the former may simply pick up the effect of a general increase in wealth on the level of energy demand. We therefore add both FD and the square thereof to the regression. We rewrite the general model as follows:β2 should be statistically significant and positive while β3 would appear as statistically significant and with a negative sign. In this vein, an inverted U-shaped relationship between financial development and environmental degradation would be validated.According to the model, if the FEKC hypothesis defined in this article holds, then In the case of environmental sustainability, the same outcome will be obtained when the relationship follows a U pattern, then the effect of initial financial development will be negative by reducing environmental sustainability up to a point, and thereafter sustainability will start to increase along with financial development.2, MET, NIT and EF. Also, HC, POP, RD and PE show a positive correlation with emissions. The correlation between FD or GDP and ANS is negative.2 > 0.8).Next tables present the outcomes of panel fixed-effect regression for each of the 6 dependent variables defined in this study. Regarding the assumptions of the regression, the Durbin-Watson statistics suggests that there is no autocorrelation in the data. The test of normality indicates that we can accept the normality assumption. The findings depict that the overall panel data regression models with fixed effects are good (except for the variable ANS adjusted R2 emissions were hypothesized to be related to the level of economic development (proxied by per capita GDP) and financial development (FD) following [The per capita COollowing . In factollowing  have beep-values higher than 0,1. The previous study of [study of  found a Secondly, the non-linear (quadratic) model seems to better capture the behavior of GHG and almost all variables appear significant. In this vein, we find that GDP, POP and HC are contributing to reduce GHG harmful emissions, while PE creates a significantly positive link with GHG. Conversely,  analyses2, NIT and MET. Results of the panel data-fixed effect model of CO2 emissions are presented in 2 reveal that PE outlines a statistically significant positive connection with carbon emissions, while HC develops a negative and significant impact on CO2. This study also demonstrates that there is a monotonically heightening (positive) association between FD and CO2. This result is in line with previous results of [2 emissions, and that this effect is reduced when including institutional factors into the analysis. The study of [2, while energy consumption is the key determinant of CO2 emissions in line with the empirical results presented. The recent study of [2.The next step of our research procedure consists of individually analyzing the three main components of GHG, namely COsults of  for 21 Nsults of  who analstudy of  specificstudy of  also dem2. Howbeit, the squared variable of (FD) is significantly positive so these findings suggest a U-shaped connection between the composite index of financial development and carbon emissions in these countries. These results are aligned with those obtained for GHG, hence FD is not contributing to the de-carbonization of countries after a threshold level . To the contrary, ref. [2 emissions in the US over the last fifty years. Ref. [The empirical findings of the non-linear model support that FD is statistically significant and negatively associated with COry, ref.  applied ry, ref.  demonstrrs. Ref.  using thResults on NIT as the proxy of environmental degradation are presented in In the quadratic model the results remain the same and GDP, POP and RD contribute to reducing levels of NIT. We can conclude that FD does not have a significant impact on NIT, mainly caused by agricultural and soil management activities. Moreover, HC and PE are also non-significant in this setting.The third pollutant analyzed in this study is MET . Empiric2 follow an inverted U-shaped pattern.In the quadratic model the picture appears more complete because a squared term of FD is introduced for appraising the non-linear effect. In this case, a 1% increase in FD is spurring MET (positive sign). The squared estimate of FD is significantly negative, hence for these sampled economies there is an inverted U-shaped association between FD and MET. In the light of these results, the FEKC hypothesis is validated. The rest of variables of the squared model present the same signs as the linear model, so GDP, POP and RD develop a significantly negative relationship with MET. In this case HC is the driving force behind increases in MET. A recent study of  applied The next variable to be analyzed is EF . Under tThe quadratic model confirms these results and that FD is non-statistically significant for explaining EF in advanced economies. On the contrary, ref.  reveal iFinally, for appraising environmental sustainability in this study we consider the variable ANS, and the results are show in In the quadratic model the same results are confirmed except for RD that appears as no significant in this setting.Within the EKC framework the results of this study make significant contributions to this area of research by adding new evidence of the linear and non-linear impact of the whole financial system on the natural environment. There is a gap in the existing literature because the role of the financial system has been basically analyzed within the domain of linear models and focusing on the channel of credit provision. In this study it has been demonstrated that when including a quadratic term of