Therefore, this novel LEO-assisted receiver has significantly improved weak signal acquisition and tracking sensitivity.Due to the low signal power, the Global Navigation Satellite System (GNSS) signal is vulnerable to interference and even cannot be captured or tracked in harsh environments. As an alternative, the Low Earth Orbit (LEO) satellite has been widely used in the navigation field due to the advantages of low cost and strong signals. It is becoming a significant component of the new combined navigation system with GNSS. The combination of an LEO Doppler signal and GNSS observables can improve the positioning accuracy and high-precision positioning convergence time of the GNSS receiver. However, the GNSS signal receiving capability cannot be improved from this data fusion level. We propose a novel assisted structure where GNSS signal acquisition and Doppler tracking are assisted by LEO Doppler positioning. The receiver uses the LEO signal to achieve Doppler positioning firstly. Then, the coarse position with the GNSS navigation messages received from LEO, as well as the estimated clock information, is used to assist in the acquisition and tracking of GNSS. In this way, the GNSS receiver’s sensitivity can get the benefit from this integrated system. The paper presents the structure of the assisted receiver and analyzes the assisted GNSS signal acquisition and carrier tracking performance in detail. Simulation experiments of this assisted structure are carried out to verify its superiority of acquisition and tracking sensitivity in comparison with standalone GNSS receivers. Theoretical analysis and experimental results show that the proposed acquisition method can achieve 90% detection probability at a carrier-to-noise ratio (C/N Due to the high satellite orbit, the Global Navigation Satellite System (GNSS) has low signal landing power and is susceptible to interference. Many works investigate various signal-processing methods to acquire and track weak signals. For weak GNSS signal acquisition, a block averaging pre-processing (BAP) approach that coherently accumulates signal blocks to improve the signal power is introduced . To solv0) as low as 14.5 dB-Hz under static conditions. Chiou designed a Doppler-aided GPS navigation system for weak signals in his dissertation, which mainly uses the FLL to track the signal under strong ionospheric scintillation [To further improve the availability and sensitivity of the Global Navigation Satellite System, augmentation from the other system is always used, including internet ephemeris and receiver Doppler information. If the receiver can get the ephemeris information in another way, FLL can be used to keep the loop on track and extract the observables, which has a higher sensitivity than PLL. Satyanarayana  proposesillation . Tao givillation . Our preillation  designs illation ,11. Thisillation . The maiillation . Neitherillation .Low Earth Orbit (LEO) satellite systems, most of which are designed for communicating, have higher received power and faster-moving velocity than GNSS, for they are running at the lower orbit. Due to these characteristics, LEO has been recently used for positioning or augmenting the GNSS system ,17. HoweA novel LEO augmented GNSS system and receiver structure is proposed in this paper so that the augmentation to the signal processing can be explored. In this designed system, LEO transmits GNSS ephemeris through its communication channel. Meanwhile, it can be used to locate the ground receiver by its Doppler frequency. In weak signal environments, the receiver realizes positioning using the LEO signal by Doppler shift first. The receiver could also obtain GNSS ephemeris information from the LEO system. Then, the ephemeris, as well as the estimated location and Doppler from the LEO satellite is used to reduce the GNSS signal searching range and extend the coherent integration time to capture weak signals in the acquisition stage. Meanwhile, the receiver clock bias and drift could be estimated in the LEO positioning. With this information, the receiver could achieve longer coherent integration and narrower loop bandwidth to reduce the noise and track the weak signal. Unlike the GNSS/INS deep coupling technology, LEO communication satellites can locate the receiver autonomously, estimate the basic position of the GNSS receiver, and provide much more aiding information, including ephemeris, navigation data, Doppler shift, and clock information assisting for the acquisition and tracking of the GNSS signal. In this contribution, we describe the new assisted acquisition and tracking scheme, with the analysis and verification of its performance by the simulation results.The paper is organized as follows: To solve the problem of the low sensitivity of GNSS receiver acquisition and tracking under weak signal conditions, we propose a novel LEO augmented system and receiver structure. The proposed system differs from the other LEO augmented system in transmitting the GNSS ephemeris to receivers. As shown in The digitized Intermediate Frequency (IF) signal received at the end of the GNSS receiver RF front-end can be presented as:We propose a method of LEO positioning-assisted GNSS signal acquisition to improve the acquisition efficiency and sensitivity. As shown in Signal acquisition can be considered as a coarse estimation of GNSS signal parameters, which is unable to meet positioning requirements. On the other hand, the relative motion between the satellite and the receiver causes the signal parameters to change over time. Carrier and code tracking loops with feedback functions are often used as estimates of fine GNSS signal parameters in the tracking stage. The rate of the PRN code is much lower than the carrier frequency. Thus, the carrier-tracking loop is so fragile to be the most important part of a GNSS receiver. Under weak signal conditions, the loop bandwidth is often reduced to improve the accuracy of the carrier tracking loop. However, as a result of the oscillator noise and dynamics on the carrier tracking loop, the bandwidth cannot be reduced arbitrarily. Otherwise, it will cause the phenomena of lock-lose.To improve the tracking ability of the receiver in weak signal environments, such as strong wideband jamming in the military, this paper proposes a carrier tracking loop structure that is LEO satellite-assisted. It is noteworthy that the receiver does not need to extract the navigation bit from the signal processing, for it can get the GNSS ephemeris from LEO. On the other hand, the receiver is supposed to work well when it starts to encounter the jamming stress. At this time, the local PNR code is still aligned to the received signal and can be used to assist the loop with ephemeris. The navigation bit is used to remove the bit reversal and extend the coherent integration time. Therefore, only FLL is considered to track the ultra-low SNR signals. As shown in To track GNSS signals with ultra-low SNR, we use a frequency-locked loop (FLL) to improve the loop’s tracking ability. The commonly used Costas discriminator has a pull-in range between iminator  with a wIn Ignoring high-frequency information items, the output of the integration and dump circuit by integrating the signal within a bit interval can be written as :(3)s(t)=D(t) in Equation (3) could be removed according to the information from the LEO, resulting in a longer integration time than a bit duration.In Equation (4), To determine the parameters of acquisition and tracking and analyze the performance of LEO positioning assistance, it is necessary to consider the errors introduced by the assistance information from the LEO satellite. These errors include the clock accuracy of the satellite and receiver, the clock stability error of the satellite and receiver, and the Doppler deviation caused by the position error introduced by the positioning error from LEO satellite. The Doppler deviation and the clock accuracy of the receiver mainly affect the acquisition of a GNSS signal. A larger deviation increases the search range, resulting in low efficiency. On the other hand, the clock stability of the receiver prevents excessive compression of the coherent integration time. This section will analyze each error in detail. In the analysis, the receiver is assumed to be static. In the analysis and simulation, GPS constellation is considered for GNSS. Moreover, the parameters for LEO positioning are mainly derived from the Iridium satellite, whose positioning technology is mature enough. The only difference is that the LEO is assumed to transit GNSS ephemeris in this work. GPS satellites follow near-circular orbits at about 20,200 km altitude, and Iridium uses 66 spacecraft orbiting at an altitude of 780 km, which is much lower than the GPS orbit altitude ,24. The v and For a static receiver, taking the Iridium satellite as an example, the position error obtained by LEO satellite through Doppler positioning is within 1 km, and the timing accuracy is about 1 μs . It is oIn addition to the relative movement between the satellite and the receiver, the oscillator frequency bias of the satellite and receiver also affects the measurement of the received carrier Doppler. It can be obtained as follows:In addition to the clock accuracy, the clock stability