Unknown Noise Covariance Research Articles

A Robust and Efficient Cubature Kalman filter based on the Variation Bayesian Method and Its Application in Target Tracking

Abstract This paper proposes a robust cubature Kalman filter (CKF) for nonlinear state-space models with unknown state and measurement noise covariance matrix (MNCM). This paper studies situations in which sensors are independent of each other. Therefore, the unknown measurement noise variance is modeled as an unknown inverse-Gamma (IG) distribution. The Gaussian-Student-t-inverse-Wishart mixture distribution (GSTIW) is used to model the one-step prediction distribution. Modeling generates a large number of unknown parameters. Therefore, this article adopts the statistical linearization method to linearize the observation function and then estimates the state and parameters separately to reduce the computational burden of estimating unknown parameters, significantly improving the algorithm's efficiency. Finally, using the variational Bayesian (VB) method, a novel and efficient robust cubature Kalman filter based on the IG distribution and GSTIW mixture distributions (IG-GSTIW-CKF) is obtained. Simulation and experimental results show that the proposed method has better estimation accuracy than several advanced algorithms when sensors are independent. In addition, the efficiency of the proposed algorithm is significantly higher than that of other CKF-based methods.

Irregular extended target tracking with unknown measurement noise covariance

To address the challenge of tracking irregular extended target while adapting to unknown measurement noise, this paper presents a novel tracking algorithm for irregular extended target. Considering the flexibility of the Gaussian process (GP) model for representing shape, in the proposed algorithm, we utilize the GP model to delineate the radial function of the tracked extended target’s contour. Then, we incorporate the GP model into the variational Bayesian technique to formulate the posterior distribution for both the unknown measurement noise and the shape state of the tracked target. Subsequently, the square-root cubature Kalman filter is employed to tackle the nonlinearity filtering in the problem of irregular extended target tracking (ETT), enabling simultaneous estimation of intricate shape details and the unknown measurement noise covariance. Through extensive experiments using both simulated and real-time lidar data, the proposed algorithm demonstrates superior performance compared to the existing ETT algorithms for extended target tracking in both accuracy and robustness.

Robust adaptive Kalman filter for structural performance assessment

SummaryStructural performance assessment is a critical stage in the health monitoring for the maintenance and risk management of engineering structures, in which the interstory drift is a key indicator. In this paper, a robust adaptive Kalman filter is proposed for an interstory drift estimation problem to show the health condition of steel structures in the case that the statistics or internal dynamics describing the signals and measurements are not known precisely. More precisely, we build an adaptive current Jerk model (ACJM) where the model parameters are updated in each time step to presuppose the statistics characterization of the steel dynamic, while the unknown measurement noise covariance is adapted based on a fixed‐lag innovation with respect to measurements. Moreover, a robust adaptive Kalman filter is designed for the modelling uncertainties in each time increment by solving a minimax game: one player tries to select an “actual” model far from the proposed ACJM with an exponential decay tolerance, while its “hostile” player, namely, the optimum filter, is designed by minimizing the estimation error according to the selected “actual” model. Finally, some simulation and experimental results show the effectiveness of the proposed algorithm.

A Stability Guaranteed Variational Bayesian Converted Measurement Kalman Filter for Radar Tracking with Unknown Noise Covariances

A Stability Guaranteed Variational Bayesian Converted Measurement Kalman Filter for Radar Tracking with Unknown Noise Covariances

A comparison of indirect and direct filter designs from data for LTI systems: the effect of unknown noise covariance matrices

Existing literature on model-based filter design for stochastic LTI systems assumes complete correspondence between the system and its model. When the system is not completely known, the standard indirect model-based (two-steps) filtering solution consists of: (i) identify a model of the system from measured input/output data; (ii) design a Kalman filter based on the estimated model. The performance of this indirect approach are limited by the model and noise covariance matrices accuracy. To overcome such limitations, this paper investigates a direct (one-step) solution to the filtering problem for SISO LTI systems in the Prediction Error Method (PEM) identification framework. Simulation results indicate the effectiveness of the direct filtering approach, especially when the noise covariance matrices are misspecified.

Adaptive Divided Difference Filter for Power Systems Dynamic State Estimation With Outliers and Unknown Noise Covariance

Adaptive Divided Difference Filter for Power Systems Dynamic State Estimation With Outliers and Unknown Noise Covariance

Adaptive and robust fractional gain based interpolatory cubature Kalman filter

In this study, we put forward the robust fractional gain based interpolatory cubature Kalman filter (FGBICKF) and the adaptive FGBICKF (AFGBICKF) for the development of the state estimators for stochastic nonlinear dynamics system. FGBICKF introduces a fractional gain to interpolatory cubature Kalman filter to increase the robustness of state estimation. AFGBICKF is developed to enhance the state estimation adaptive to stochastic nonlinear dynamics system with unknown process noise covariance through recursive estimation. The simulations on re-entry target tracking system have shown that the performance of FGBICKF is superior to that of cubature Kalman filter and interpolatory cubature Kalman filter, and standard deviation of FGBICKF is closer to posterior Cramér-Rao lower bound. Moreover, our simulations have also demonstrated that AFGBICKF remains stable even when the initial process noise covariance increase, proving its adaptiveness, robustness, and effectiveness on state estimation.

