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The robust and high-precision estimation of position and attitude information using a combined global navigation satellite system/inertial navigation system (GNSS/INS) model is essential to a wide range of applications in intelligent driving and smart transportation. GNSS systems are susceptible to inaccuracies and signal interruptions in occluded environments, which lead to unreliable parameter estimations in GNSS/INS based on filter models. To address this issue, in this paper, a GNSS/INS combination model based on factor graph optimization (FGO) is investigated and the robustness of this optimization model is evaluated in comparison to the traditional extended Kalman filter (EKF) model and robust Kalman filter (RKF) model. In this paper, both high- and low-accuracy GNSS/INS combination data are used and the two sets of urban scene data are collected using high- and low-precision consumer-grade inertial guidance systems and an in-vehicle setup. The experimental results demonstrate that the position, velocity, and attitude estimates obtained using the GNSS/INS and the FGO model are superior to those obtained using the traditional EKF and robust EKF methods. In the simulated scenarios involving gross interference and GNSS signal loss, the FGO model achieves optimal results. The maximum improvement rates of the position, velocity, and attitude estimates are 81.1%, 73.8%, and 75.1% compared to the EKF method and 79.8%, 72.1%, and 57.1% compared to the RKF method, respectively. [ABSTRACT FROM AUTHOR]

In this study, robustness of sparse processing particle image velocimetry (SPPIV) of high spatial resolution was improved, and the flow velocity field was measured in real time by improved SPPIV, whereas SPPIV estimates the entire flow field from limited results of sparsely located PIV analysis interrogation windows in real time but suffers from estimating high spatial resolution field because of outliers appearing in the cross correlation analysis. The high-resolution velocity field estimation was conducted by reducing the interrogation window size from 32 × 32 pixel 2 to 16 × 16 and 8 × 8 pixel 2 , and the robustness of the improved SPPIV was investigated. We developed two methods of high-resolution SPPIV which is capable of real-time flow field measurement. One is robust SPPIV which incorporates with robust Kalman filter and eliminates the outliers, while the other is multiresolution SPPIV which adopts the large interrogation area for real-time measurements and projects it into the high-resolution velocity fields. Robust and multiresolution SPPIV can estimate the velocity fields more accurately than high-resolution standard SPPIV with 16 × 16 or 8 × 8 pixel 2 interrogation windows. The detailed discussion and comparison of those two methods are conducted. In addition, the sensor optimization is compared in the present framework and it shows that the sensors optimized by the Kalman filter index are better than those by the snapshot-to-snapshot index for SPPIV application. [ABSTRACT FROM AUTHOR]

The Kalman filter provides an optimal estimation for a linear system with Gaussian noise. However, when the noises are non‐Gaussian in nature, its performance deteriorates rapidly. For non‐Gaussian noises, maximum correntropy Kalman filter (MCKF) is developed which provides a more accurate result. In a scenario, where the actual system model differs from nominal consideration, the performance of the MCKF degrades. For such cases, in this article, we have proposed a new robust filtering technique for a linear system which maximizes a cost function defined by exponential of weighted past and present errors weighted with the kernel bandwidth. During filtering, at each time step, the kernel bandwidth is selected by maximizing the correntropy function of error. Further, a convergence condition of the proposed algorithm is derived. Numerical examples are presented to show the usefulness of the proposed filtering technique. [ABSTRACT FROM AUTHOR]

This paper introduces a novel robust Kalman filter designed to leverage symmetrical properties within the Pearson Type VII-Inverse Wishart (PVIW) distribution, enhancing state estimation accuracy in the presence of time-varying biases and non-stationary heavy-tailed (NSHT) noise. The filter includes a shape parameter from the normal distribution and an extra variable from the Gamma distribution, which are used to symmetrically adjust the average and variation measures of the data to fit better under difficult noise conditions. To deal with unknown noise that changes over time, the filter uses the Inverse Wishart distribution to model and estimate the scale matrix deviations, making it easier to adapt to changes. The filter also uses a technique called Variational Bayesian to estimate both the state and the parameters at the same time. The results from simulations show that this new filter greatly improves the accuracy and strength of the estimation compared to the usual Kalman filters that assume a normal distribution, especially when there is non-stationary heavy-tailed noise. The main objective is to improve estimation in signal processing and control systems where heavy-tailed noise is prevalent. [ABSTRACT FROM AUTHOR]

Sensor fusion is a major field in autonomous mobile robots navigation research. These methods integrate information obtained from accelerometers, rate gyros and monocular cameras to provide pose and orientation of the robot, which are known in the literature as Visual-Inertial Simultaneous Localization and Mapping systems. For outdoor navigation, sensor fusion algorithms may also use magnetometers and GPS modules, since in indoor environments and certain urban areas they may suffer from measurements corruption in the presence of ferromagnetic materials and signal occlusion, respectively. To avoid combining corrupted or noisy data, we propose a Robust Kalman Filter (RKF) for Discrete-time Markovian Jump Linear Systems which estimates the position and orientation of the platform considering the best Markovian mode at each instant. The proposed RKF approach reduces the degradation of the filter performance due to parametric uncertainties present in the system models. We present experimental results in comparison with standard and state-of-the-art sensor fusion techniques to show that our system is robust even in challenging conditions.