of the satellite and receiver can also cause the frequency bias, resulting in signal attenuation when a long coherent integration is adopted. The frequency stability of the clock refers to the relative change in frequency caused by the oscillator noise. This noise is usually expressed in the form of power-law noise, and its power spectral density can be expressed as:mined by :(8)δy2 with better stability , while GWhen Doppler positioning is performed on a GNSS receiver through an LEO satellite, the GNSS receiver will absorb the LEO satellite’s clock error. Therefore, the impact of the LEO satellite’s clock and GNSS receiver’s clock on signal processing should be considered at the same time. For the GNSS receiver, the clock frequency error caused by instability will cause the attenuation of the coherent gain. The power attenuation caused by coherent integration can be given by:The purpose of the LEO-assisted GNSS structure is to improve the sensitivity of GNSS signal acquisition and tracking. With the assistance of LEO, the influence of navigation bit reversal is eliminated. Then, the coherent integration time can be extended to improve the SNR of the GNSS signal. However, it can be seen from the above analysis that the extension of the coherent integration time is prevented by the oscillator noise. Therefore, it is necessary to analyze the SNR gain and the performance benefits of acquisition and tracking that can be obtained after the coherent integration extension with LEO assistance.The selection of coherent integration time is a key part of the design of GNSS receivers. It is the result of a compromise between various factors. On the one hand, to reduce noise and improve SNR, the integration time should be as long as possible. On the other hand, the integration time cannot be too long due to the attenuation of clock noise according to the analysis above. The selection of coherent integration time must consider both the noise and clock dynamic impact of the receiver. The coherent integral gain can be expressed as:P is a given autocorrelation amplitude, In the equation above, Using the equations above, we compare the SNR gain under different combinations of coherent integration and non-coherent integration. The noise bandwidth before the correlator is set to 2046 MHz. The range of the pre-detection SNR is from −48 to −28 dB. According to the analysis in Using LEO to assist GNSS signal acquisition, one benefit is the reduction of the signal search range. The total number of search units in the two-dimensional search range of code phase and frequency can be expressed as:The typical standalone receiver’s code search range for a single GPS satellite is 1023 chips. However, in the LEO-assisted acquisition method, according to the pseudo-range error of the Iridium satellite is Concerning frequency searching, a different coherent integration time corresponds to different frequency steps. According to the analysis of k represents the degrees of freedom. Here, k is twice the non-coherent number. Assuming that the false alarm probability 0 = 15 dB-Hz using the proposed method, which combines 200 ms coherent integration and two non-coherent integrations. However, the detection probability with 91% of the standalone receiver is at 22 dB-Hz. That means that the LEO-assisted acquisition has about 7 dB gain with regard to the detection probability.The LEO-assisted GNSS acquisition method not only can improve the efficiency of acquisition but also can improve the acquisition sensitivity. As we know, a long coherent integration time can be used to improve the detection probability in weak signal environments. In the acquisition, the longest coherent integration is limited to 10 ms for a standalone receiver because of the navigation bit reversal. The non-coherent integration method could be used to improve the SNR furtherly but with a square loss due to the analysis above. However, the LEO-assisted acquisition can extend the coherent integration time with aiding of the received navigation information. On the other hand, according to the preliminary estimation of the Doppler and code phase obtained from LEO assistance, a higher false alarm probability can be set to improve the detection probability. Due to non-coherent integration being used in the acquisition, the results of correlation obey the central chi-square distribution when there is no signal. The probability density function (pdf) of the chi-square distribution is as follows:P/IPQ), and that of the FLL is For comparison, the performance of the third-order PLL filter with second-order FLL assist  in a staTo solve the problem of the loss of lock under an ultra-low SNR condition, such as wideband jamming and signal blocked navigation, we propose the LEO-assisted GNSS tracking method in 0 increases. A long coherent integration time of 400 or 200 ms can greatly reduce the frequency jitter compared to that of the 20 ms. Nevertheless, the combination of 200 ms coherent integration and two non-coherent integrations can achieve almost the same performance as the 400 ms coherent integration. The result is coincident with the SNR analysis above. In addition, we can also figure out that the proposed method can track weak signals of 4 dB-Hz, just considering the thermal noise.To verify the performance of the LEO augmented acquisition and tracking structure, we use the GPS signal software simulator to generate the GPS IF signal with the augmentation of LEO. A software receiver  is used 0 = 15 dB-Hz, which is consistent with the performance analysis result in 0 gain. Moreover, the C/N0 in the proposed method is 10 dB higher than that in the traditional method before non-coherent integration, which causes about 5 dB squaring loss in the weak C/N0. Therefore, the profits of the assisted acquisition method on sensitivity is consistent with the analysis above.Firstly, we compare the sensitivity performance of the proposed acquisition method with the standalone conventional half-bit acquisition method. According to the analysis in the last section, we select a coherent integration time of 200 ms with two non-coherent combinations for the LEO-assisted method. The total integration time of the two methods is set to 400 ms. A statistical analysis of 100 times detection probability simulations is shown in 0 decreases from 21 to 1 dB-Hz with a speed of 2 dB per 40 s. The traditional tracking method without assisted information is realized for comparison, where the total integration time is set to 400 ms, including a 20 ms coherent integration time and 20 non-coherent integrations. The tracking results are shown in 0 at 5 dB-Hz. It is consistent with the performance analysis in In the signal tracking performance test, we generate a set of intermediate frequency data whose C/NWith the rapid development of LEO satellites, the joint positioning method of LEO and GNSS has been extensively studied. However, as in most studies, it just stays at the level of observed value fusion. To improve the performance of GNSS receivers under ultra-weak signal conditions, we propose a novel receiver structure with an LEO-augmented GNSS system, in which LEO-assisted GNSS signal acquisition and tracking methods are adopted. By utilizing the LEO satellite to realize Doppler positioning, this method initializes the position and time of the GNSS receiver and effectively reduces the acquisition and tracking search range of the receiver. Through the ephemeris information broadcasted by the LEO satellite, GNSS receivers can eliminate the impact of bit reversal and increase the coherent integration time. We carry out theoretical analysis and simulation experiments on the proposed acquisition and tracking scheme. Results show that the acquisition efficiency is improved by 170 times, acquisition sensitivity is improved by 8 dB, and the tracking sensitivity is improved by 4 dB compared with the traditional standalone receivers. Concerning LEO positioning, we only use the existing Iridium Doppler positioning as an example. Our proposed LEO-augmented GNSS receiver structure is based on the LEO positioning. The information LEO provided is independent of specific LEO constellations. Moreover, we choose the positioning error range within 1 km, which is wide enough. The only difference is that the LEO is assumed to transit GNSS ephemeris in this work. Thus, the presented results are generic with other LEO constellations if the LEO satellite is transmitting the GNSS ephemeris.This paper mainly discusses the high-sensitivity benefits of an LEO-assisted GNSS receiver, which is considered to be used in the ultra-weak signal environment, such as the strong wideband jamming background. Our next research work will focus on the performance of the structure under high-precision and high-dynamic applications. For high-precision applications, the PLL or FLL-assisted PLL should be used to get the carrier phase. With regard to the high dynamic applications, the GNSS/INS coupled system will be considered to reduce the impact of the receiver motion. In addition, with the development of LEO positioning technology, LEO satellite constellations with multiple satellites can effectively improve the initial positioning and timing accuracy, which means that the augmented effect will be further increased.