financial development new results arise, so the real nature of this relationship can be better appraised. Until recently the impact of financial development has been classified as positive, negative or non-significant. This study provides empirical evidence demonstrating that this relationship is non-permanent, and it evolves with the country’s phase of financial development.In addition, financial development has been appraised by simultaneously including the development of financial intermediaries, like banks providing credits to the private system, and the development of financial markets as liquidity providers. Only by jointly analyzing these two pillars of financial systems it would be possible to deeply comprehend the overall impact of the financial system and extract some useful conclusions.2 emissions change from the linear to the non-linear models. Under linear specifications results prove that financial systems are contributing to increasing levels of GHG and CO2, but when introducing a non-linear term, this relationship becomes non-linear and follow a U-shaped form.Empirical findings show that the sign of the relationship between financial system development and GHG and COWhat is more, it seems vital to perform a disaggregated analysis of the three main GHG, whose behaviors are markedly different as it has been showed in this study and aligned with previous studies. Findings reveal that the overall impact of financial system development on GHG emissions is the net result of positive and negative impacts on its components, and these should be separately analyzed. This study identifies the presence of a U-shaped relationship between financial development and carbon emissions, while the opposite outcome of an inverted U-shaped pattern is identified in the case of methane emissions (the FEKC hypothesis).2 levels in the long run. This is a consequence of the shorter period of oxidation of methane gas than that of carbon emissions. It is estimated in 10 years the period of oxidation after which methane molecules will be transformed into CO2, so having a warming potential 28 times higher than CO2 [These days increasing attention is being paid to the relevance of methane emissions due to its properties and potential for reducing COthan CO2 . Thus, aAcross all models analyzed in this study some interesting conclusions can be drawn. First, primary energy consumption is one of the major forces behind increasing pollution levels in advanced economies. It seems imperative to advance towards a new economic model more reliable on clean sources of energy and that simultaneously help reduce countries’ energy dependence on fossil fuel energies. Additionally, any improvement in energy efficiency and the promotion of high-tech innovations can help reduce energy intensity levels.2 levels within the sampled economies.Secondly, economic growth measured by GDP per capita exerts a positive effect in terms of environmental protection by reducing GHG, methane and nitrous oxide emissions as well as increasing environmental sustainability. Howbeit, the study does not find a statistically significant association with CO2 and the EF. This is the expected sign considering that human capital index is based on average years of schooling and the return to education, so it could be expected that the better educated the people the higher their concerns for environmental protection.The effect of human capital in all models is positive and contributes to reducing GHG, CO2 and EF models. This is a consequence of the increasing process of urbanization in big cities in detriment of rural areas, and this process has not been accompanied by significant increases in pollution levels because cities are becoming greener and numerous initiatives have been put into practice in the attempt to achieve sustainable and smart cities aligned with the SDG. It seems that efforts are rendering positive results.Regarding the effect of POP on environmental degradation the findings reveal that it is negative, except for CO2 emissions. Some reflections should be made about whether or not these public and private resources are being correctly managed and maybe some adjustments should be made by policymakers on this area.Finally, despite of the efforts that have been made by advanced economies on research and development expenditures, according to the empirical results RD have only generated the expected outcomes in terms of methane and nitrous oxide reduced emissions. However, there are not significant relationships between these expenses and GHG and COThis study relied on panel data estimation techniques to empirically analyze the impact of economic growth, financial development, population density, expenditure on research and development, primary energy consumption and human capital on environmental degradation and sustainability for the group of G7 countries over the period 1990–2019.2 and GHG emissions.This work is unique and differ from previous studies since instead of testing the non-linear effect of GDP on the environment (the EKC hypothesis), it appraises the non-linear impact of financial development on the natural environment. The so-called FEKC supports that as countries financially develop they can alleviate existing levels of financial degradation and promote a higher environmental sustainability. In this study the specific impact of the financial system development on the natural environment has been analyzed under a linear and non-linear specification. Results reveal the existence of an inverted U-shaped relationship between methane emissions and financial development