Multi-source heterogeneous information fusion based on the Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS)/odometer is an important technical means to solve the problem of navigation and positioning in complex environments. The measurement noise of the GNSS/INS/odometer integrated navigation system is complex and non-stationary; it approximates a Gaussian distribution in an open-sky environment, and it has heavy-tailed properties in the GNSS challenging environment. This work models the measurement noise and one-step prediction as the Gaussian and Student's t mixture distribution to adjust to different scenarios. The mixture distribution is formulated as the hierarchical Gaussian form by introducing Bernoulli random variables, and the corresponding hierarchical Gaussian state-space model is constructed. Then, the mixing probability of Gaussian and Student's t distributions could adjust adaptively according to the real-time kinematic solution state. Based on the novel distribution, a robust variational Bayesian Kalman filter is proposed. Finally, two vehicle test cases conducted in GNSS-friendly and challenging environments demonstrate that the proposed robust Kalman filter with the Gaussian–Student's t mixture distribution can better model heavy-tailed non-Gaussian noise. In challenging environments, the proposed algorithm has position root mean square (RMS) errors of 0.80 m, 0.62 m, and 0.65 m in the north, east, and down directions, respectively. With the assistance of inertial sensors, the positioning gap caused by GNSS outages has been compensated. During seven periods of 60 s simulated GNSS data outages, the RMS position errors in the north, east, and down directions were 0.75 m, 0.30 m, and 0.20 m, respectively. [ABSTRACT FROM AUTHOR]

Abstract A dynamic nonline-of-sight (NLOS) angle discrimination method is proposed to address the insufficiency of current research on the NLOS error characteristics of ultrawideband (UWB) signals in dynamic environments as well as the problem that UWB signals frequently suffer from occlusion, leading to poor or impossible localization. The experimental results indicate that the degree of UWB signal occlusion increases as the horizontal angle decreases, and when the horizontal angle is less than 167°, the UWB ranging error is so large that no ranging value is available. On this basis, a tightly integrated UWB/MEMS IMU positioning algorithm incorporating NLOS angle discrimination and map constraints is proposed; it employs horizontal angles to discriminate UWB ranging values in NLOS environments in accordance with the dynamic NLOS characteristics of UWB signals to assign better weights to UWB observations. Through comparative analysis of the results from both groups of experiments, the algorithm achieved northward, eastward, and planar positioning errors of 0.189 m and 0.126 m, 0.119 m and 0.134 m, 0.243 m and 0.211 m, respectively. Compared to the Robust Adaptive Kalman Filtering algorithm, the positional accuracy in the plane improved by 22.9% and 28.5%, respectively.

A dynamic nonline-of-sight (NLOS) angle discrimination method is proposed to address the insufficiency of current research on the NLOS error characteristics of ultrawideband (UWB) signals in dynamic environments as well as the problem that UWB signals frequently suffer from occlusion, leading to poor or impossible localization. The experimental results indicate that the degree of UWB signal occlusion increases as the horizontal angle decreases, and when the horizontal angle is less than 167°, the UWB ranging error is so large that no ranging value is available. On this basis, a tightly integrated UWB/MEMS IMU positioning algorithm incorporating NLOS angle discrimination and map constraints is proposed; it employs horizontal angles to discriminate UWB ranging values in NLOS environments in accordance with the dynamic NLOS characteristics of UWB signals to assign better weights to UWB observations. Through comparative analysis of the results from both groups of experiments, the algorithm achieved northward, eastward, and planar positioning errors of 0.189 m and 0.126 m, 0.119 m and 0.134 m, 0.243 m and 0.211 m, respectively. Compared to the Robust Adaptive Kalman Filtering algorithm, the positional accuracy in the plane improved by 22.9% and 28.5%, respectively. [ABSTRACT FROM AUTHOR]

Attitude determination based on a micro-electro-mechanical system inertial measurement unit (MEMS-IMU) has attracted extensive attention. The non-gravitational components of the MEMS-IMU have a significant effect on the accuracy of attitude estimation. To improve the attitude estimation of low-dynamic vehicles under uneven soil conditions or vibrations, a robust Kalman filter (RKF) was developed and tested in this paper, where the noise covariance was adaptively changed to compensate for the external acceleration of the vehicle. The state model for MEMS-IMU attitude estimation was initially constructed using a simplified direction cosine matrix. Subsequently, the variance of unmodeled external acceleration was estimated online based on filtering innovations of different window lengths, where the acceleration disturbance was addressed by tradeoffs in time-delay and prescribed computation cost. The effectiveness of the RKF was validated through experiments using a three-axis turntable, an automatic vehicle, and a tractor tillage test. The turntable experiment demonstrated that the angle result of the RKF was 0.051° in terms of root mean square error (RMSE), showing improvements of 65.5% and 29.2% over a conventional KF and MTi-300, respectively. The dynamic attitude estimation of the automatic vehicle showed that the RKF achieves smoother pitch angles than the KF when the vehicle passes over speed bumps at different speeds; the RMSE of pitch was reduced from 0.875° to 0.460° and presented a similar attitude trend to the MTi-300. The tractor tillage test indicated that the RMSE of plough pitch was improved from 0.493° with the KF to 0.259° with the RKF, an enhancement of approximately 47.5%, illustrating the superiority of the RKF in suppressing the external acceleration disturbances of IMU-based attitude estimation. [ABSTRACT FROM AUTHOR]