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.

Adaptive tracking of non-ellipsoidal extended target with varying number of sub-objects based on variational Bayesian

High-resolution sensors make it less difficult to detect the true shape of an extended target, and the method of using a single ellipsoid to approximate the extended state of the target is no longer applicable. We can use multiple ellipsoids to approximate the shape of non-ellipsoidal extended targets, but the method of fixing number of sub-objects again fails due to changes in the target shape. In this work, we propose a novel variational Bayesian adaptive filter for non-ellipsoidal extended target tracking (NETT) with a varying number of sub-objects called VN-NETT-VBAF. The proposed filter is used to estimate the motion, extended states, and mixture probabilities of sub-objects describing a non-ellipsoidal extended target. First, the framework of VN-NETT-VBAF is established based on the spawning and combination of sub-objects. Second, the inverse Gamma (IG) distribution is used to model the unknown measurement noise covariance. Based on the variational Bayesian theory, the joint posterior probability density function (PDF) of the system parameters is iteratively updated to achieve the joint estimation of the extended target state and the measurement noise covariance. Finally, an adaptive forgetting factor is designed to update the noise covariance to further improve the robustness of the algorithm to abrupt noise. The simulation results show that the algorithm in this paper can reasonably change the number of sub-objects to adapt to the change of the target extended state, and effectively deal with the abrupt noise to obtain higher filtering accuracy.

Dynamic event-triggered fault detection for rotary steerable systems with unknown time-varying noise covariances

This paper is concerned with the fault detection problem for the rotary steerable drilling tool system under unknown vibrations and limited computational resources. Firstly, the drilling tool system can be modeled by a nonlinear stochastic system with unknown time-varying noise covariances. Then, the dynamic event-triggered mechanism is introduced to save computational resources, and the caused transmission error is completely decoupled by nonuniform sampling. Subsequently, a novel unscented Kalman filter is proposed by combining the expectation maximization method to estimate states when noise covariances are unknown. A residual and an evaluation function are constructed to detect faults. Finally, a numerical simulation and an experiment on a drilling tool prototype validate the superior performance of the proposed fault detection scheme, which has lower missed alarm rates and consumes less time than existing methods.

A Tunable Adaptive Detector for Distributed Targets When Signal Mismatch Occurs

Aiming at the problem of detecting a distributed target when signal mismatch occurs, this paper proposes a tunable detector parameterized by an adjustable parameter. By adjusting the parameter, the tunable detector can achieve robust or selective detection of mismatched signals. Moreover, the proposed tunable detector, with a proper tunable parameter, can provide higher detection probability compared with existing detectors in the case of no signal mismatch. In addition, the proposed tunable detector possesses the constant false alarm rate property with the unknown noise covariance matrix.

Unconstrained feedback controller design using Q-learning from noisy process data

This paper develops a novel model-free Q-learning based approach to estimate linear, unconstrained feedback controllers from noisy process data. The proposed method is based on an extension of an available approach developed to estimate the linear quadratic regulator (LQR) for linear systems with full state measurements driven by Gaussian process noise of known covariance. First, we modify the approach to treat the case of an unknown noise covariance. Then, we use the modified approach to estimate a feedback controller for linear systems with both process and measurement noise and only output measurements. We also present a model-based maximum likelihood estimation (MLE) approach to determine a linear dynamic model and noise covariances from data, which is used to construct a regulator and state estimator for comparisons in simulation studies. The performances of the model-free and model-based controller estimation approaches are compared with an example heating, ventilation, and air-conditioning (HVAC) system. We show that the proposed Q-learning approach estimates a reasonably accurate feedback controller from 24 h of noisy data. The controllers estimated using both the model-free and model-based approaches provide similar closed-loop performances with 3.5 and 2.7% losses respectively, compared to a perfect controller that uses the true dynamic model and noise covariances of the HVAC system. Finally, we give future work directions for the model-free controller design approaches by discussing some remaining advantages of the model-based approaches.

An Adaptive Federated Filter Based on Variational Bayes With Application to Multisource Navigation

Information fusion is one of the key technologies in airborne multi-source navigation, where federated filter is widely used due to its simple structure. However, the sensor measurement of multi-source navigation system will become unreliable in some interferential environment, which leads to the state and measurement noise covariance matrix change over time and estimate difficultly. Inaccurate covariance matrice cause the loss of positioning accuracy in traditional federated filter. To address the problems, this paper puts forward an adaptive federal Kalman filtering algorithm based on Variational Bayesian and applies it to the INS/GPS/Terrain/Geomagnetic multi-source navigation system. Simulation and experiment results show that the proposed filter outperforms the traditional federated filter at improving the positioning accuracy under the condition of time-varying or even unknown state and measurement noise covariance matrix, which plays a positive role in UAV multi-source navigation.