We present a novel simultaneous localization and mapping (SLAM) system that extends the state-of-the-art ORB-SLAM2 for multi-camera usage without precalibration. In this system, each camera is tracked independently on a shared map, and the extrinsic parameters of each camera in the fixed multi-camera system are estimated online up to a scalar ambiguity (for RGB cameras). Thus, the laborious precalibration of extrinsic parameters between cameras becomes needless. By optimizing the map, the keyframe poses, and the relative poses of the multi-camera system simultaneously, observations from the multiple cameras are utilized robustly, and the accuracy of the shared map is improved. The system is not only compatible with RGB sensors but also works on RGB-D cameras. For RGB cameras, the performance of the system tested on the well-known EuRoC/ASL and KITTI datasets that are in the stereo configuration for indoor and outdoor environments, respectively, as well as our dataset that consists of three cameras with small overlapping regions. For the RGB-D tests, we created a dataset that consists of two cameras for an indoor environment. The experimental results showed that the proposed method successfully provides an accurate multi-camera SLAM system without precalibration of the multi-cameras. In robotics, vision-based simultaneous localization and mapping (SLAM) is a geometric problem of mapping an unknown environment while tracking the camera pose simultaneously. Vision-based SLAM systems have a wide range of applications, such as autonomous navigation, search and rescue in natural disasters, and undersea exploration. Thus, the most important characteristics required in the SLAM system are to be accurate and robust. Liu et al.  show thaOne of the solutions to obtain a wide field of view is to use a single camera with an omnidirectional lens. Yet, in , it showThe primary challenge to be discussed in the use of multi-camera SLAM is the calibration of extrinsic parameters between cameras. For efficient localization and mapping, a SLAM system requires the integration of each information from cameras. For this reason, the available methods are reviewed depending on the necessity of multi-camera calibration.SLAM systems where all cameras work as a single unit require precalibrated extrinsic parameters. The first example of this approach is the multi-camera parallel tracking and mapping with a nonoverlapping field of view (MCPTAM) , which iOn the other hand, some approaches do not require the extrinsic parameters between cameras in advance. For instance, Heng et al.  developeWhether a multi-camera SLAM system precalibrates or calculates the extrinsic parameters online, slight errors in extrinsic parameters may cause significant errors in the reprojection of map points, and this causes failure during initialization and tracking. To overcome this issue, we present a novel solution to an uncalibrated multi-camera SLAM system. We aim to develop a robust multi-camera SLAM system in which each camera is tracked independently on a single map, and the extrinsic parameters are estimated online. In the camera tracking, we do not use the extrinsic parameters explicitly to avoid the tracking loss by the error in the parameters which affect robustness. However, in the mapping stage, we still estimate and refine the extrinsic parameters to gather and utilize all the observations from the multiple cameras that improve the map accuracy. Like the monocular SLAM systems, our system has a scale ambiguity problem for RGB cameras. RGB cameras are not able to set the scale factor  concerning corresponding feature matching. Even though the proposed system uses multiple cameras, it is not possible to solve the scale ambiguity since the extrinsic parameter calculation is not in the Euclidean space. For resolving the scale ambiguity problem, RGB-D camera usage is one solution. RGB-D sensors provide both the Euclidean geometry and the image texture of an environment by integrating a depth map measured by a depth sensor, and color information comes from an RGB camera. We resolve the scale ambiguity problem since a depth sensor presents the scale information, and the proposed system is compatible with RGB-D cameras.Since each camera performs its tracking, the proposed method might be considered similar to the collaborative SLAM systems. However, there are some significant differences. In collaborative SLAM systems like ,14, multOur method extends the state-of-the-art monocular ORB-SLAM2  algorithSLAM framework for an uncalibrated multi-camera system in which each camera is tracked independently on a shared map.Online calibration of extrinsic parameters in the multi-camera systemInitialization of multi-camera configuration.Simultaneous refinement of the SLAM components and extrinsic parameters by a multi-edge based graph optimization.The SLAM components are described in the In conventional multi-camera SLAM systems, all cameras work as a single unit. To work as a single unit, such systems use given extrinsic parameters between cameras from the first frame to the last frame. In cases where the extrinsic parameters are not accurate, the system may fail on the map initialization or camera tracking due to the wrong map point projection from multiple cameras. As a solution to this problem, our method introduces two new concepts. The first one is an uncalibrated multi-camera system in which each camera is tracked independently on a single map. The second one is self-calibration and refinement of the extrinsic parameters for better localization and mapping.When each camera works independently, the system does not need to use precalculated extrinsic parameters, which could be inaccurate. Unlike conventional multi-camera SLAM systems, the proposed independent tracking of each camera is not affected by the incorrect extrinsic parameters, even though they observe the same map points. Furthermore, in case a multi-camera SLAM system that operates as a single unit loses its track, it cannot relocalize itself unless it revisits the places previously observed. However, in the proposed system, as long as just one camera keeps tracking, the system can relocalize the other cameras by obtaining the reference keyframe tracking camera.In the mapping process, we collect observations from all the cameras and estimate the map points and keyframe poses. We also estimate the extrinsic parameters simultaneously for more accurate mapping. Once the system calculates the initial extrinsic parameters online, it updates them iteratively to estimate a more accurate map. The optimization process will be explained in detail in ‘TIMA SLAM–Tracking Independent and Mapping Altogether for an uncalibrated multi-camera system’. This is because all the cameras in the system are being tracked independently while a map is built by observations from all cameras.Considering the advantages of the proposed method, we call it In the TIMA SLAM, despite operating multiple cameras, the initial map is generated by a camera selected as a reference. For that purpose, the system calculates the relative poses between the consecutive frames and triangulates the map points. For the relative pose estimation, two geometric models are evaluated in parallel. According to the assumption of planar and nonplanar scenes, the system calculates a homography and the fundamental matrix respectively. The selection of the appropriate model is determined by the equation given in . AdditioAfter the reference camera generates the initial map, each nonreference camera in the system localizes itself using the reference keyframe and the map points sent by the reference camera. For the nonreference camera localization, the system estimates each camera pose by performing RANSAC iterations with the perspective-n-point(PNP) algorithm . If enouIn the next stage, the extrinsic parameters (the relative poses between the cameras and the reference camera) are calculated upon the moment each camera localizes itself because of all cameras in the system being fixed to each other. Let There should be more than 20 frames processed since the last global relocalization.There should be more than 20 frames processed since the latest keyframe addition and local mapping should be idle.There should be at least 50 points tracked on the current frame.The current frame should track less than Since each camera performs independent tracking, we use the original ORB-SLAM2’s tracking thread for the proposed system . The traThe local mapper primarily manages the covisibility between the keyframes via the map points and optimizes the local keyframe poses and the map points using local bundle adjustment (LBA). For that purpose, it follows several steps, and these steps are keyframe insertion, map point culling, new map point insertion, local bundle adjustment. and local keyframe culling.In the processing of a new keyframe, the local mapper updates the covisibility graph and adds a new node for the current keyframe. Then, it links a current keyframe to another keyframe that shares the most map points in common via updating the spanning-tree. Lastly, it calculates a bag of words (BoW) representation (benefits for the data association to triangulate new map points) of the current keyframe.The local mapper eliminates the low-quality map points repetitively considering two conditions. The first condition is that a tracking thread must see the map point in more than 25% of the frames predicted to be visible. The second one is that at least three keyframes should observe the map point.The local mapper creates new map points through triangulating ORB from associated keyframes in the covisibility graph. In case there