In recent years, there has been increasing attention to positioning, navigation, and timing applications with smartphones. Because of frequently disrupted carrier phase observations, code observations remain critical for smartphone-based positioning. Considering a realistic stochastic model is mandatory to obtain the utmost positioning performance, this study proposes a sound stochastic approach for code observations from Android smartphones. The proposed approach includes a modified version of the SIGMA-ɛ variance model with different coefficients for each GNSS constellation and a robust Kalman filter method. First the noise characteristics of observations from the Xiaomi Mi 8 smartphone are analyzed utilizing code-minus-phase combinations to estimate the coefficients for each GNSS constellation. This includes the determination of a variance model as well as a check of the probability distribution. Finally, the proposed approach is validated in the positioning domain using single-frequency code observation-based real-time standalone positioning. The results show that more than 95% of observations follow the normal distribution when the proposed approach is applied. Compared with the conventional stochastic approach, including a C/N0-dependent model and standard Kalman filter, it improves the positioning accuracy by 45.8% in a static experiment, while its improvement is equal to 26.6% in a kinematic experiment. For the static and kinematic experiments, in 50% of the epochs, the 3D positioning errors are smaller than 3.0 m and 3.4 m for the proposed stochastic approach. The results exhibit that the stochastic properties of code observations from smartphones can be successfully represented by the proposed approach. [ABSTRACT FROM AUTHOR]

This article proposes two robust Kalman filters to solve the issue of inaccurate modeling in multiplicative noise systems due to epistemic limitations. First, we construct all conceivable state/measurement transition probability densities as an ambiguity set. This ambiguity set chooses the Wasserstein distance or the moment‐based metric as the distance metric. Besides, this set is an inequality set with a chosen tolerance, which can be seen as a non‐negative radius ball. Then, by combining the robust solution of the least favorable model in that ball with the alternating direction method of multipliers or an efficient direct solution method, we propose two robust Kalman filters based on the minimum mean square error criterion. A classical example is provided to verify the effectiveness of the proposed robust filters in comparison to existing state‐of‐the‐art filters. [ABSTRACT FROM AUTHOR]

The centimeter-level positioning accuracy of real-time kinematic (RTK) depends on correctly resolving integer carrier-phase ambiguities. To improve the success rate of ambiguity resolution and obtain reliable positioning results, an enhanced Kalman filtering procedure has been developed. Based on a posteriori residuals of measurements and state predictions, the measurement noise variance–covariance matrix for double-differenced measurements is adaptively estimated, rather than approximated by an empirical function which uses satellite elevation angle as input. Since, in real-world situations, unexpected outliers and carrier-phase outages can degrade the filter performance, a stochastic model based on robust Kalman filtering is proposed, for which the double-differenced measurement noise variance–covariance matrix is computed empirically with a modified version of the IGG (Institute of Geodesy and Geophysics) III method in order to detect and identify outliers. The performance of the proposed method is assessed by two tests, one with simulated data and one with real data. In addition, the performance of F-ratio and W-ratio tests as proxies for the success of ambiguity fixing is investigated. Experimental results reveal that the proposed method can improve the reliability and robustness of relative kinematic positioning for simulation scenarios as well as in a real urban test. [ABSTRACT FROM AUTHOR]

In addition to traditional tide gauges, the ground-based global navigation satellite system reflectometry (GNSS-R) that utilizes signal-to-noise ratio data from a single GNSS receiver has become another promising alternative for sea level monitoring. However, its application is limited by retrieval precision, especially in large tidal variation environments. On the other hand, previous studies have focused on performance improvement by using post-processing strategies, which cannot support practical (near-) real-time applications. In this work, we present a method using a robust Kalman filter to provide near real-time sea level measurements based on cloud service, achieving both high precision and high temporal resolution. A coastal GNSS station BRST with large tidal variations was selected for experimental validation. First, 30 days of archived GNSS observations were used for performance assessment. It is observed that high-precision sea level retrievals with a 5-min sampling interval can be obtained, which reaches a root-mean-square error of 5.87 cm and a correlation of 99.93% compared to the tide gauge records. Then, based on the Alibaba cloud service, we implemented a near real-time sea level monitoring system by using the real-time GNSS observations streamed by the International GNSS Service real-time service. It is shown that no detectable bias is found compared with the retrievals obtained in post-processing mode, which indicates that we can remotely sense sea level variations in near real-time and further promotes ground-based GNSS-R in practical sea level monitoring applications. [ABSTRACT FROM AUTHOR]