for the group of G7 countries and validate the FEKC hypothesis. Conversely, this relationship follows a U-shaped pattern for COThese outcomes are of particular interest because the role of the financial system should be reinforced in order to alleviate existing levels of environmental burden. What is more, banking systems and financial markets have the capacity and the obligation to redirect financial flows to fight against climate change and enhance environmental sustainability in the medium term.2 emissions because if countries expand too rapidly their financial systems this can generate negative externalities. On this regard, one suggestion is that financialization should come along with a process of raising environmental awareness among financial intermediaries, investors, shareholders and corporations.In the light of these results policymakers should pay attention to the potential of reducing GHG and COIn this study it has been emphasized the need to disaggregate the analysis of GHG emissions into its components to have a whole perspective of the environment reality, because each local pollutant behaves differently as empirical results reveal.The question that immediately follows is how can developed countries fight against increasing levels of pollutant emissions. It should be assumed that the reduction of pollution levels within advanced economies cannot be realized at the expense of economic growth. Instead, urgent changes need be made at different levels. In particular, developed countries should change the prevailing economic paradigm and evolve towards a model that integrates sustainability principles into the equation of shareholder value maximization. Only by doing so the SDG would be achieved.Some recommendations for regulators and policymakers that are gaining momentum these days will be outline.One initiative is the circular economy model. The conception of a circular economy is based on the idea that waste must be minimized and a reduction in the consumption of natural resources can be achieved by reintroducing recycled materials into the circular flow therefore reducing pollution levels.It is also recommended that governments should promote a more efficient use of energy and the use sources of energy like wind, bio-diesel, solar and geothermal energy, which can reduce environmental degradation. This goal seems unattainable without a decisive public support for research and development activities. A key element that policymakers should bear in mind is the importance of technological progress because only by investing in innovative and environmental oriented activities a real advance towards environmental protection could be achieved. Two parallel energy transitions are currently taking place in developed countries: the electrification of the energy demand and the decarbonization of the energy supply. In this vein, renewables energies are making significant contributions to this double end and governments can subsidize interest rates for energy-efficient projects in parallel to tax on projects that rely heavily on non-renewable energies. Equally important for improving environmental quality is the proper use of land and some proposals have been suggested by the Common Centre for Research (European Commission) like afforestation, reforestation, better agricultural practices and bioengineering, among othersThus, the transition process in which advanced economies are immersed should come hand in hand with adequate economic policies and incentives, technological availability, and changes in consumers preferences as the main drivers for the change of paradigm. Educating societies is playing a vital role in protecting the environment and controlling polluting emissions.All the aforementioned changes pose potential threats to financial systems. On the one hand, financial intermediaries are highly exposed to climate risks , while at the same time these institutions are an important lever for social and economic changes through their credit channel. On the other hand, financial markets are relevant players in project assessment in terms of ESG criteria and play a fundamental role in the process of greening the economy. Over the last five years the financial regulatory framework has made a significant progress for protecting the environment, and authorities of developed countries have introduced more controls and transparency requirements for financial intermediaries aligned with the SDG.Even though significant improvements have been achieved in the protection of the natural environment and people seem to be increasingly more concerned about its importance, there is a long road ahead for advanced economies in the attempt of guaranteeing the long-lasting wellbeing of our planet.This study has some limitations because cross-country datasets are always limited to specific variables, therefore, availability of data on all such potential variables is always a limitation.We suggest as lines for future research to continue analyzing the impact of the financialization process on the environment and try different methodological approaches to test the existence of a N-shape (cubic) relationship or apply some spatial data techniques that accounts for geographical attributes that can play a significant impact in terms of environmental quality. In addition, it is recommended to extend the research and include specific variables related to the role of education in promoting a peoples’ change towards more friendly-environmental attitudes. It is also advisable to further analyze the efficiency of private and public expenditures on research and development activities to devise whether or not these resources are being directed to their most efficient uses and are effectively protecting the natural environment.