is an unmatched ORB in the current keyframe, the system looks for a match with another unmatched ORB in other keyframes. The ORB match should meet the epipolar constraint to be accepted. To insert a new map point, the local mapper triangulates ORB pairs and checks both frames if they have a positive depth. Additionally, it checks the reprojection error, parallax, and scale consistency.The LBA optimizes the local keyframes and all the map points observed by the local keyframes. The local keyframes consist of the current keyframe and the other keyframes which are connected to the current keyframe by the covisibility graph . Unlike Lastly, to keep a functional simplicity, a local mapper searches for the redundant keyframes and eliminates them from the map. Keyframes, where more than 90% of the map points are observable to three other keyframes with the same scale level, are deleted from the map.The proposed system merges the information that comes from multiple cameras to improve the accuracy of the map by an optimization. One possible way is to apply a conventional bundle adjustment which optimizes the map points and all the keyframes registered, even though the keyframes belong to different cameras. However, this requires more degrees of freedom to be optimized than the actual system, because each camera in the rigidly fixed camera system cannot move independently. We utilize the fact that the cameras are rigidly mounted, and thus, the extrinsic parameters must be fixed, while they are not known in advance.We keep estimating the extrinsic parameters explicitly online by optimizing them along with the other SLAM parameters in the whole sequence. To achieve this, we propose to modify the SLAM formulation in the bundle adjustment. The initial estimates for the extrinsic parameters are obtained by the multi-camera initialization explained in virtual keyframes for the reference camera. This problem conversion ensures the minimum degree-of-freedom (DOF) parameterization of the unknowns for keyframes to be optimized. To convert the problem, all the keyframes of nonreference cameras are transformed into the corresponding keyframe of the reference camera, as if all the map points are observed from the reference camera. To transform the keyframes of nonreference cameras into those of the reference camera, the system uses the current estimation of the extrinsic parameters. If there are no corresponding keyframes of the reference camera, the system creates sets of c corresponding reference keyframe k whose pose is represented as We solve the converted problem as a nonlinear minimization and represent a nonlinear cost function describing reprojection errors. A 3D point The cost function is to be minimized is the sum of the squared reprojection errors denoted as: The projection function i and j.Like the ORB-SLAM, all optimizations are solved by a graph-based approach in this study. However, in the proposed method, it is not possible to represent the graph by the binary edge that connects two vertices. The main reason is that all the keyframes of nonreference cameras are transformed into the corresponding keyframe of the reference camera. Thus, the extrinsic parameters as unknowns require multi-edges that make connections to two or more vertices, as shown in Each time the system adds a new keyframe, loop closer searches for possible corresponding keyframes in the map to detect a loop. If a loop is detected, the loop closer first calculates a similarity transformation between the current keyframe and the loop candidate keyframe to check the drift in the loop. Then, the system fixes the pose of the current keyframe and covisible keyframes that are connected to the current keyframe to align both sides of the loop using the computed similarity transformation. Next, it merges the duplicated map points by checking the inliers that match both with the current keyframe and the loop keyframe with its neighbors. In the last step of the loop closing, the conventional global bundle adjustment (GBA) fixes all keyframe poses and map points from the initial keyframe whose id is zero. Unlike the original GBA, we use our GBA module based on the multi-edge-based graph optimization to update the extrinsic parameters between cameras, all the keyframes’ poses, and all the map points in the map. Since LBA optimizes the SLAM components locally, the system needs to update everything from scratch using the proposed GBA with the updated extrinsic parameters.To test the performance of the proposed method, various tests are performed on three different datasets created for both indoor and outdoor environments. The first two datasets (EuRoC/ASL and KITTI odometry) are publicly available and set to stereo configuration. The third dataset (KIST) has been created by us that consists of sequences RGB and RGB-D cameras separately. The RGB camera rig consists of three cameras with certain overlaps of their fields of view, and the RGB-D camera rig consists of two cameras that are set similar to stereo configuration. We made comparisons between our method and the other state-of-the-art algorithms on public datasets. Since we use multiple cameras, for the evaluation, we defined the body frame (BF) as the pose of the reference camera.The EuRoC/ASL visual-inertial dataset created by ETH Zurich contains stereo images and synchronized inertial measurement unit (IMU) measurements . The imabold, and the second-best results are indicated in blue. The results show that the proposed method achieves the best accuracy in all sequences.To calculate the absolute trajectory error (ATE), the estimations are aligned to the ground truth using sim(3) Umeyama alignment via the EVO package . Table 2sequence-V1_03. To show the performance of the trajectory estimation, the comparison of the proposed method with the ground truth data is presented in sequence-V1_03.Besides, the experiments also confirm that the relative poses between cameras stay stable throughout the entire trajectories of the dataset. bold, and the second-best results are indicated in blue. The proposed system has the best performance on the sequence 00, 02, 03 while it has comparable performances for the rest of the sequences. Additionally, The KITTI odometry dataset  includessequence 00. All of the state-of-the-art algorithms in this comparison are precalibrated based stereo SLAM systems. Considering this, our proposed method shows comparable results, even though there are no given extrinsic parameters in advance. Furthermore, the average ATE of the trajectory estimations shows that the proposed method has improved the performance of the conventional ORB-SLAM2. Another result showing how accurate the proposed method is that the relative poses between cameras remain stable throughout the entire trajectories of the dataset. The last dataset used in this experiment has been made by the department of the Center for Intelligent and Interactive Robotics, Korea Institute of Science and Technology (KIST). The dataset has sequences captured by RGB and RGB-D cameras.For the RGB camera data, the camera rig consists of three separate cameras with small overlapping regions. The images have 1288 × 964 resolutions and were captured in 30 fps by using FLIR Chameleon3 cameras. The dataset consists of three sequences that contain loops and is a composition of image sequences captured from an indoor environment. All the images between cameras are synchronized properly. The first sequence (KIST-00) is taken in a large hall that is 550 mUnlike the EuRoC/ASL and the KITTI datasets, the cameras are outward-looking and not a stereo camera, and it provides a much smaller overlapping region in the dataset. Even though the overlapping region is small, relative poses between cameras stay stable for whole sequences. For the RGB-D camera data, a sequence (KIST-03) is taken using two Intel Realsense D435 RGB-D sensors (640 × 480 resolutions with 30 fps) in the same environment with KIST-02. In this sequence, we used unsynchronized camera sequences. To evaluate the performance of the system, we first created a 3D octomap with a ROS package . Next, wIn this study, we have introduced a novel approach for a multi-camera SLAM system, which does not require precalculated extrinsic parameters between cameras. We have aimed to merge the information that comes from independently working multiple cameras to improve the accuracy of the map by an optimization. Unlike a conventional multi-camera SLAM system which regards all the cameras as a single unit, we have proposed to track each camera independently while a shared map maintains for all cameras. By doing that, the tracking failure caused by erroneous extrinsic parameters is avoided. To improve the map accuracy, we have also proposed a new bundle adjustment which keeps refining the extrinsic parameters online as well as the map points and the keyframe poses. We have converted from a bundle adjustment for conventional multiple cameras into that for multiple cameras fixed to each other to obtain the minimum number of unknowns to be optimized. A new initialization method has been introduced for the map and multiple uncalibrated cameras on the single map. To test the performance of our method, we have used three different datasets that include 21 sequences. The experiments have shown that our system works robustly and accurately with various camera configurations in both indoor and outdoor environments. The fact that our system gives accurate results in scenarios with different numbers of cameras and different viewing angles proves the consistency of the proposed method, while our method does not require a precalibration of the multi-camera system at all.


