Variational Bayesian Adaptive Kalman Filter Research Articles

Maximum Mixture Correntropy Criterion-Based Variational Bayesian Adaptive Kalman Filter for INS/UWB/GNSS-RTK Integrated Positioning

The safe operation of unmanned ground vehicles (UGVs) demands fundamental and essential requirements for continuous and reliable positioning performance. Traditional coupled navigation systems, combining the global navigation satellite system (GNSS) with an inertial navigation system (INS), provide continuous, drift-free position estimation. However, challenges like GNSS signal interference and blockage in complex scenarios can significantly degrade system performance. Moreover, ultra-wideband (UWB) technology, known for its high precision, is increasingly used as a complementary system to the GNSS. To tackle these challenges, this paper proposes a novel tightly coupled INS/UWB/GNSS-RTK integrated positioning system framework, leveraging a variational Bayesian adaptive Kalman filter based on the maximum mixture correntropy criterion. This framework is introduced to provide a high-precision and robust navigation solution. By incorporating the maximum mixture correntropy criterion, the system effectively mitigates interference from anomalous measurements. Simultaneously, variational Bayesian estimation is employed to adaptively adjust noise statistical characteristics, thereby enhancing the robustness and accuracy of the integrated system’s state estimation. Furthermore, sensor measurements are tightly integrated with the inertial measurement unit (IMU), facilitating precise positioning even in the presence of interference from multiple signal sources. A series of real-world and simulation experiments were carried out on a UGV to assess the proposed approach’s performance. Experimental results demonstrate that the approach provides superior accuracy and stability in integrated system state estimation, significantly mitigating position drift error caused by uncertainty-induced disturbances. In the presence of non-Gaussian noise disturbances introduced by anomalous measurements, the proposed approach effectively implements error control, demonstrating substantial advantages in positioning accuracy and robustness.

Self-Tuning Process Noise in Variational Bayesian Adaptive Kalman Filter for Target Tracking

Many practical systems, such as target tracking, navigation systems, autonomous vehicles, and other applications, are usually applied in dynamic conditions. Thus, the actual noise statistics characteristics of these systems are generally time varying and unknown, which will deteriorate the state estimation accuracy of the Kalman filter (KF) and even cause filter diverging. To address this issue, this paper proposes an adaptive process noise covariance (Qk)-based variational Bayesian adaptive Kalman filter (AQ-VBAKF) algorithm. Firstly, the adaptive factor is introduced to self-tune the process noise covariance; the adaptive factor is obtained based on the innovation sequences, which can adapt to the input measurement values. Then, the VB solution is applied to approximate the time variant and unknown measurement noise covariance. Therefore, this proposed algorithm can adjust the process noise covariance and the measurement noise covariance simultaneously based on the variable input signals, which can improve the self-adaptive ability of the state estimation filter in dynamic conditions. According to the dynamic target tracking test results, the proposed AQ-VBAKF outperforms several other existing filtering methods in estimation accuracy, robustness, and computational efficiency.

Maximum correntropy criterion variational Bayesian adaptive Kalman filter based on strong tracking with unknown noise covariances

The performance of the current state estimation will degrade in the existence of slow-varying noise statistics. To solve the aforementioned issues, an improved strong tracking maximum correntropy criterion variational-Bayesian adaptive Kalman filter is presented in this paper. First of all, the inverse-Wishart distribution, as the conjugate-prior, is adopted to model the unknown and time-varying measurement and process noise covariances, then the noise covariances and system state are estimated via the variational Bayesian method. Secondly, the multiple fading-factors are obtained and evaluated to modify the prediction error covariance matrix to address the problems associated with inaccurate error estimation. Finally, the maximum correntropy criterion is employed to correct the filtering gain, which improves the filtering performance of the proposed algorithm. Simulation results show that the proposed filter exhibits better accuracy and convergence performance compared to other existing algorithms.