The multi-sonar distributed fusion system has been pervasively deployed to jointly detect and track marine targets. In the realistic scenario, the origin of locally transmitted tracks is uncertain due to clutter disturbance and the presence of multi-target. Moreover, attributed to the different sonar internal processing times and diverse communication delays between sonar and the fusion center, tracks unavoidably arrive in the fusion center with temporal out-of-sequence (OOS), both problems pose significant challenges to the fusion system. Under the distributed fusion framework with memory, this paper proposes a novel multiple forward prediction-integrated equivalent measurement fusion (MFP-IEMF) method, it fuses the multi-lag OOST with track origin uncertainty in an optimal manner and is capable to be implemented in both the synchronous and asynchronous multi-sonar tracks fusion system. Furthermore, a random central track initialization technique is also proposed to detect the randomly born marine target in time via quickly initiating and confirming true tracks. The numerical results show that the proposed algorithm achieves the same optimality as the existing OOS reprocessing method, and delivers substantially improved detection and tracking performance in terms of both ANCTT and estimation accuracy compared to the existing OOST discarding fusion method and the ANF-IFPFD method. The multi-sonar system is usually collaboratively deployed to realize the perception of the marine situation. Compared with the single sonar system, the multi-sonar system integrates multi-source information and can provide a much more comprehensive and accurate as well as reliable perception image of the marine environment. It has been widely applied in civil and military fields, such as underwater mapping ,2, fish The multi-sonar fusion detection system can be roughly divided into the centralized and distributed ,16. In tThe OOSM fusion arises in the centralized fusion framework, in which each local sonar directly transmits its origin-unknown raw measurements to the fusion center with arriving OOS . The mulposed in  and achiposed in  proposedposed in , the tarposed in  combinedposed in  to efficBl1 to achieve suboptimal but computationally efficient fusion of OOST fusion of OOST. Under the same assumption, Ref. [Propose a novel multiple forward prediction-integrated equivalent measurement fusion (MFP-IEMF) algorithm to fuse the multi-lag OOSTs with track origin uncertainty in an optimal manner, which is applicable in both synchronous and asynchronous multi-sonar fusion systems.Recursively calculate the probability of target existence as a track quality measure to detect marine targets.Propose a random central track initialization technique to timely detect the randomly born marine target.Different from the OOSM fusion, the OOST fusion usually arises in the distributed fusion framework, in which the sonar local tracks arrive in the fusion center with temporal OOS, and the correlation between local tracks and central tracks needs to be carefully considered due to common prior information and process noise. Compared to the OOSM fusion, the multi-sonar OOST fusion problem has been less investigated in the open literature. However, to save communication resources, most realistic multi-sonar systems send track information instead of raw measurements to the fusion center, thus the multi-sonar OOST fusion becomes practically important. Most existing methods combine the OOSM fusion algorithms with the track decorrelation techniques to solve the multi-sonar OOST fusion problem. The authors in  proposedon, Ref.  completeon, Ref.  proposedon, Ref.  proposedon, Ref.  investigThe rest of the paper is organized as: The target kinematic state comprises a two-dimensional position and velocity component and is discretized at time Due to the marine target stochastically disappearing and appearing at any time, the existence of the target is a stochastic event. Denoting the target existence and non-existence event at time At time Except for possible target detection, sonar returned measurements In the distributed fusion architecture with memory, each sonar However, due to different communication delays between the sonar and the fusion center and the diverse sonar internal processing time, the fusion center receives data out of sequence. Aiming at the multi-lag OOST with memory fusion, the fusion center is required to solve three problems. Firstly, since the fusion center processes data in real-time, the OOSTs cannot be directly fused. Therefore, the fusion center is required to make reasonable use of OOSTs to improve the detection and tracking performances. Secondly, the local tracks and the central track have the same prior information and the same process noise that is caused by the measurements of all sonar being obtained by the same target model, so the fusion center ought to rule out the common information by using a decorrelation procedure. Thirdly, since the uncertain origin of the local tracks which are caused by multi-targets and clutter, the fusion center is required to initiate and maintain true tracks and delete false tracks.In the realistic fusion system, multiple sonars measure the targets information in a synchronous or asynchronous manner. While the proposed MFP-IEMF method is capable of fusing both synchronous and asynchronous OOSTs, and their main fusion steps follow