Shaping is very necessary in order to obtain a wide and flat supercontinuum (SC). Via numerical simulations, we accurately demonstrated shaping the SC using the fiber cascading method to significantly increase the width as well as the flatness of the spectrum in silica photonic crystal fiber (PCF). The cascaded PCF contains two segments, each of which has dual zero-dispersion frequencies (ZDFs). The spectral range of the SC can be expanded tremendously by tuning the spacing between the two ZDFs of the first segmented cascaded PCF. Increasing the pump power generates more solitons at the red edge, which accelerates solitons trapping and improves the spectral flatness of the blue edge. Furthermore, cascading the second segmented PCF by choosing appropriate fiber parameters ensures the flatness of the red end of SC. Therefore, a cost-effective alternative method for broad and flat supercontinuum generation in the near-infrared range is proposed here, which can be implemented easily in any photonics laboratory, where dual ZDFs PCFs are commonly found. Since Alfano and Shapiro firstly reported supercontinuum (SC) in 1970 in bulk glass , opticalRecently, studies on ultrafast dynamics in mode-locked lasers have broadened our horizons in complex nonlinear systems and contributed to laser design. It is convenient for us to obtain a femtosecond pulse with few-cycle and high peak power as a pump source for supercontinuum generation (SCG). That further revives interests in broad and flat SCG ,17. NumeIn this paper, we propose a method of accurately shaping SC via cascaded PCF. Here, each PCF needs to be tapered and spliced to the next stage; the splicing loss is directly ignored to get a better physical understanding of various effects. In the first part of our simulation, several PCFs with different ZDF spacing are used as the propagation medium of the first segmented cascaded PCF. We found that increasing the ZDF spacing is beneficial for extending the SC by R-DW and trapping blue-shifted dispersion wave (Trapping B-DW). Although increasing pump power is adequate to generate more solitons, accelerating solitons capture will improve the spectral flatness of the blue edge. Then, in the second part of our simulation, we analyze the output spectrum of the first segment and appropriately choose the fiber parameters of the second segmented cascaded PCF, realizing the accurate shaping of the red edge spectrum.T and z are, respectively, the time parameter related to group velocity at the central frequency Femtosecond pulse propagation in cascaded single-mode PCF can be described by the generalized nonlinear Schrödinger equation(G-NLSE) ,18:(1)∂Aattering ; and R. The GVD at central frequency From the output spectrum of PCF3 in The total length of the cascaded PCF constructed by PCF3 and PCF4 is 60 cm, in which the first 40 cm is PCF3 and the remaining 20 cm is PCF4. The frequency domain and temporal domain evolution of the pump pulse in this cascaded PCF are shown in However, the second ejected soliton in PCF3 plays a major role in shaping the SC, which turns into a higher-order soliton, but its central frequency is far from the two ZDFs of PCF4. Therefore, only SRS acts as the perturbation on its transmission and the HOD effect on the spectrum is negligible. Accordingly, only one fundamental soliton (marked by the blue arrow in N = 8), increasing the pump power (N = 10), and after cascade (N = 10), respectively. We use the standard deviation In In order to clearly demonstrate the evolution of the pump pulse in the cascaded PCF, we used the X-FROG trace to record the time-frequency diagram of the pulse in nine selected locations. For a short propagation distance of 2 cm, the pump pulse rapidly symmetrical stretches in frequency by SPM a. PropagThis section mainly discusses the influence of several main factors on the output spectrum flatness of cascaded fiber. In From In In We can conclude that, specifically in this manuscript, the optimum conditions for large spectral width and high spectral flatness (~1 um at −15 dB) are as follows; pumped at the frequency of 375 THz in the anomalous dispersion region in 60 cm fiber, incident power of 2600 W, the ZDF spacing of the first segmented fiber is 178 THz, and the second ZDF of the second segmented fiber is 251 THz. However, there are potential challenges and limitations in the practical applications of this method, where we need to consider access loss, transmission loss, and splicing loss. It is necessary to increase the pump power appropriately to compensate for actual total loss to ensure the same results as the theory analysis. Besides, when designing ZDF spacing, we need to consider the power endurability of the PCFs to ensure the spectral width and spectral flatness. What is more, it is difficult to achieve accurate control of the dispersion for practical devices, so detailed error analysis mechanism is very important in practical application.In this work, we numerically demonstrate accurately shaping the SC to acquire wider and flatter SC via cascaded PCF, which consists of two silica PCFs with dual ZDFs. These results suggest that choosing a larger spacing between the two ZDFs of the first segmented cascaded PCF can not only redistribute energy between DWs and Trapping DWs, but also raise the red-shift of R-DW, which is beneficial to broaden the spectrum. Moreover, increasing the pump power can tremendously increase soliton trapping to improve the flatness of the blue edge of the spectrum. More importantly, we analyzed the output of the first segmented fiber and reasonably selected the second segmented PCF parameters, especially the second ZDF position, to reshape the SC to attain a flatter SC over the entire spectrum. We believe the result of this work can serve as a guideline in SCG, which can promote the technical applications of SC. In a next step, we will study the device with more cascaded PCFs to improve spectral width and spectral flatness more efficiently, which would be an interesting and important subject.


Memories of past events and common knowledge are critical to flexibly adjust one’s future behavior based on prior experiences. The formation and the transformation of these memories into a long-lasting form are supported by a dialogue between populations of neurons in the cortex and the hippocampus. Not all experiences are remembered equally well or equally long. It has been demonstrated experimentally in humans that memory strength positively relates to the behavioral relevance of the associated experience. Behavioral paradigms that test the selective retention of memory in rodents would enable further investigation of the neuronal mechanisms at play. We developed a novel paradigm to follow the repeated acquisition and retrieval of two contextually distinct, yet concurrently learned, food-place associations in rats. We demonstrated the use of this paradigm by varying the amount of reward associated with the two locations. After delays of 2 h or 20 h, rats showed better memory performance for experience associated with large amount of reward. This effect depends on the level of spatial integration required to retrieve the associated location. Thus, this paradigm is suited to study the preferential retention of relevant experiences in rats. Memory is the ability of the brain to encode and store information for later use. The ability to remember past events and facts, is critically dependent on the medial temporal lobe and its connections to the cortex . FollowiHowever, not all experiences are remembered equally well or equally long. A growing body of literature in humans has shown that behaviorally relevant aspects of experience, such as emotional content or expected outcome during learning , enhanceRodents are commonly used as animal models to study cognitive functions and in particular the neurobiology of learning and memory. They present a combination of several advantages. First, rodents require relatively few resources to maintain and can be trained in various behavioral assays . Second,We developed a novel paradigm to study the selective retention of memories in rodents in which the retention of two, concomitantly acquired food-place associations is assessed every day. This behavioral paradigm was successfully used to confirm the improved memory retention of experiences associated with large reward size, and further, to demonstrate the causal role of post-learning hippocampal replay in the reward-related enhancement of memory consolidation .A total of 23 male Long Evans rats  were food deprived to 85–90% of their free-feeding weight. Of these, 13 animals received an implant for electrical recording (as part of another study), and 10 rats did not undergo surgical procedures and were only tested behaviorally. Upon arrival, the 10 weeks old animals were housed in the animal facility in pairs to acclimate for 1 week. In the following week, the animals were placed in individual housing and on food restriction. In addition, the rats were gently handled for at least 5 min every day to reduce stress and habituate to the experimenters. The animals were kept on a normal light cycle throughout the entire time of the experiment. All experiments were carried out in accordance with protocols approved by KU Leuven Animal Ethics Committee (P119/2015) in accordance with the European Council Directive, 2010/63/EU.The behavioral testing apparatus was located in one of two 4 m by 4 m rooms with black walls and distinctive extramaze distal cues  were attached to each of the walls. The apparatus was elevated 40 cm off the ground and consisted of a home platform that gave access to the left and right side of the room via a short 30 cm track . The lefThe goal of the task was for the rat to associate one of the 6 arms in each environment with a reward. In each daily session, one environment was associated with a large reward (9 pellets) and the other with a small reward (1 pellet). After the instruction phase, during which the animal could explore the rewarded target arms across five instruction trials per environment, and after a subsequent 2 h or 20 h delay, the rats were tested for their memory of the reward-place association in the presence of three distractor arms . Across Prior to experimental sessions, the animals were trained to run back and forth on an elevated linear track (40 cm high and 90 cm long) to obtain food rewards (3 pellets) until the animals executed at least 20 laps within 10 min for three sessions in a row . During Next, the rats were familiarized with the experimental procedure and the maze environment of the dual reward-place association task (pre-training phase). During the instruction phase, only the two target arms were physically present in the two environments. The instruction phase consisted of five blocks of alternating trials to the right and left environment. Each trial began with the animal constrained to the home platform. It was then given access to only one of the two environments. The following trial started after the rat had consumed the reward at the end of the target arm and returned to the home platform. The presentation order of the environments within the trial blocks was constant within a session and randomized across sessions. After the instruction phase and before the memory test phase, the rat was removed from the maze apparatus for a short delay and kept in his home cage . After the delay, rats were subjected to three reinstatement trials separately for the two environments in the presence of the distractor arms (routine test). In each reinstatement trial, rats were rewarded for visiting the target arm with 3 pellets. The aim of the reinstatement trial was for the animal to learn to seek for a reward at the end of the target arm and to ignore the distractor arms. Each reinstatement trial lasted until the animal consumed the reward at the end of the target arm .The pre-training phase ended when the rats first visited the target arm during the first reinstatement trial in both environments for 3 days in a row. During the experimental phase, the rules of the dual reward-place association task and topography of the maze were kept the same, but different reward sizes (1 and 9 pellets) and longer delays (2 h or 20 h) were introduced. During the delay phase, the rat was either returned to its home cage or placed in a 40 cm × 40 cm rest box with 60 cm high walls that was located inside the behavioral room. In one out of every two sessions, the routine memory test was replaced by a probe memory test. During the probe test, the