A novel variational Bayesian adaptive Kalman filter with mismatched process noise covariance matrix

AbstractThis paper proposes a novel variational Bayesian (VB) adaptive Kalman filter with mismatched process noise covariance matrix (PNCM). Firstly, this paper explains the reason why the predicted error covariance matrix (PECM) is chosen for variational inference. Secondly, compared with the earlier VB adaptive Kalman filter (VB‐AKF‐Q), the proposed filter calculate the dynamic model of the PECM with its historical estimation information. Therefore, the proposed filter can overcome the influence of mismatched PNCM on the initial value setting of PECM in the VB‐AKF‐Q. Finally, we use the evidence lower bound for the proposed filter and give the convergence criterion on this basis. Some examples with a target tracking simulation are carried out to demonstrate the superiority of the proposed filter.

A Novel State Estimation Approach for Suspension System with Time-Varying and Unknown Noise Covariance

In this paper, a novel state estimation approach based on the variational Bayesian adaptive Kalman filter (VBAKF) and road classification is proposed for a suspension system with time-varying and unknown noise covariance. Using the VB approach, the time-varying noise covariance can be inferred from the inverse-Wishart distribution and then optimized state estimation by the finite sampling posterior probability distribution function (PDF) of noise covariance and backward Kalman smoothing. In addition, a new road classification algorithm based on multi-objective optimization and the linear classifier is proposed to identify the unknown noise covariance. Simulation results for a suspension model with time-varying and unknown noise covariance show that the proposed approach has a higher performance in state estimation accuracy than other filters.

Maintaining the long-term accuracy of water distribution models with data assimilation methods: A comparative study

The upgrading of water supply services is calling for more accurate and adaptive numerical models to give insight into actual water distribution systems (WDSs), which underlines the importance of carefully calibrating model parameters. Due to unavoidable uncertainties in the calibration process such as measurement errors, errors in model parameters assumed to be known, and local-optimum of calibration algorithms, calibrated parameters could still contain non-negligible latent errors, and the calibrated model may not able to maintain its long-term accuracy when operating conditions change. To solve this problem, there is growing interest in adopting data assimilation (DA) methods to utilize more comprehensive information in long-term measurements to reduce the impact of uncertainties and maintain the accuracy and stability of calibrated models. In this study, two traditional calibration methods and four DA methods were tested and compared in two WDSs with different structures, which aims to form a general understanding of the behavior and applicability of different methods. The calibration results show that DA methods perform better than traditional methods and are more robust to different types of uncertainties, which provide an effective way to maintain the long-term accuracy of WDS models to enable better management of WDSs. Ensemble-based DA methods such as Particle Filter (PF) and Inferential-Measurement Kalman Filter (IMKF) performed well in the real-life system. They avoid linear approximation and can better estimate the impact of uncertainties to assimilate accurate correction information of the parameters. Gradient-based DA methods such as Extended Kalman Filter (EKF) and Variational Bayesian Adaptive Kalman Filter (VBAKF) have lower computational demand, but they are found to be less robust when dealing with large system uncertainties and nonlinearities.

A Multi-Mode Switching Variational Bayesian Adaptive Kalman Filter Algorithm for the SINS/PNS/GMNS Navigation System of Pelagic Ships.

The ocean-going environment is complex and changeable with great uncertainty, which poses a huge challenge to the navigation ability of ships working in the pelagic ocean. In this paper, in an attempt to deal with the complex uncertain interference that the environment may bring to the strap-down inertial navigation system/polarization navigation system/geomagnetic navigation system (SINS/PNS/GMNS) integrated navigation system, the multi-mode switching variational Bayesian adaptive Kalman filter (MMS-VBAKF) algorithm is proposed. To be more specific, to identify the degrees of measurement interference more effectively, we design an interference evaluation and multi-mode switching mechanism using the original polarization information and geomagnetic information. Through this mechanism, the interference to the SINS/PNS/GMNS navigation system is divided into three cases. In case of slight interference (case SI), the variational Bayesian method is adopted directly to solve the problem that the statistical characteristics of measurement noise are unknown. By the fixed-point iteration mechanism, the statistical properties of the measurement noise and the system states can be estimated adaptively in real time. In case of interference-tolerance (case TI), the estimation of the statistical characteristics of measurement noise need to weigh the measurement information at the moment and a priori value information comprehensively. In case of excessive interference (case EI), the SINS/PNS/GMNS integrated navigation system will perform mode switching and filtering system reconstruction in advance. Then, the information fusion and navigation states estimation can be completed. Consequently, the reliability, robustness, and accuracy of the SINS/PNS/GMNS integrated navigation system can be guaranteed. Finally, the effectiveness of the algorithm is illustrated by the simulation experiments.