the framework of The MFP-IEMF consists of five steps. Synchronous OOSTs fusion is described in detail below.At time The Let The pseudo-function of the OOSEM conversion is described byDue to the fusion center receiving the local tracks of multiple sonars at different times, it is necessary to sort the OOSEMs according to the time sequence. Let To fuse the central track The posterior pdf can be decomposed asImplementation steps of the IEMF method are introduced in detail next.1.Gating techniqueIn order to reduce the computation burden, only a subset of OOSEMs Let 2.Hybrid state estimationThe posterior PTE of the central track is calculated byThe posterior pdf of the kinematic state is obtained by using the Gaussian mixture process, i.e.,  The central equivalent measurement of the central track The mean and error covariance of The hybrid state posterior pdf of the central track It is worth noting that the detection probability To update the hybrid state posterior pdf Due to all sonar sampling times being exactly the same in the synchronous sampling system, in Equation (15), the posterior hybrid state pdf of the central track is obtained by straightforward fusing the OOSTs with the pre-stored hybrid state of the central track at the OOS time. In the asynchronous sampling system, the sampling time of the central track is not the same as that of the local track. Therefore, the central track needs forward prediction processing, after that the OOSTs fusion method can be carried out. The OOSEM conversion of the asynchronous sampling system is calculated in the same way as Equation (11). Due to the central track does not have the posterior pdf updated at time The predicted PTE The posterior hybrid state pdf In the realistic marine environment, the sonar returned measurement may either originate from targets of interest or clutter, and a huge number of tracks are initiated without prior knowledge on whether they are following the marine targets or not. In this paper, the recursively calculated PTE is utilized as a track quality measure to detect the marine targets in time, and also recognize and detect false tracks not following any targets.The status of an initialized track is tentatively set to be unknown and subsequently updated based on its recursively calculated PTE. When the value of PTE exceeds the confirmation threshold, the track is raised to a confirmation status. Thus, it is deemed to follow a marine target of interest and remains at the to-be-confirmed status until its termination. Conversely, if the PTE falls below the termination threshold, the corresponding track is recognized as a false track not following any marine targets and is deleted from memory. Thanks to the proposed marine target detection strategy, the local sonar terminates the majority of false tracks, thus hugely saving the communication burden. At the same time, the fusion center can automatically detect the marine targets in time and maintain them effectively.In the distributed fusion architecture with memory, the marine targets are randomly born and may be detected by part of the sonars in the system, which causes the fusion center to fail to observe the newborn targets in time and then greatly increase the probability of subsequent decision-making mistakes. Therefore, a random central track initialization technique is proposed to timely initiate and maintain the central track following the newborn targets, which initiates tracks by using the free equivalent measurements and operates fusion when the number of measurements within the gate is more than zeros.Taking two sonars as an example, it is assumed that the randomly born marine target A can only be detected through the OOS sonar 2. As shown in The red circle in The novelty of the proposed multi-sonar distributed fusion method lies in three aspects: (1) the proposed MFP-IEMF is able to effectively fuse multi-lag OOSTs with track origin uncertainty and achieves optimal detection and tracking performance which delivers significant improvement over simply discarding the OOSTs; (2) the proposed method can be applied in both synchronous and asynchronous multi-sonar systems to improve the distributed fusion performance; (3) the MFP-IEMF enables the timely detection of the randomly born marine targets particularly when these targets can only be observed by the OOS sonars. To validate the novelty claimed above, three numerical experiments are carried out in the rest of the section.A scenario of deploying the two-sonar system to detect and track three submarines is shown in Suppose the sampling interval of each sonar is The fusion center adopts the MFP-IEMF to fuse the multi-sonar OOSTs with track origin uncertainty in an optimal way to detect and track submarines automatically. In order to verify the superiority of the proposed method, this method is compared with the existing ANF-IFPFD method, OOS-D method, and OOS-Reprocessing (OOS-Re) method . The ANFExperiment 1: This experiment is used to verify the superiority of the proposed MFP-IEMF over existing methods in the synchronous sampling scenario. In this experiment, the sampling interval of the two sonars is The root mean square error (RMSE) and the averaged number of confirmed true tracks (ANCTTs) are designed to evaluate the detection and tracking performance of the algorithm. In order to give a fair comparison of the ANCTTs among compared methods, the track termination threshold, the track confirmation threshold, and the initial PTE are tuned to deliver the same number of confirmed false tracks (CFTs); it is 11 CFTs in this experiment.In addition to the