first reinstatement trial was replaced by a 2-min-long unrewarded memory probe trial separately for the large and small reward environments. After pauses in training , the subsequent experimental session was always preceded by a pre-training session. This procedure was followed to make sure that the rats retained their motivation to search for reward at the target arm in the memory probe trials .The animals underwent an average of 13 pre-training sessions during the pre-training phase (inter-quartile range: 9–18). On average, the experimental phase lasted for 51 sessions (inter-quartile range: 37–67) including preceding pre-training sessions. The 20 h delay was systematically introduced for animals first tested after 2 h delay .Data analysis was performed using Python  extendedIn the instruction trial, the average running speed to and from the reward platform was quantified only for implanted animals, based on video tracking of the head-mounted LEDs. Average speed was computed over the journey that started when the animal left the home platform and ended when the animal reached the reward platform at the end of a target arm (and vice-versa for the homebound journey).In the memory probe trial, the number and pattern of visits to the target and distractor arms were quantified as measures of performance in the reward-place association task. A visit to an arm was only counted if the animal reached the reward platform at the end of an arm. We defined the following quantities and  probabilities to characterize the reward-seeking behavior in the probe trial:The total number of arm visits in the 2-min memory probe trial.The across session mean probability that the first visit is on target.p(T). This probability is further split in the conditional probabilities p(T|D) and p(T|T) that measure the mean probability of visiting the target arm given that the immediately preceding arm visit was also on target [p(T|T)] or was to a distractor [p(T|D)].The across session mean probability that a visit is made to the target, computed by averaging the equivalent per session The across session mean probability that a repeat visit is made to any one of the three distractor arms, computed by averaging the equivalent per session.t-test. To test for a difference in two sample proportions, we used either the McNemar test (for paired samples) or the two-proportion z-test.To test a difference in two sample means, we used either the Wilcoxon signed rank test (for paired samples) or the Welch’s p(visit1 = T) and an ordinary linear regression model for p(T).To analyze the dependence of behavioral metrics on predictor variables, we fitted Bayesian generalized linear models (GLMs) using the PyMC3 package for Python . We applModel fitting and inference was performed using Markov chain Monte Carlo (MCMC) sampling methods in PyMC3 . Broad normal distributions were used as priors on the parameters.Z = 707.00, p = 2.3×10−19]. When analyzed separately for each of the 5 trial blocks, we observed that running speed was low in the first trial block and increased in the second trial block for both large and small reward conditions . As we reported previously , rats wep = 0.25) to visit the target arm .We computed the conditional probability ctor arm . In bothp(Dk|Dk); mean (99% CI), large: 0.01 , small: 0.02 ]. However, rats did show an increased tendency to immediately return to the target arm without visiting any other arm in between, expressed as the conditional probability p(T|T) (p(T|T) developed from the fourth visit in both small and large reward conditions, but the increase was only temporary for the small reward condition. On average the probability p(T|T) was lower than chance for both large and small reward conditions .Rats have a natural tendency to alternate maze arms and to avoid visiting the same arm twice in succession. Accordingly, rats made virtually no repeat visits to the same distractor arm  but was only statistically significant for center and intermediate locations, due to a higher variability for the edge locations . During the probe trials, rats were more likely to repeat visit to target arms p(T|T) associated to large reward amount compared with small reward for the center and intermediate locations, but not the edge locations .We quantified the conditional probabilities, revisit probability p(T|D)  and repe (p(T|T)  separateZ = 3285.50, p = 0.059] (p(visit1 = T) during the memory probe  (p(T) was marginally lower for the environment tested first  : 0.34 ; Wilcoxon signed-rank test: = 0.059]  and the p = 0.1]  were not= 0.033] .slopesmall: −0.019 , slopelarge: −0.022 ]. This indicates that the animals reduced their reward-seeking behavior, possibly because they learned to recognize a memory probe trial that is never rewarded. The probability p(visit1 = T) increased significantly across sessions, but only for the small reward condition . In contrast, the decrease in total number of visits did not affect the average probability p(T) to visit the target arm . Thus, while rats were familiar with the basic task rules prior to the experimental phase, we still observed an increase of performance across sessions, possibly because the introduction of small/large reward size and extended delay.Rats were pre-trained to be familiar with the task rules and subsequently repeatedly trained/tested with daily varying reward-place associations for several weeks. We asked if the animals’ performance varied over time. With increasing experience in the task, the total number of arm visits during the 2-min memory probe trial decreased for both reward conditions . Overall, the preference for visiting the target arm (over distractor arms) was stronger in the large reward condition as compared to the small reward condition . The average probability to visit the target arm p(T) was only higher than chance in the large reward condition . On their first journey, the probability of visiting the target arm p(visit1 = T) was higher than chance level for both large and small reward conditions . Despite a tendency for the probability of first visiting the target arm associated to the large reward to be higher than for the small, the difference between the two reward conditions was not significant when including the probe memory test sessions only . However, the conditions in which the rats choose the first arm to visit are the same between probe and routine test sessions. When combining all test sessions, the difference between reward conditions was then significant .Rats were also tested for their memory of the target arm locations after 20 h delay . They made similar number of total visits within the 2-min probe trials in large and small reward environments [Our aim was to develop a behavioral paradigm to study the enhanced memory retention of salient experiences in rodents. Each day, rats were trained to learn a different food-place association on two contextually distinct semi-radial arm mazes. One arm was associated with a large amount of reward, and the other with a small amount of reward. The locations of the arm and the reward associated to the two environments were pseudo-randomly assigned every day. After a delay of 2 h or 20 h the animals were placed again in the two environments separately to be tested on their memory for the previously rewarded locations.During training, rats showed a rapid increase in average run speed on journeys toward the reward. Moreover, a difference in speed developed throughout the training. The speed on journeys to the large reward remained stable while the speed to the small reward decreased toward the end of the training sessions, suggesting different motivational states consistent with the two different rewarded outcomes. These results indicate that the animals were able to quickly learn the food place associations.Following a previous study showing that rats remember better locations associated with larger reward amount after 1 and 24 h , the perFurther analysis revealed that other aspects of the experience in the paradigm influenced the performance of the animals after 2 h of retention delay. The performance varied in function of the location of the baited arm relative to the boundaries of the environments. The more radially distant the arm was from the boundary, the more the performance of the animals decreased. This effect was particularly pronounced in the small reward condition, so that performance for target arms close to the boundary were similar between the two reward conditions and the difference progressively increased for the target arms located centrally. First, these results confirm a modulation of memory retention by the amount of reward as the differences in performance cannot solely be explained by different seeking strategies related to motivational state. Second, it indicates that the reward-related enhancement of memory was interacting with other features of the experience potentially dependent on different memory systems . Rats usDespite being highly familiarized with the majority of the task parameters, the performance of the animal improved over time, at the scale of weeks of training (meta learning). The improvement in performance may reflect learning associated with the changes introduced at the start of the experimental procedure, such as the increased retention delays, the different rewarded outcomes or the non-rewarded trials used as probe memory tests. The increase in memory performance was accompanied with a reduction of the seeking behavior during the probe tests, suggesting that the animals had adjusted their behavior to the fact that these trials were unrewarded, which argues in favor of the fact that at least part of the meta learning reflected the learning of the changes in the tasks. The meta learning related to memory performance was mainly observed for the small reward condition, while performance in the large reward conditions were already close to their maximum from the early phase in the training. This suggests that higher value outcome during training accelerates meta-learning.The dual reward-place association task is suited to study the modulation of memory retention by features of experience as was demonstrated with varying the amount of reward associated to two similar but distinct experiences. However, the current paradigm can be further optimized, in particular, to circumvent two observed limitations. First, the enhancement of memory for highly rewarded experience was dependent on locations presumably requiring the use of an allocentric strategy. The dependence of the reward-enhancement of memory to two third of the arm locations  reduces the efficacy of the paradigm. Maximizing the number of locations requiring higher level of spatial integration would thus optimize data collection. For example, increasing the total number of possible arm locations would increase the ratio between the number of central and edge arms locations. In addition, the increased density of rewarded location is also expected to more strongly depend on the hippocampus . Second,The choice of behavioral assay is critical, not only to ensure a behavioral read out of the cognitive process of interest, but also as it participates in optimizing the amount and reliability of the data collected. Experiments combining neuronal recording and/or manipulations with behavior are critical to understand how brain activity supports cognitive functions, but they require a large investment for each animal. Repetitive and behaviorally constrained paradigms have the potential to increase the outcomes from experiments correlating brain activity with behavior by reducing variability and increasing the number of datasets collected per animal. Moreover, experiment involving manipulations, for example of particular aspects of an experience or directly of brain activity, benefits from the ability to compare the effects with internal controls from the same animals, between or within the same experimental sessions. The dual reward-place association paradigm is suitable for neuronal recordings and manipulations : the useThe datasets generated for this study are available on request to the corresponding author.The animal study was reviewed and approved by the KU Leuven Animal Ethics Committee (P119/2015).FM and FK conceived and designed the study and wrote the manuscript. FM, CK, and J-JS carried out the experimental work. FM, CK, J-JS, and FK analyzed and interpreted the data. CK and J-JS reviewed the manuscript. FK coordinated and provided funding for the project.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.