Owing to the developments of satellite-based and network-based real-time satellite precise products, the Precise Point Positioning (PPP) technique has been applied far and wide, especially since the PPP-B2b service was provided by the third-generation BeiDou Navigation Satellite System (BDS-3). However, satellite outages during dynamic application lead to significant degradation of the accuracy and continuity of PPP. A generally used method is integrating PPP with Inertial Measurement Units (IMUs) to enhance positioning performance. Previous works on this topic are usually based on IMU data at a high sampling rate and are mostly implemented in post-processing mode. This paper will carry out a compressive assessment of the impacts of different types of precise satellite products (real-time products from the CAS, DLR, GFZ, WHU, and the final one from GFZ), Doppler observations, and different sampling rates of IMU data on the performance of the tightly coupled integration of the BDS-3 B1I/B2b and the Inertial Navigation System (INS). Results based on a group of on-board experimental data illustrate that (1) the positioning accuracy with products supplied by the CAS and WHU are roughly consistent with those using the final products; (2) the Doppler observations can effectively improve the accuracies of velocity, attitude, and vertical position at the initial epochs and during the reconvergence periods, but have invisible influences on the overall positioning, velocity, and attitude determination; and (3) the impact of IMU data interval on the performance of PPP/INS tightly coupled integration is insignificant when there are enough available satellites. However, the divergent speed of position is visibly affected by the IMU sampling rate during satellite outage periods. [ABSTRACT FROM AUTHOR]

The proper stochastic model of a global navigation satellite system (GNSS) makes a significant difference on the precise point positioning (PPP)/inertial navigation system (INS) tightly coupled solutions. The empirical Gaussian stochastic model is easily biased by massive gross errors, deteriorating the positioning precisions, especially in the severe GNSS blockage urban environment. In this paper, the distributional characteristics of the gross-error-contaminated observation noise are analyzed by the epoch-differenced (ED) geometry-free (GF) model. The Student's t distribution is used to express the heavy tails of the gross-error-contaminated observation noise. Consequently, a novel sequential Student's t-based robust Kalman filter (SSTRKF) is put forward to adjust the GNSS stochastic model in the urban environment. The proposed method pre-weights all the observations with the a priori residual-derived robust factors. The chi-square test is adopted to distinguish the unreasonable variances. The proposed sequential Student's t-based Kalman filter is conducted for the PPP/INS solutions instead of the standard Kalman filter (KF) when the null hypothesis of the chi-square test is rejected. The results of the road experiments with urban environment simulations reveal that the SSTRKF improves the horizontal and vertical positioning precisions by 57.5% and 62.0% on average compared with the robust Kalman filter (RKF). [ABSTRACT FROM AUTHOR]

Autonomous underwater vehicles (AUVs) play an increasingly essential role in the field of polar ocean exploration, and the Doppler velocity log (DVL)-aided strapdown inertial navigation system (SINS) is widely used for it. Due to the rapid convergence of the meridians, traditional inertial navigation mechanisms fail in the polar region. To tackle this problem, a transverse inertial navigation mechanism based on the earth ellipsoidal model is designed in this paper. Influenced by the harsh environment of the polar regions, unknown and time-varying outlier noise appears in the output of DVL, which makes the performance of the standard Kalman filter degrade. To address this issue, a robust Kalman filter algorithm based on Mahalanobis distance is used to adaptively estimate measurement noise covariance; thus, the Kalman filter gain can be modified to weight the measurement. A trial ship experiment and semi-physical simulation experiment were carried out to verify the effectiveness of the proposed algorithm. The results demonstrate that the proposed algorithm can effectively resist the influence of DVL outliers and improve positioning accuracy. [ABSTRACT FROM AUTHOR]

The tracking of satellite signals with the passive linearly polarized embedded global navigation satellite system (GNSS) antenna of smartphones in dynamic scenarios is susceptible to the changing multipath and obstructions in urban environments, which lead to a significant decrease in the availability and reliability of GNSS solutions. Accordingly, based on the characteristics of smartphone GNSS and inertial measurement unit (IMU) sensors data in GNSS-degraded environments, we established an IMU-aided uncombined precise point positioning (PPP) mathematical model that is suitable for smartphones. To enhance the reliability of initial alignment in dynamic mode, the step function variances depending on carrier-to-noise density ratio were established with the variances of GNSS measurements, and the inertial navigation system (INS) parameters were initialized while both the velocity of smartphones and the position dilution of precision (PDOP) reached corresponding thresholds. Considering the measurement noise and observations gaps of smartphones, the robust Kalman filter (RKF) with equivalent variance matrix was used for parameter estimation to improve the convergence efficiency of the coupled PPP/INS model. Experimental results indicated that the proposed PPP/INS method can effectively improve the positioning performance of smartphones in GNSS-degraded environments. Compared with the conventional smartphone PPP scheme, the PPP/INS horizontal errors in the eastern and western areas of the long trajectory experiment decreased by 49.37% and 48.29%, respectively. Meanwhile, the trajectory deviation of smartphones can remain stable in the tunnel where GNSS signals are blocked. [ABSTRACT FROM AUTHOR]

This paper addresses the robust Kalman filtering problem for multisensor time-varying systems with uncertainties of noise variances. Using the minimax robust estimation principle, based on the worst-case conservative system with the conservative upper bounds of noise variances, the robust local time-varying Kalman filters are presented. Further, the batch covariance intersection (BCI) fusion and a fast sequential covariance intersection (SCI) fusion robust time-varying Kalman filters are presented. They have the robustness that the actual filtering error variances or their traces are guaranteed to have a minimal upper bound for all admissible uncertainties of noise variances. Their robustness is proved based on the proposed Lyapunov equations approach. The concepts of the robust and actual accuracies are presented, and the robust accuracy relations are proved. It is also proved that the robust accuracies of the BCI and SCI fusers are higher than that of each local Kalman filter, the robust accuracy of the BCI fuser is higher than that of the SCI fuser, and the actual accuracies of each robust Kalman filter are higher than its robust accuracy for all admissible uncertainties of noise variances. The corresponding steady-state robust local and fused Kalman filters are also presented for multisensor time-invariant systems, and the convergence in a realization between the local and fused time-varying and steady-state Kalman filters is proved by the dynamic error system analysis (DESA) method and dynamic variance error system analysis (DVESA) method. A simulation example is given to verify the robustness and the correctness of the robust accuracy relations. [ABSTRACT FROM AUTHOR]