detection performance and the tracking performance, the fusion time of each method in experiment 1 is compared in Experiment 2: This experiment is used to verify the superiority of the proposed MFP-IEMF over existing methods in the asynchronous sampling scenario. In this experiment, the two sonars start sampling at different times, with sonar 1 in the 1st second and sonar 2 in the 2nd second. Other parameters are the same as experiment 1.As can be seen from This experiment is used to verify how the number of OOS lags affects the performance of the proposed MFP-IEMF. Sonar 2 is set to arrive at the fusion center in OOS with five lags and with thirty-five lags, respectively. Other simulation parameters are the same as experiment 1.This paper considers the multi-sonar information fusion for targets detection and tracking in the marine environment, and specifically investigates the multi-lag OOST fusion with track origin uncertainty under the distributed fusion framework with memory. The authors propose a novel multiple forward prediction-integrated equivalent measurement fusion (MFP-IEMF) method, which is capable of dealing with both synchronous and asynchronous multi-sonar tracks fusion problems. The proposed method fuses the multi-lag OOST with track origin uncertainty in an optimal manner and delivers substantially improved detection and tracking performance in terms of both ANCTT and estimation accuracy compared to the existing OOST discarding fusion method and the ANF-IFPFD method. Furthermore, a random central track initialization technique is also proposed by only using sonar measurements and few basic prior information, to detect the randomly born marine target in time via quickly initiating and confirming true tracks. The numerical results show that the proposed algorithm can be potentially implemented in the practical multi-sonar detection and tracking system. However, the proposed MFP-IEMF method is suitable for sparse multi-target scenarios with low target maneuvering. In the dense multi-target scenarios or target high maneuvering scenarios, the detection and tracking performance of the MFP-IEMF degrades. It is necessary to study the optimal fusion algorithm of OOST in a more complex environment.


This paper presents an efficient path-planning algorithm for microrobots attempting to pass through environments with narrow passages. Because of the extremely small size of a microrobot, it is suitable for work in this kind of environment. The rapidly exploring random tree (RRT) algorithm, which uses random sampling points, can quickly explore an entire environment and generate a sub-optimal path for a robot to pass through it; however, the RRT algorithm, when used to plan a path for a microrobot passing through an environment with narrow passages, has the problem of being easily limited to local solutions when it confronts with a narrow passage and is unable to find the final path through it. In light of this, the objectives of the considered path planning problem involve detecting the narrow passages, leading the path toward an approaching narrow passage, passing through a narrow passage, and extending the path search more efficiently. A methodology was proposed based on the bidirectional RRT in which image processing is used to mark narrow passages and their entrances and exits so that the bidirectional RRT can be quickly guided to them and combined with the deterministic algorithm to find paths through them. We designed the methodology such that RRT generates the sampling points for path growth. The multiple importance sampling technique is incorporated with bidirectional RRT, named MIS-BiRRT, to make the path grow faster toward the target point and narrow passages while avoiding obstacles. The proposed algorithm also considers multiple candidate paths simultaneously to expand the search range and then retain the best one as a part of the planning path. After validation from simulation, the proposed algorithm was found to generate efficient path planning results for microrobots to pass through narrow passages. Due to the development of MEMS technology over the past decade, microrobots, which are constructed using small-sized sensors, actuators, processors, etc., have continued to be innovatively designed. Microrobots are characterized by extremely small size, light weight, low power consumption, and low cost . Among mThe field of path planning can be divided into two major methodologies: deterministic and stochastic. Common deterministic methodologies include Dijkstra’s algorithm , the artDue to the random sampling characteristic of RRT, several researches ,16 have The related works of RRT improvement mentioned above can assist the RRT path in growing toward the narrow passages. These works could successfully plan a path passing through the rooms where only the entrance of each room is considered a narrow passage. However, when a narrow passage is thin and long, these related works may still hard find a path through this kind of narrow passage. Due to the characteristics of RRT uniform sampling, the search range easily affects the path-searching efficiency. The adaptive RRT  draws seIn addition to the problem of crossing narrow passages, the path-searching process of traditional RRT methodology is often aimless due to its use of random sampling in complex environments. Even if the last generated waypoint is close to the target point, random sampling of the entire space could easily result in the next waypoint being far away from the target. This kind of aimless sampling during path searching makes path planning