The objective of this study was to quantify the benefit from the inclusion of genomic information in the estimation of breeding values for lactation yields of milk, fat, and protein or somatic cell score in a New Zealand dairy goat herd. The dataset included lactation yields of milk, fat, and protein and average somatic cell score of 839 does and genotypes from 388 does. A prototype single-step BayesC model was developed to predict genomic breeding values and demonstrated that including genomic information into the evaluation can increase the accuracy of predictions compared with the traditional best linear unbiased prediction methods based on pedigrees alone, which is currently implemented in the New Zealand dairy goat industry.Selection on genomic breeding values (GBVs) is now readily available for ranking candidates in improvement schemes. Our objective was to quantify benefits in terms of accuracy of prediction from including genomic information in the single-trait estimation of breeding values (BVs) for a New Zealand mixed breed dairy goat herd. The dataset comprised phenotypic and pedigree records of 839 does. The phenotypes comprised estimates of 305-day lactation yields of milk, fat, and protein and average somatic cell score from the 2016 production season. Only 388 of the goats were genotyped with a Caprine 50K SNP chip and 41,981 of the single nucleotide polymorphisms (SNPs) passed quality control. Pedigree-based best linear unbiased prediction (PBLUP) was used to obtain across-breed breeding values (EBVs), whereas a single-step BayesC model (ssBC) was used to estimate across-breed GBVs. The average prediction accuracies ranged from 0.20 to 0.22 for EBVs and 0.34 to 0.43 for GBVs. Accuracies of GBVs were up to 103% greater than EBVs. Breed effects were more reliably estimated in the ssBC model compared with the PBLUP model. The greatest benefit of genomic prediction was for individuals with no pedigree or phenotypic records. Including genomic information improved the prediction accuracy of BVs compared with the current pedigree-based BLUP method currently implemented in the New Zealand dairy goat population. The purpose of selection is to improve the performance of a population. Selection based on genomic breeding values (GBVs) can improve the rate of genetic gain compared with using only pedigree and performance records and has become a widely adopted method for ranking candidates for improvement schemes . The benUntil recently, the standard method of estimating breeding values was from a best linear unbiased prediction procedure that uses phenotypic records (PBLUP) of the individual and its relatives . That meLegarra et al.  suggesteFernando et al.  proposedEstimating GBVs conceptually involves a training population that has phenotypes and genotypes. In ssBR, the prediction model uses this “training data” to predict the influence of genetic markers by regression of the observed phenotypes on dosage covariates formed from marker genotypes. Then, the marker effects are summed across all loci to get the GBVs of individuals in a validation population that may not have observed phenotypic records.The Dairy Goat Cooperative (DGC) Ltd.  processes approximately 80% of goat milk in New Zealand. Farms that supply DGC and undertake herd testing participate in an annual genetic evaluation for lactation yields of milk (MY), fat (FY), and protein (PY) and for the average somatic cell score (SCS). Breeding values for these traits are estimated for each animal from an across-breed multi-trait repeatability animal model using the available pedigrees . CurrentThe aim of this study was to quantify the benefits from the inclusion of genomic information in the estimation of breeding values for a single New Zealand dairy goat herd.Phenotypic and pedigree records were provided for a single dairy goat herd by Dairy Goat Co-operative (NZ) Ltd.  from a herd test database maintained by Livestock Improvement Corporation (LIC) . The original dataset comprised lactation records from the 2016 season for 883 dairy goats. The phenotypic records were estimates of 305-day lactation yield records for MY, FY, PY, and SCS. The test interval method  was usedwww.goldenhelix.com). Individuals were discarded if they had a call rate < 95% or if they did not have phenotypic records. SNPs were discarded if they had a call rate < 90%, MAF < 1%, or deviated significantly from the Hardy-Weinberg equilibrium based on a threshold of p < 10−6. The majority of genotypes were from does in their second parity , while the remaining genotyped animals were in parity one , three , four , or beyond the fourth parity . The 388 genotyped animals were of Saanen (14) or ANTO (374) breed compositions.Skin samples were collected for SNP genotyping with the Illumina Caprine 50K BeadChip  in 2016. Of the 51,462 SNPs obtained, a total of 41,981 SNPs per animal remained after quality control. Quality control was performed using the SNP & Variation Suite v8 (SVS) software . A single-step BayesC model (ssBC) was used to estimate across-breed GBVs. Phenotypic and pedigree records from 839 animals were included in both models, and genotypes of the 388 animals were included in the ssBC model.y is the vector of phenotypes comprising at most one lactation record for MY, FY, PY, or SCS; b is the vector of fixed effects; d is the vector of effects of ANTO and unknown breeds; a is the vector of additive genetic effects ; e is the vector of random residual effects ; X and Z are design matrices relating the fixed and additive genetic effects, respectively; and D is a matrix with a row for each animal in the pedigree and columns for the proportion of ANTO and the proportion of unknown breeds (the regression coefficient for the Saanen breed effect was constrained to zero). Fixed effects included in b were the contemporary group and, as covariates, DMKD, DIM, and general heterosis. General heterosis was calculated as 1 − ∑fj = 1d2j, where dj is the proportion of each of the f = 3 breed groups  [Dd and variance Aσg2, where A is the numerator relationship matrix from the pedigree, and σg2 is the within-breed additive genetic variance. Residuals were assumed to have a normal distribution, with mean zero and variance Iσe2, where I is an identity matrix of size equal to the number of animals with a lactation record, and σe2 is the residual variance.The PBLUP was fitted using the ASReml 3.0 software package  with theunknown) . The addEstimated breeding values were calculated as:In this population, there is a known QTL with a large effect on milk traits ; therefoyn and yg are the vectors of the phenotypes; Xn and Xg are the incidence matrices for the fixed effects; and b is a vector of the fixed effects, including the contemporary group (does kidding in the same parity) and, as covariates, DMKD, DIM, and general heterosis. Dn and Dg are matrices with a row for each non-genotyped and genotyped animal in the pedigree and columns for the proportion of ANTO and the proportion of unknown breed, d is a vector of effects of the ANTO and unknown breeds, and Jn and Jg are matrices with a row for each non-genotyped and genotyped animal in the pedigree and columns for the J covariate for each breed group that were included as fixed effects to fit the difference between the genotyped founder and non-genotyped founder breeds. The matrix Jn is computed as AngAgg−1Jg, for breed f, where Ang and Agg−1 are submatrices of the numerator relationship matrix A, Jg is the matrix of the breed fractions identical to Dg, except that it includes the vector of breed fractions for Saanen, q is the vector containing the regression covariates for J, which account for the difference in breeding values between genotyped and non-genotyped animals of the same breed [Zn and Zg are incidence matrices that relate the breeding values of animals, Mg is the matrix of the centered marker covariates for the genotyped animals, Mn = AngAgg−1Mg is the matrix of the marker covariates for the non-genotyped animals that are imputed from the genotyped relatives, a is the vector of random marker effects, ε is the vector of genetic imputation error effects, Wn and Wg are incidence matrices that relate the residual polygenic effects, u is the vector of residual polygenic effects, and e is a vector of residuals.The model in matrix notation wasme breed , Zn and ak2, and the prior probability p that SNP k has zero effect and follows a two-component mixture prior:2ak ~ va,Sa2 X2va. A previous study in this population reported that the markers captured 12% of the genetic variance [Ann−AngAgg−1Agn)(1−w)sg2) [Ann, Ang, Agg, and Agn are submatrices of A; sg2 is the total genetic variance with  ~ vg,Sg2 Xvg2; w is the ratio of residual polygenic to total genetic variance (0.88); u ~ N that are not captured by markers; and e is ei|se2 ~ iidN, with  ~ ve Se2 Xve2.The fixed effects are assumed to have flat priors. The prior for the marker effects depends on the marker variance, svariance . To reco1−w)sg2) , where AJ covariates for each breed group, Genomic breeding values were calculated as:The BayesC mixture model requires that unknowns be estimated using MCMC techniques. Due to the limited number of observations in this evaluation (a single herd), variance components were estimated using the ssBC model and data from a larger dataset first . The posterior residual variance and heritability values previously estimated for