This paper presents an M-estimation-based Improved Interacting Multiple Model (IIMM) algorithm for inertial navigation system (INS)/Doppler velocity logs (D VL) integrated method to directly apply in complex underwater environment without empirical parameters. Considering the time-varying measurement noise covariance, a variable model structure based on Bayesian estimation law is proposed to adapt to the environment and an adaptive state transition probability matrix is generated to promote the model adaption. Meanwhile, M-estimation-based filter is employed as primary model to save IIMM from the effect of outliers. The performance of the IIMM algorithm is evaluated on simulation, land vehicle, and Yangtze River test, where the state-of-the-art is compared adequately. The robustness simulation test is also performed. It is highlighted that IIMM approach can adapt to actual model rapidly and can resist outliers efficiently. The proposed IIMM method can improve the accuracy and robustness of the navigation system in a severe and unknown environment without increasing the computational load. [ABSTRACT FROM AUTHOR]

In order to meet the requirements of high-precision vehicle positioning in complex scenes, an observation noise adaptive robust GNSS/MIMU tight fusion model based on the gain matrix is proposed considering static zero speed, non-integrity, attitude, and odometer constraint models. In this model, the robust equivalent gain matrix is constructed by the IGG-Ⅲ method to weaken the influence of gross error, and the on-line adaptive update of observation noise matrix is carried out according to the change of actual observation environment, so as to improve the solution performance of filtering system and realize high-precision position, attitude and velocity measurement when GNSS signal is unlocked. A real test on a road over 600km demonstrates that, in about 100km shaded environment, the fixed rate of GNSS ambiguity resolution in the shaded road is 10% higher than that of GNSS only ambiguity resolution. For all the test, the positioning accuracy can reach the centimeter level in an open environment, better than 0.6m in the tree shaded environment, better than 1.5m in the three-dimensional traffic environment, and can still maintain a positioning accuracy of 0.1m within 10s when the satellite is unlocked in the tunnel scene. The proposal and verification of the algorithm model show that low-cost MIMU equipment can still achieve high-precision positioning when there are scene feature constraints, which can meet the problem of high-precision vehicle navigation and location in the urban complex environment.

Nowadays, Autonomous Underwater Vehicles (AUV) are used in environmental studies, ocean floor mapping, and measuring water properties. Navigation of these vehicles is one of the most challenging issues due to the unavailability of global positioning system (GPS) signal underwater. Inertial navigation is a method commonly used for underwater navigation. If a low-cost Inertial Measurement Unit (IMU) is used, navigation quality will decline rapidly due to sensor inherent error. Although using a Doppler Velocity Log (DVL) speedometer sensor helps limit this error to some extent, it does not yield acceptable accuracy in low-cost IMUs. Filtering the gyro based on the AUV rotational dynamics model can improve the quality of angular velocity measurements and increase the Inertial Navigation System (INS)-DVL navigation accuracy. The presence of uncertainty in the rotational model parameters reduces the navigation algorithm’s performance. In this paper, at first, a simplified rotational model of AUV is presented, and its parameters are identified utilizing data acquired in real experiments. Then a robust Kalman filter for gyro output is proposed to enhance the navigation algorithm performance in the presence of model parameter uncertainty. To evaluate the performance of the proposed method, non-robust and robust filtered gyro outputs are used in the INS-DVL algorithm, and the results are compared with each other. Two types of the robust Kalman filter, stationary and finite horizon, are invoked. According to the field tests, navigation error decreases by 50% using the stationary robust Kalman filter compared to the non-robust Kalman filter. [ABSTRACT FROM AUTHOR]

In this brief, the state estimation problems of systems with unknown non-stationary heavy-tailed noises are investigated. First, we present a new switching Gaussian-heavy-tailed (SGHT) distribution, which can model the noises by adaptive learning of the switching probability between the Gaussian distribution and the newly designed heavy-tailed distribution. Then, the SGHT distribution is expressed as a hierarchical Gaussian presentation by utilizing two auxiliary variables satisfying the categorical distribution and the Bernoulli distribution respectively. After-wards, a new SGHT distribution based robust Kalman filter (SGHT-RKF) is derived by applying the variational Bayesian (VB) inference. Finally, the simulations are performed to illustrate the superior performance of the developed filter as compared with existing filters. [ABSTRACT FROM AUTHOR]