inefficient and consumes considerable time, especially in vast and complex environments. Therefore, several improvements were proposed for the waypoint sampling of RRT so that unnecessary searching and computational time can be reduced. The rapidly exploring random disjointed tree* (RRdT*)  establisIn this paper, we integrated the concepts of several waypoint sampling mechanisms to guide the path planning of a microrobot. Specifically, this paper proposes a multiple importance sampling bidirectional rapidly exploring random tree (MIS-BiRRT) to remedy the problem of RRT path planning through narrow passages that suffer from aimless path searching. The environmental map is first considered as an image for detecting the feature points of obstacles and narrow passages. The multiple importance sampling mechanism is used to draw the waypoints of a growing RRT path toward the target point, toward the entrance of a narrow passage, or so as to avoid obstacles. When the path grows into the entrance of a narrow passage, the RRT methodology switches to the deterministic path planning method to quickly obtain the optimal path through the narrow passage.The rest of this paper is structured as follows. The path planning problem is first formulated, and the path planning plus image feature detection for narrow passages is explained in τ that can lead the microrobot from the starting pointE may also contain several unlabeled narrow passagesr could pass, i.e.,τ using just the RRT algorithm would be difficult because of the small search area of the narrow passage. Since the map can be known in advance, marking the narrow passages can quickly guide the RRT to pass through them. The objectives of the considered path planning problem can be defined as detecting the narrow passages, leading the path toward an approaching narrow passage (instead of blindly leading to a narrow passage), passing through a narrow passage, and extending the path search more efficiently. Hence, the concept of the path planning algorithm proposed here is to design the paths in the narrow passages and those in the broad areas separately using two methodologies. The environment map E is illustrated in i-th narrow passage is labeled with the identification point, IPi. The bidirectional rapidly exploring random trees (BiRRT) [A two-dimensional environment map  (BiRRT) , which clgorithm . The environment in the broad areas, which are outside the narrow passages  (BiRRT)  to efficAs illustrated in i-th narrow passage, where i-th narrow passage. The identification points, which indicate the entrance or exit of the narrow passages, are later employed to design the path through the narrow passages.The white points in the location map of narrow passages i-th narrow passage to construct the path of the microrobot. The closest identification point The identification points of the narrow passages are to assist the RRT methodology employed in the broad areas to quickly find the narrow passages. Since the width of a narrow passage is small, this subsection also explains path planning through a narrow passage with its assigned identification points. In addition, since the selected identification points are the entrance or exit of a narrow passage to the broad areas, the selected identification points would also be regarded as the starting and target points when planning the path through the narrow passage. As mentioned at the beginning of nearq in the planned path tree. A new waypoint nearq toward the random guiding point In the traditional RRT methodology , the dirAlthough traditional RRT is fast, this kind of aimless, random generation of guiding point randq of path growth in a complex environment. The importance function for target i-th narrow passage, i.e., The importance function is a way to provide cues for random sampling generation. Multiple importance sampling  aggregat concept , and it k-th obstacle that blocks the guiding direction to the target point (green dotted line). The endpoint If there is an obstacle in front of the guiding direction of the previous two importance functions, the importance function of obstacle avoidance obstacle . We applizations , which cIn order to increase the searching range of the RRT methodology, Multi-RRT  draws seIt was explained in the previous subsection how to determine the path growth of a new waypoint When designing the path tree We illustrate six environmental maps, as shown in Quantitative indicators, including the computational time (time) and the total length (length) of the planned path, are used to evaluate the path planning algorithms in the following simulation results. The better a path planning algorithm is, the shorter its computational time and the shorter the planned path it can generate for the microrobot through the environment. The total number of new sampled waypoints  and successfully extended new waypoints (successful waypoints) are also recorded as quantitative indicators for evaluating the algorithms. Since the new sampled waypoints could clash with obstacles and have to be resampled repeatedly, the successfully extended ratio (success ratio) is defined to calculate the ratio of successful waypoints to total waypoints. An efficient sampling mechanism in an RRT-type methodology should have a higher success ratio, which indicates that a smaller number of new sampled waypoints fail to grow the path.The simulation results of the proposed MIS-BiRRT compared with the RRT, BiRRT, RRT*, PRM, A*, and hybrid A* algorithms are presented in In terms of path length, the hybrid A* algorithm, a deterministic algorithm, is the best and can