Multiple fading factors-based strong tracking variational Bayesian adaptive Kalman filter

If the system model or the statistical characteristics of noise are inaccurate, the past measurements will directly affect the accuracy of current state estimation or even lead to filtering divergence. To overcome above difficulties, a multiple fading factors-based strong tracking variational Bayesian adaptive Kalman filter is proposed. Firstly, the inverse Wishart distribution is adopted to model the measurement noise covariance matrix. Secondly, the remodified measurement noise covariance matrix and the innovation covariance matrix estimated by exponential weighting method are employed to construct the scalar fading factor. Next, the multiple fading factors are calculated to correct the predicted error covariance matrix. Finally, the local optimal estimations of measurement noise covariance matrix and state are obtained by variational Bayesian approach. The target tracking simulations verify that the proposed algorithm has better tracking ability for the predicted error covariance matrix and the measurement noise covariance matrix compared with the existing filters.

Robust Particle Filtering With Time-Varying Model Uncertainty and Inaccurate Noise Covariance Matrix

This article proposes a robust particle filtering (PF) approach for a generic class of nonlinear systems with both additive time-varying uncertainty (ATVU) in the state transition equation and inaccurate process noise covariance matrices. To avoid sampling efficiency degradation of the PF approach caused by ATVU, we employ the disturbance observer-based PF (DOBPF) approach where the effect of ATVU is compensated in the particle generation stage. Different from the existing DOBPF method where disturbance estimation is achieved via the Kalman filter, the disturbance observer adopted in this article is in the form of variational Bayesian adaptive Kalman filter (VBAKF) which deals with the inaccurate process noise covariance matrices in both the dynamic models of the state and the ATVU. Compared with conventional PF approaches, the proposed method, named VBAKF-PF, exhibits enhanced robustness against both the ATVU in the state transition equation and the uncertainties of process noise covariance matrices. The simulation results demonstrate the superiority of VBAKF-PF over both the VBAKF and DOBPF methods.

Variational Bayesian adaptive Kalman filter for asynchronous multirate multi-sensor integrated navigation system

This study considers an asynchronous multirate data integration problem in the linear state space model with unknown and time-varying statistical parameters of the measurement noises. To improve performance of the multirate adaptive Kalman filter algorithm, a multi-sensor adaptive Kalman filtering algorithm based on variational Bayesian approximations has been developed in an asynchronous multirate multi-sensor integrated navigation system. The proposed filtering algorithm estimates measurement noise variances of the sensors adaptively and also it is robust to anomalous measurements of sensors and however, multirate adaptive Kalman filter is required to use an appropriate algorithm for outlier rejection to achieve a reliable and optimal estimation of position, velocity, and orientation. A navigation system composed of a strapdown inertial navigation system along with Doppler velocity log, inclinometer and depth meter with different sampling rates is designed to evaluate performance of multirate error state Kalman filter (MESKF) and multirate adaptive error state Kalman filter (MAESKF) algorithms and the proposed algorithm. Results of two experimental tests show that the average relative root mean square error (RMSE) of the position estimated by the proposed filtering algorithm can be decreased approximately 57% and 36% when compared to that of MESKF and MAESKF algorithms, respectively.

Adaptive Metropolis algorithm using variational Bayesian adaptive Kalman filter

Markov chain Monte Carlo (MCMC) methods are powerful computational tools for analysis of complex statistical problems. However, their computational efficiency is highly dependent on the chosen proposal distribution, which is generally difficult to find. One way to solve this problem is to use adaptive MCMC algorithms which automatically tune the statistics of a proposal distribution during the MCMC run. A new adaptive MCMC algorithm, called the variational Bayesian adaptive Metropolis (VBAM) algorithm, is developed. The VBAM algorithm updates the proposal covariance matrix using the variational Bayesian adaptive Kalman filter (VB-AKF). A strong law of large numbers for the VBAM algorithm is proven. The empirical convergence results for three simulated examples and for two real data examples are also provided.