Battery energy systems are playing significant roles in smart homes, e.g., absorbing the uncertainty of solar energy from root-top photovoltaic, supplying energy during a power outage, and responding to dynamic electricity prices. For the safe and economic operation of batteries, an optimal battery-management system (BMS) is required. One of the most important features of a BMS is state-of-charge (SoC) estimation. This article presents a robust central-difference Kalman filter (CDKF) method for the SoC estimation of on-site lithium-ion batteries in smart homes. The state-space equations of the battery are derived based on the equivalent circuit model. The battery model includes two RC subnetworks to represent the fast and slow transient responses of the terminal voltage. Moreover, the model includes the nonlinear relationship between the open-circuit voltage (OCV) and SoC. The proposed robust CDKF method can accurately estimate the SoC in the presence of the time-varying model uncertainties and measurement noises. Being able to cope with model uncertainties and measurement noises is essential, since they can lead to inaccurate SoC estimations. An experiment test bench is developed, and various experiments are conducted to extract the battery model parameters. The experimental results show that the proposed method can more accurately estimate SoC compared with other Kalman filter-based methods. The proposed method can be used in optimal BMSs to promote battery performance and decrease battery operational costs in smart homes. [ABSTRACT FROM AUTHOR]

Spoofing attacks have become an increasing threat to global navigation satellite system receivers. Existing anti-spoofing algorithms concentrate on the detection of these attacks; however, they are unable to prevent the counterfeit signal, which causes false position and timing results. Some defense techniques require the assistance of other sensors or measurement devices located at different positions. These impose many restrictions on the practical applications of anti-spoofing algorithms. In this study, the multicorrelator estimator, designed initially to prevent multipath signals, is applied to detect and mitigate spoofing. A statistic is proposed for spoofing detection based on the code phase difference between counterfeit and authentic signals. This statistic can significantly reduce the rate of false and missed alarms. Assuming there is no spoofing at the beginning, the pseudorange difference between epochs is derived for spoofing validation, allowing spoofing suppression in a single receiver. Based on this study, an estimation-validation-mitigation structure is presented. A robust extended Kalman filter is proposed to reduce gross errors in the multicorrelator measurements and improve estimation accuracy. Public-spoofing datasets recorded in real environments were used to verify the performance of different parameters. A total of 81 complex correlators were introduced in the experiments. Results show that using the proposed scheme, the position or time offsets caused by spoofing drop from 600 m to approximately 20 m, and the spoofing is mitigated considerably. The proposed method provides an effective anti-spoofing structure that requires only a single antenna and does not require additional sensors. [ABSTRACT FROM AUTHOR]

Abstract Inertial navigation is an edge computing-based method for determining the position and orientation of a moving vehicle that operates according to Newton’s laws of motion on which all the computations are performed at the edge level without need to other far resources. One of the most crucial struggles in Global Positioning System (GPS) and Inertial Navigation System (INS) fusion algorithms is that the accuracy of the algorithm is reduced during GPS interruptions. In this paper, a low-cost method for GPS/INS fusion and error compensation of the GPS/INS fusion algorithm during GPS interruption is proposed. To further enhance the reliability and performance of the GPS/INS fusion algorithm, a Robust Kalman Filter (RKF) is used to compensate the influence of gross error from INS observations. When GPS data is interrupted, Kalman filter observations will not be updated, and the accuracy of the position will continuously decrease over time. To bridge GPS data interruption, an artificial neural network-based fusion method is proposed to provide missing position information. A well-trained neural network is used to predict and compensate the interrupted position signal error. Finally, to evaluate the effectiveness of the proposed method, an outdoor test using a custom-designed hardware, GPS, and INS sensors is employed. The results indicate that the accuracy of the positioning has improved by 67% in each axis during an interruption. The proposed algorithm can enhance the accuracy of the GPS/INS integrated system in the required navigation performance.

UWB indoor positioning is a research hotspot, but there are few literatures systematically describing different positioning algorithms for different scenes. Therefore, several positioning algorithms are proposed for different indoor scenes. Firstly, for the sensing positioning scenes, a sensing positioning algorithm is proposed. Secondly, for the straight and narrow scenes, a two anchors robust positioning algorithm based on high pass filter is proposed. Experimental results show that this algorithm has better positioning accuracy and robustness than the traditional algorithm. Then, for ordinary indoor scenes, a robust indoor positioning model is proposed based on robust Kalman filter and total LS, which considers the coordinate error of UWB anchors. The positioning accuracy is 0.093m, which is about 29.54% higher than that of the traditional LS algorithm. Finally, for indoor scenes with map information, a map aided indoor positioning algorithm is proposed based on two UWB anchors. This algorithm can effectively improve the reliability and reduce the cost of UWB indoor positioning system, which average positioning accuracy is 0.238m. The biggest innovation of this paper lies in the systematic description of multi-scene positioning algorithm and the realisation of indoor positioning based on double anchors. [ABSTRACT FROM AUTHOR]

This paper addresses the robust Kalman filtering problem for multisensor time-varying systems with uncertainties of noise variances. Using the minimax robust estimation principle, based on the worst-case conservative system with the conservative upper bounds of noise variances, the robust local time-varying Kalman filters are presented. Further, the batch covariance intersection (BCI) fusion and a fast sequential covariance intersection (SCI) fusion robust time-varying Kalman filters are presented. They have the robustness that the actual filtering error variances or their traces are guaranteed to have a minimal upper bound for all admissible uncertainties of noise variances. Their robustness is proved based on the proposed Lyapunov equations approach. The concepts of the robust and actual accuracies are presented, and the robust accuracy relations are proved. It is also proved that the robust accuracies of the BCI and SCI fusers are higher than that of each local Kalman filter, the robust accuracy of the BCI fuser is higher than that of the SCI fuser, and the actual accuracies of each robust Kalman filter are higher than its robust accuracy for all admissible uncertainties of noise variances. The corresponding steady-state robust local and fused Kalman filters are also presented for multisensor time-invariant systems, and the convergence in a realization between the local and fused time-varying and steady-state Kalman filters is proved by the dynamic error system analysis (DESA) method and dynamic variance error system analysis (DVESA) method. A simulation example is given to verify the robustness and the correctness of the robust accuracy relations.

