The accuracy and robustness of tightly coupled GNSS/SINS integrated navigation parameter estimation are hindered by outliers caused by GNSS measurements under multipath interference and non-line-of-sight (NLOS) conditions. To address the limitations of robust estimation and the mismatch of state posterior PDF approximation, a novel M-estimation-based robust iterated cubature kalman filter (ICKF) is developed to minimize the impact of GNSS outliers while improving the correction effect of high-quality LOS GNSS measurement in this paper. The nonlinear weighted least squares regression model and objective function are established for outlier mitigation, including a sigma-point iterative filtering framework and an M-estimation method of down-weighting GNSS measurements. Specifically, the maximum a posteriori (MAP) estimation idea is used to design the sigma-point iterated filtering framework, which makes the posteriori probability density function (PDF) constantly close to the high likelihood confidence interval to obtain excellent nonlinear approximation effects. Furthermore, to avoid the inherent non-convexity of the traditional M-estimation method, the relaxation compensation scheme based on the adaptive control factor is introduced into the robust loss function to accelerate the convergence of the penalty weight of GNSS outliers. The availability of the proposed method for GNSS outlier mitigation is proved by vehicle field tests under multipath interference and NLOS conditions. 

Robust M-Estimation-Based ICKF for GNSS Outlier Mitigation in GNSS/SINS Navigation Applications

This paper presents a novel online adaptive method for estimating the process and measurement noise covariance matrices in Kalman filters (KFs) to address the challenge of varying noise characteristics in practical applications. Specifically, the proposed method decomposes the noise covariance matrix into an element distribution matrix and a noise intensity and employs an improved Sage filter to estimate the element distribution matrix. Additionally, a calibration and correction method is introduced to accurately determine and adaptively correct the online bias of the noise intensity. The unbiasedness and convergence of the proposed method are mathematically proven under the condition that the system is detectable. Moreover, this method is applied to multiobject tracking (MOT) based on KFs and light detection and ranging (LiDAR), and it is evaluated on the KITTI dataset and the official KITTI server. The experimental results demonstrate that the proposed method achieves significantly improved MOT performance based on KFs and outperforms other LiDAR-based methods on the KITTI leaderboard. This method provides a new approach for enhancing the performance of KFs and assisting with MOT, and it has practical feasibility for real-world applications. 

A Novel Adaptive Noise Covariance Matrix Estimation and Filtering Method: Application to Multiobject Tracking

Integrating global navigation satellite systems (GNSSs) with inertial navigation systems (INSs) has been widely recognized as an ideal solution for autonomous vehicle navigation. However, GNSSs suffer from disturbances and signal blocking inevitably, making the performance of GNSS/INSs degraded in the occurrence of measurement outliers. It has been proven that the sigma points-based Kalman filter (KF) performs better than an extended KF in cases where large prior uncertainty is present in the state estimation of a GNSS/INS. By modifying the sigma points directly, the resampling-free sigma point update framework (SUF) propagates more information excepting Gaussian moments of prescribed accuracy, based on which the resampling-free cubature Kalman filter (RCKF) was developed in our previous work. In order to enhance the adaptivity and robustness of the RCKF, the resampling-free SUF depending on dynamic prediction residue should be improved by suppressing the time-varying measurement outlier. In this paper, a robust observability-constrained RCKF (ROCRCKF) is proposed based on adaptive measurement noise covariance estimation and outlier detection, where the occurrence of measurement outliers is modelled by the Bernoulli variable and estimated with the state simultaneously. Experiments based on car-mounted GNSS/INSs are performed to verify the effectiveness of the ROCRCKF, and result indicates that the proposed algorithm outperforms the RCKF in the presence of measurement outliers, where the heading error and average root mean square error of the position are reduced from 1.96° and 6.38 m to 0.27° and 5.95 m, respectively. The ROCRCKF is robust against the measurement outliers and time-varying model uncertainty, making it suitable for the real-time implementation of GNSS/INSs in GNSS-challenged environments.

Observability-Constrained Resampling-Free Cubature Kalman Filter for GNSS/INS with Measurement Outliers

Spectral regression (SR), a graph-based learning regression model, can be used to extract features from graphs to realize efficient dimensionality reduction. However, due to the SR method remains a regularized least squares problem and being defined in L2-norm space, the effect of artifacts in EEG signals cannot be efficiently resisted. In this work, to further improve the robustness of the graph-based regression models, we propose to utilize the prior distribution estimation in the Bayesian framework and develop a robust hierarchical Bayesian spectral regression framework (named HB-SR), which is designed with the hierarchical Bayesian ensemble strategies. In the proposed HB-SR, the impact of noises can be effectively reduced by the adaptive adjustment approach in model parameters with the data-driven manner. Specifically, in the current work, three different distributions have been elaborately designed to enhance the universality of the proposed HB-SR, i.e., Gaussian distribution, Laplace distribution, and Student-t distribution. To objectively evaluate the performance of the HB-SR framework, we conducted both simulation studies and emotion recognition experiments based on emotional EEG signals. Experimental results have consistently indicated that compared with other existing spectral regression methods, the proposed HB-SR can effectively suppress the influence of noises and achieve robust EEG emotion recognition. 

EEG based emotion recognition by hierarchical bayesian spectral regression framework

Distributionally Robust Kalman Filtering for INS/GPS Tightly Coupled Integration with Model Uncertainty and Measurement Outlier

A Gaussian-multivariate Laplacian mixture distribution based robust cubature Kalman filter

In inertial navigation system and global navigation satellite system (INS/GNSS) integration, the practical stochastic measurement noise may be non-stationary heavy-tailed distribution due to outlier measurements induced by multipath and/or non-line-of-sight receptions of the original GNSS signals. To address the problem, a new switching Gaussian-heavy-tailed (SGHT) distribution is presented, which models the measurement noise with the help of switching between the Gaussian and the an existing heavy-tailed distribution. Then, utilizing two auxiliary parameters satisfying categorical and Bernoulli distributions respectively, we construct the SGHT distribution as a hierarchical Gaussian presentation. Furthermore, applying variational Bayesian inference , a novel SGHT distribution based robust Gaussian approximate filter is derived. Meanwhile, to reduce the computational complexity of the filtering process, an improved fixed-point iteration method is designed. Finally, the simulation of integrated navigation for an aircraft illustrates effectiveness and superiority of the proposed filter as compared the existing robust filters. 

Switching Gaussian-heavy-tailed distribution based robust Gaussian approximate filter for INS/GNSS integration

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.

A Novel Robust Kalman Filter Based on Switching Gaussian-Heavy-Tailed Distribution

A novel switching Gaussian-heavy-tailed distribution based robust fixed-interval smoother

This letter investigates the robust state estimation of the nonlinear systems with outlier-contaminated measurements. Due to the advantage of mixture error entropy with two kernel bandwidths in handling non-Gaussian noise caused by the outliers, a novel minimum mixture error entropy (MMEE) criterion-based robust cubature Kalman filter is proposed, in which the cost function is constructed by MMEE criterion, and the nonlinear measurement model is linearized by the statistical linear regression method. By a benchmark target tracking scenario with non-Gaussian measurement noise and INS/GNSS loose combination vehicle tracking experiment, the effectiveness of the proposed filter is demonstrated.

Minimum Mixture Error Entropy-Based Robust Cubature Kalman Filter for Outlier-Contaminated Measurements

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