this population  for eachPrediction accuracy for each model and trait were assessed using a validation process by splitting the herd into two subsets: the training set of the oldest 70% of the herd  and the validation set comprising the youngest 30% .The prediction accuracy was assessed and summarized based on the different levels of pedigree information available in the evaluation. Using predicted EBVs of animals in the validation set , the average prediction accuracies were calculated when the animal had: (A) both the sire and dam recorded , (B) the sire was recorded and had ≥5 progeny in the herd , (C) the dam was recorded and had ≥1 lactation record , or (D) neither the sire nor dam were recorded . To demonstrate the impact on prediction accuracy when both the sire and dam are unknown, the PBLUP evaluation was rerun an additional time but, by masking the pedigree records of animals that previously had records of both the sire and dam, resulted in 162 animals in the evaluations for scenario (D).Reliabilities of PBLUP EBVs were calculated as (1-(PEV/sg2)), where PEV is the predicted error variance calculated by inverting the coefficient matrix of the MME , and sg2The across-breed EBVs and GBVs were standardized to a consistent base for the independent PBLUP and ssBC evaluations by subtracting off each EBV the mean EBV of the base and similarly for GBV. The slope of standardized GBV against standardized EBV is used as a measure of genomic inflation. The expected value is one, indicating that the genomic predictions are on a similar scale as the EBVs, i.e., not inflated of deflated.The descriptive statistics are in The average accuracies of the GBVs obtained for MY, FY, PY, and SCS were greater than the average accuracies of EBVs . The greFor all scenarios and all traits, the GBVs had greater accuracies than the EBVs . When inThe breed and J covariate coefficients for each breed group obtained from the ssBC model are shown in The results of this study indicate that the ssBC model using genotypes, pedigrees, and phenotypic records can be used to obtain more accurate predictions of animal genetic merit compared with the PBLUP model currently used for the genetic evaluation of dairy goats in New Zealand. The increase in accuracy is particularly valuable, as these GBVs can be estimated for all individuals in the evaluation, even those without phenotypes or pedigree information. Whereas, with the PBLUP evaluation, those animals without phenotypic or pedigree records would have otherwise been excluded.The prediction accuracies obtained from the PBLUP model suggest the current pedigree records provide limited information to the genetic evaluation of animals in this herd. Whereas the genomic information provides a significant contribution to the evaluation, as shown by the increased prediction accuracies. Despite this increase, these accuracies are much lower than those reported in other dairy goat populations. Multiple studies using ssGBLUP approaches have published prediction accuracies for milk traits in dairy goats, including accuracies of 0.61 for MY in the UK ; 0.69 foThe accuracy of the GBVs of the FY and ASCS was slightly greater when the dam was recorded in the pedigree and had her own lactation record, compared with the animal having no pedigree records. However, the prediction accuracy was lower for the prediction of the MY and PY GBVs. These contradictory accuracies of GBVs could be due to the limited number of animals in the validation population that had dams with lactation records  and, therefore, was not an accurate representation of the true effect of having this additional information in the reference population. On the other hand, these differing accuracies between traits could suggest that the inclusion of the dam and her lactation records does not add much to the accuracy of the genomic predictions. The latter coincides with other genomic prediction studies, which also suggest that adding females to the reference population does not contribute a great deal to the accuracy of genomic predictions ,26.When the animals have a sire recorded in the pedigree that has at least five progeny records, the average prediction accuracy of both models was greater than the accuracies obtained when the dam was recorded in the pedigree and had her own lactation record. This difference in accuracy suggests that most of the information is captured by the males present in the reference population, rather than the females. Although actual sires were not included in the reference population, the link between the sires and their progeny provides greater benefits to the predictions compared with the information provided by the dams with lactation records.The prediction accuracies of EBVs and GBVs when animals have a sire recorded that has at least five progenies obtained the same prediction accuracies of EBVs and GBVs when both the sire and dam are known. This suggests that animals in the validation population that have recorded sires linked to the reference population provide as much information to the prediction of breeding values as the animals with both the sire and dam recorded.The accuracy of predictions is important in livestock genetic improvement programs, as this gives confidence of a reliable estimate of the individuals true breeding values. If the accuracy is low, there is greater risk that the EBVs and GBVs are not reliable, and there is more chance of selecting an animal with an inflated breeding value. The accuracy of genomic prediction largely depends on the size of the reference population , the relUnlike the dairy cattle industry that has high accuracies due to a well-established recording system and large reference populations , the daiThe prediction accuracies obtained in this study were lower than those obtained in other studies that used ssGBLUP approaches; however, this could be due to the limited information available in the current evaluation rather than the model used. The prediction accuracies are expected to increase as the size of the reference population increases.In this study, the regression coefficient of the GBV on the EBV for the MY was very close to one, indicating that the GBV and EBV for this trait were obtained in the same scale. The regression coefficients of the GBV on the EBV for the FY, PY, and SCS were less than one, indicating that the GBVs of these traits were slightly deflated or the EBVs were inflated. However, these regression coefficients give confidence that the standardized GBVs are similar to the EBVs and, given the improved accuracy of the GBVs, reiterates the potential of including genomic information in the genetic evaluation of these traits. Genomic relationships estimated from marker data provide more accurate estimates of the genetic covariance between relatives than the genetic relationships estimated from pedigree information . This, iThe breed effects included in the multibreed genetic evaluations can have a large influence on the accuracy of the EBVs and GBVs and will be important for the ranking of animals. Although this dataset is relatively small, the regression coefficients obtained for each breed group illustrate the importance of these breed effects. Likewise, the J coefficients obtained for the differences between the genotyped founder and non-genotyped founder breeds are included in the across-breed GBVs for each animal, where the values for the non-genotyped animals will vary widely, depending on how closely related they are to the genotyped animals and their breed proportions of each breed group. Previously, the GBVs were predicted based solely on their pedigrees and genotypes, which led to overestimation, as the genotyped animals were generally the most superior in the population. However, correcting for the differences between the genotyped and non-genotyped founder breeds enables the prediction of genetic merit in a population where selection is absent as the analysis is conditional on the data used for selection.A single-step approach that includes both genotyped and non-genotyped animals would be recommended for the genetic evaluation of the New Zealand dairy goat population, as the inclusion of genomic information improved the accuracy of prediction of the across-breed breeding values for all traits and for all scenarios. The accuracies obtained for the different scenarios demonstrated what farmers could expect with varying degrees of relationships to the reference animals. The results from this study suggest genomic prediction is possible in the New Zealand dairy goat population; however, this was based on a single herd and requires further investigation before implementing for the entire population.Including genomic information improved the prediction accuracy of breeding values compared with the pedigree-based BLUP method currently implemented in the New Zealand dairy goat industry. The prediction accuracies were slightly lower than other populations, but these accuracies are expected to increase as more animals enter the reference population. The use of a higher density SNP chip or whole-genome sequencing would increase the extent of the LD, which would improve accuracies of the across-breed genomic predictions. The inclusion of genomic information would enable the prediction of the GBVs for all animals, even those without known pedigree or phenotypic records, which would benefit the New Zealand dairy goat population.