In practical applications, due to the complexity of the system, the process equation of the state space model is difficult to match the actual state transition model. In addition, the unreliability of the sensor will cause the measurement to be accompanied by outliers. In this paper, a novel robust Kalman filter with fading factor is proposed to improve the accuracy of state estimation for the linear system under state transition model mismatch and outliers interference. Firstly, in order to modify the state transition model, this filter introduces a fading factor which is modelled as the inverse gamma distribution to update the state prediction covariance. Then, aiming at the phenomenon that the measurement noise does not follow the Gaussian distribution and has nonzero mean characteristics due to outliers interference, the measurement noise is modelled as the generalized hyperbolic skew Student's t distribution. Finally, the state estimation is realized by using the variational Bayesian. The simulation results show that the estimation accuracy of the proposed filter is higher than that of the Kalman filter and the strong tracking filter. [ABSTRACT FROM AUTHOR]

In this paper, a fast-initial alignment method with angular rate aiding based on robust Kalman filter is proposed. First, the traditional system model of the initial alignment is derived, and the angular rate aiding method in the navigation frame is studied. To address the defects of the traditional angular rate aiding alignment method, the angular rate aiding method in body frame is derived. Then, a state augmentation method is employed to address the correlation between process noise and the measurement noise, which exists in the angular rate aiding methods. Considering the practical application, it is hard to keep completely still when the initial alignment is carried out on the vehicle. Therefore, a Huber's M-estimation has been adopted to eliminate the external interferences, and the robustness of the proposed method has been improved. Then, an analytical method for the observability of the proposed method is studied. The reason why the proposed method is faster than the traditional method is analyzed in detail. Finally, simulated and field tests are designed to validate the performance of the proposed method. The results show that the proposed method can finish the initial alignment when it is carried on the vehicle.

Based on the dual vector quaternions, this paper modeled both the kinematics and dynamics of the disabled satellites. In addition, considering the complex space environment may lead to the measurements failure of the target, a novel robust federal Kalman filter based algorithm (DVQ-REKF) is proposed by this paper. By utilizing the designed algorithm, both the pose and inertial parameters can be estimated in the same time when the measurements by each of the monocular camera on the service satellite failed for a certain period of time. Finally, the simulation shows the validity of the designed DVQ-REKF.

The tightly coupled global navigation satellite system (GNSS) precise point positioning (PPP) and inertial navigation system (INS) can provide high-precision position, velocity and attitude information. The coupled system utilizes single receiver, which is particularly suitable for the environment without reference station, such as marine survey. In the former works, the integer ambiguity resolution of PPP/INS in terrestrial environment is researched. However, the GNSS observation is severely affected by the multipath effect in marine environment. In addition, the sideslip caused by wind and sea wave also impact float ambiguity estimation, consequently introducing difficulty for PPP ambiguity fixing. Therefore, the PPP/INS tightly coupled model with fixed ambiguity is proposed for marine survey. The correction model of INS gyroscope bias in closed-loop is deduced in detail. The influence of ship motion noise and multipath in marine environment is reduced by introducing the robust factor to the Kalman filter. The feasibility of the method is verified in a real marine experiment, with a detail evaluation of the data quality and positioning accuracy. The results show that the accuracy of PPP/INS can reach centimeter level after fixing the ambiguity in marine environment. Furthermore, the precise INS-predicted position can significantly shorten the re-fixed time of PPP/INS, which proves the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

A new robust quaternion Kalman filter is developed for accurate alignment of stationary strapdown inertial navigation system. Most fine alignment algorithms have tried to estimate the biases of gyroscopes and accelerometers to reduce the errors of the alignment process. In stationary platforms, due to fixed inputs for sensors, the summation of various errors such as fixed bias, misalignment, scale factor, and nonlinear errors acts like one bias error, and then the identification of each error will be impossible. The observability of gyros and accelerometers' biases has also been studied. But, nowadays, we know that all of these unknown parameters are not observable. Then this problem can increase the complication of the alignment algorithm. The accelerometers' errors mainly affect the errors of the roll and pitch angles, but a big portion of the heading's error results from the gyroscopes' errors. Modeling of all errors as additional states without considering the observability parameters has no benefits, but will increase the filter's dimension, so the filter's performance will decrease. In this study, due to the observability problem, a new robust multiplicative quaternion Kalman filter is designed for the alignment of a stationary platform. The presented algorithm does not estimate the sensors' errors, but it is robust to uncertainty in the sensors' errors. In the proposed scheme, the bounds of parameters' errors are introduced to filter, and the filter tries to remain robust with respect to these uncertainties. The method uses the benefits of quaternions in attitude modeling, and then the robust filter is adapted to work with quaternions. The ability of the new algorithm is evaluated with MATLAB simulations. The outcomes show that the presented algorithm is more accurate than other traditional methods. The extended Kalman filter with accelerometers' outputs and the horizontal velocities as the measurement equations and additive quaternion Kalman filter are used for comparisons. [ABSTRACT FROM AUTHOR]