Matrix denoising with partial noise statistics: optimal singular value shrinkage of spiked F-matrices

Abstract We study the problem of estimating a large, low-rank matrix corrupted by additive noise of unknown covariance, assuming one has access to additional side information in the form of noise-only measurements. We study the Whiten-Shrink-reColour (WSC) workflow, where a ‘noise covariance whitening’ transformation is applied to the observations, followed by appropriate singular value shrinkage and a ‘noise covariance re-colouring’ transformation. We show that under the mean square error loss, a unique, asymptotically optimal shrinkage nonlinearity exists for the WSC denoising workflow, and calculate it in closed form. To this end, we calculate the asymptotic eigenvector rotation of the random spiked F-matrix ensemble, a result which may be of independent interest. With sufficiently many pure-noise measurements, our optimally tuned WSC denoising workflow outperforms, in mean square error, matrix denoising algorithms based on optimal singular value shrinkage that do not make similar use of noise-only side information; numerical experiments show that our procedure’s relative performance is particularly strong in challenging statistical settings with high dimensionality and large degree of heteroscedasticity.

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.

Event‐triggered adaptive stabilization control of stochastic nonlinear systems with unmodeled dynamics

AbstractIn this paper, we present a novel controller design method for stochastic nonlinear systems with unmodeled dynamics, uncertain parameters, and unknown covariance noise. In order to deal with these uncertainties, a new event‐based small gain controller is designed. The event‐triggered scheme can reduce the computational burden caused by disturbance and noise. By combining the technique of changing supply rate with small gain condition, a stochastic input‐to‐state practically stability Lyapunov function is obtained for the subsystem. Simultaneously, the changing supply function is used to treat with unmodeled dynamics. Based on backstepping process and adaptive control approach, the influence of unknown covariance noise is overcome. It is proved that the designed state‐feedback controller can ensure the overall system is stochastic input‐to‐state practically stability.

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.

Variational Bayesian-Based Moving Horizon Estimation of Toolface for Rotary Steerable Drilling Tool Systems

This article is concerned with the estimation problem of Toolface for dynamic point-the-bit rotary steerable drilling tool systems. First, considering the unknown frequency and amplitude of vibration during the drilling process, the Toolface system is modeled as a time-varying stochastic system with unknown and time-varying noise covariance matrices. Under the assumption that the noises and their covariance matrices, respectively, obey the Gaussian distribution and the inverse Wishart distribution, the variational Bayesian-based moving horizon estimation algorithm is proposed. Then, the state and the noise covariance matrices are inferred by iteratively updating their approximate posterior probability distributions. Finally, simulations and experiments are provided to demonstrate the effectiveness and superiority of the developed estimation scheme.

Detector Design and Performance Analysis for Target Detection in Subspace Interference

It is often difficult to obtain sufficient training data for adaptive signal detection, which is required to calculate the unknown noise covariance matrix. Additionally, interference is frequently present, which complicates the detecting issue. We provide a two-step method, termed interference cancellation before detection (ICBD), to address the issue of signal detection in the unknown Gaussian noise and subspace interference. The first involves projecting the test and training data to the interference-orthogonal subspace in order to suppress the interference. Utilizing traditional adaptive detector design ideas is the next stage. Due to the smaller dimension of the projected data, the ICBD-based detectors can function with little training data. The ICBD has two additional benefits over traditional detectors. Lower computational burden and proper operation with interference being in the training data are two additional benefits of ICBD-based detectors over conventional ones. We also give the statistical properties of the ICBD-based detectors and demonstrate their equivalence with the traditional ones in the special case of a large amount of training data containing no interference.

A Novel Adaptive Kalman Filter Based on Credibility Measure

It is quite often that the theoretic model used in the Kalman filtering may not be sufficiently accurate for practical applications, due to the fact that the covariances of noises are not exactly known. Our previous work reveals that in such scenario the filter calculated mean square errors (FMSE) and the true mean square errors (TMSE) become inconsistent, while FMSE and TMSE are consistent in the Kalman filter with accurate models. This can lead to low credibility of state estimation regardless of using Kalman filters or adaptive Kalman filters. Obviously, it is important to study the inconsistency issue since it is vital to understand the quantitative influence induced by the inaccurate models. Aiming at this, the concept of credibility is adopted to discuss the inconsistency problem in this paper. In order to formulate the degree of the credibility, a trust factor is constructed based on the FMSE and the TMSE. However, the trust factor can not be directly computed since the TMSE cannot be found for practical applications. Based on the definition of trust factor, the estimation of the trust factor is successfully modifled to online estimation of the TMSE. More importantly, a necessary and sufficient condition is found, which turns out to be the basis for better design of Kalman filters with high performance. Accordingly, beyond trust factor estimation with Sage-Husa technique (TFE-SHT), three novel trust factor estimation methods, which are directly numerical solving method (TFE-DNS), the particle swarm optimization method (PSO) and expectation max-imization-particle swarm optimization method (EM-PSO) are proposed. The analysis and simulation results both show that the proposed TFE-DNS is better than the TFE-SHT for the case of single unknown noise covariance. Meanwhile, the proposed EM-PSO performs completely better than the EM and PSO on the estimation of the credibility degree and state when both noise covariances should be estimated online.