be regarded as the optimal path solution in each environment. Because the solution to the problem is explicit, the A* and the hybrid A* algorithms yield shorter paths than the stochastic algorithms. However, the A* algorithm requires an enormous amount of calculation and the computational time is considerably large, which can be seen from the comparison. The overall efficiency of the A* algorithm is not high. Except in Map 5, the hybrid A* algorithm takes even less time than some RRT-type methods. However, in a complex environment such as Map 5, the hybrid A* algorithm is obviously slower than all RRT-type methods.Next, we discussed the simulation differences of each method in these six maps. Maps 1–4 all contain significant narrow passages in the environments. Map 2 has a long and straight, narrow passage, and Map 3 has a crooked narrow passage. Map 4 looks like two rooms with narrow passages as the entrances. Since there are thin and long narrow passages in Map 1–4, the path lengths in Map 1–4 obtained by the proposed MIS-BiRRT algorithm are close to those obtained by the A* or the hybrid A* algorithm. This is due to the fact that a deterministic algorithm can easily yield the optimal solution in a narrow space. In contrast, in Map 5, with several short narrow passages, or in Map 6, with no narrow passages, where the RRT methodologies would have stochastic results in the broad areas, the path length planned by the proposed MIS-BiRRT algorithm is close to that obtained by RRT, BiRRT, or RRT*. In addition, since there are multiple long narrow passages in Map 1, 3, or 4, which would be multiple difficulties to block the waypoints sampling, the computational time spent by RRT* algorithm in Map 1, 3, or 4 is longer than that in Map 2, 5, or 6. Due to the proposed MIS-BiRRT could adaptively switch between the stochastic and deterministic manners, the computational time taken by our method does not vary much in different environments. Since there are no narrow passages at all in Map 6, which would not block the waypoints sampling of RRT-type methodology, the success ratio of RRT, BiRRT, or RRT* in Map 6 is higher than that in Map 1 to 5.Then, we visualized and compared the results of path planning for Map 5. randq.For the following simulations, we tried to remove certain modules of the proposed MIS-BiRRT methodology to see the effectiveness of each see . The BiRulti-RRT  concept BiRRT + G, which employs Goal Bias  as a simIn contrast, Multi-BiRRT generates multiple new waypoints to increase its path-searching hypotheses compared with the BiRRT + G and BiRRT + GO methods. Since more samples are drawn from the importance functions, the diversity of sampled waypoints is increased, and the searched space is wider, causing most of the Multi-BiRRT length results to be shorter than those of the BiRRT + G and BiRRT + GO methods. We also can see that Multi-BiRRT spent less computational time to obtain the path in Maps 1, 2, 3, and 5 than in Map 4 or 6, in which the path is not so obvious to be obtained. Since Map 5 only contains several short narrow passages, and Map 6 has no narrow passages, due to the efficient multiple important sampling of the proposed MIS-BiRRT, the path length of MIS-BiRRT is much better than that of the other algorithm in Map 5 or 6.Compared with the proposed MIS-BiRRT, however, the diversity of Multi-BiRRT is still insufficient. Due to its extremely small size, a microrobot is especially suitable for performing tasks in narrow spaces. This paper proposed the MIS-BiRRT path planning algorithm to efficiently navigate a microrobot through a complex environment with narrow passages. Unlike general RRT algorithms that use purely stochastic methods for path planning, MIS-BiRRT adopts both the stochastic and deterministic methods during path planning, utilizing the advantages of each. The narrow passages are detected by image processing, and the identification points are labeled to denote the entrance or exit of a narrow passage. Once the MIS-BiRRT path growth is connected to an identification point, the A* algorithm is then utilized to quickly find the optimal path through the narrow passage. After exiting the narrow passage, the path planning switches back to the MIS-BiRRT methodology such that the inefficiency of the stochastic algorithm in planning a path through narrow passages can be reduced. In order to increase the sampling efficiency of the RRT path growth in the broad space, the multiple importance sampling mechanism of MIS-BiRRT is designed to integrate several importance functions to guide the path growth toward the target point, ultimately connecting to the identification point of a narrow passage and avoiding any obstacles. Multiple waypoint sampling and selection are also incorporated into MIS-BiRRT to increase the variance of generated waypoints while reducing useless ones. Through simulation and comparison, it is proved that the proposed MIS-BiRRT improves the overall performance of microrobot path planning in complex environments.Since the proposed MIS-BiRRT involves more calculations for image processing, multiple waypoints generation and selection, and the integration of multiple samples, the computational time is longer than for simple RRT methodologies. It could be reduced by being implemented via low-level programming libraries when practical. In the future, the proposed algorithm can be applied in microrobots with microprocessors or embedded computation systems. The proposed path-planning method will also be further revised for practical applications by considering the dynamics of the microrobots.