Inertial navigation is an edge computing-based method for determining the position and orientation of a moving vehicle that operates according to Newton's laws of motion on which all the computations are performed at the edge level without need to other far resources. One of the most crucial struggles in Global Positioning System (GPS) and Inertial Navigation System (INS) fusion algorithms is that the accuracy of the algorithm is reduced during GPS interruptions. In this paper, a low-cost method for GPS/INS fusion and error compensation of the GPS/INS fusion algorithm during GPS interruption is proposed. To further enhance the reliability and performance of the GPS/INS fusion algorithm, a Robust Kalman Filter (RKF) is used to compensate the influence of gross error from INS observations. When GPS data is interrupted, Kalman filter observations will not be updated, and the accuracy of the position will continuously decrease over time. To bridge GPS data interruption, an artificial neural network-based fusion method is proposed to provide missing position information. A well-trained neural network is used to predict and compensate the interrupted position signal error. Finally, to evaluate the effectiveness of the proposed method, an outdoor test using a custom-designed hardware, GPS, and INS sensors is employed. The results indicate that the accuracy of the positioning has improved by 67% in each axis during an interruption. The proposed algorithm can enhance the accuracy of the GPS/INS integrated system in the required navigation performance. [ABSTRACT FROM AUTHOR]

Misalignment angle will result in a considerable error for the integration of Doppler velocity log (DVL) and of Strapdown Inertial Navigation System (SINS). In this article, a robust initial alignment method for SINS/DVL is proposed to solve a practical applicable issue, which is that the outputs of DVL are often corrupted by the outliers. First, the alignment principle for SINS/DVL is summarized. Second, based on the principle of this alignment method, the apparent velocity model is investigated, and the parameters expression of the apparent velocity model are derived detailed. Using the apparent velocity model, the unknown parameters of the apparent velocity model are estimated by the developed robust Kalman filter, then the reconstructed observation vector, where the outliers are detected and isolated, is reconstructed by the estimated parameters. Based on the reconstructed observation vectors, the initial attitude is determined. Finally, the simulation and field tests are carried out to verify the performance of the proposed method. The test results are shown that the proposed method can detect and isolate the outliers effectively and get better performance than the previous work. [ABSTRACT FROM AUTHOR]

In this paper, a fast robust in-motion alignment method is proposed for the strapdown inertial navigation system (SINS) with DVL aided. The proposed method is divided into two procedures, which are coarse alignment procedure and fine alignment procedure. In the coarse alignment procedure, an apparent velocity modeling method is investigated. Building upon this model, a robust Kalman filter (RKF) is designed for parameter estimation, then an optimal observation vector, in which the outliers of the Doppler Velocity Log (DVL) outputs are eliminated, is reconstructed. As compared with the existing method, in the proposed method, the robustness of coarse alignment procedure is enhanced. To improve the accuracy of the coarse alignment method, a fine alignment method is designed. Different from the traditional fine alignment method, the error model of the proposed fine alignment method is constructed in n0-frame. With this advantage, the time-varying error attitude estimation for the traditional method has transformed into a time-invariant error attitude estimation. Thus, the raw data and intermediate data, which are collected in the coarse alignment procedure, can be reused in the fine alignment procedure. Take advantage of the high performance of the navigational computer, the forward-forward data processing can be carried on repeatedly, the one cycle of the forward-forward procedure consumes about 0.3 s in the real-time system. Simulation and field tests showed that the proposed method can obtain a high-accuracy initial alignment results and suppress the interference of the outliers of the DVL outputs. [ABSTRACT FROM AUTHOR]

This article aims to attempt to increase the number of satellites that can be used for monitoring soil moisture to obtain more precise results using GNSS-IR (Global Navigation Satellite System-Interferometric Reflectometry) technology to estimate soil moisture. We introduce a soil moisture inversion model by using GPS SNR (Signal-to-Noise Ratio) data and propose a novel Robust Kalman Filter soil moisture inversion model based on that. We validate our models on a data set collected at Lamasquère, France. This paper also compares the precision of the Robust Kalman Filter model with the conventional linear regression method and robust regression model in three different scenarios: (1) single-band univariate regression, by using only one observable feature such as frequency, amplitude, or phase; (2) dual-band data fusion univariate regression; and (3) dual-band data fusion multivariate regression. First, the proposed models achieve higher accuracy than the conventional method for single-band univariate regression, especially by using the phase as the input feature. Second, dual-band univariate data fusion achieves higher accuracy than single-band and the result of the Robust Kalman Filter model correlates better to the in situ measurement. Third, multivariate variable fusion improves the accuracy for both models, but the Robust Kalman Filter model achieves better improvement. Overall, the Robust Kalman Filter model shows better results in all the scenarios.