Measurement Noise Covariance Matrices Research Articles

Adaptive Recursive Decentralized Cooperative Localization for Multirobot Systems With Time-Varying Measurement Accuracy

Decentralized cooperative localization (DCL) is a promising method to determine accurate multirobot poses (i.e., positions and orientations) for robot teams operating in an environment without absolute navigation information. Existing DCL methods often use fixed measurement noise covariance matrices for multirobot pose estimation; however, their performance degrades when the measurement noise covariance matrices are time-varying. To address this problem, in this article, a novel adaptive recursive DCL method is proposed for multi-robot systems with time-varying measurement accuracy. Each robot estimates its pose and measurement noise covariance matrices simultaneously in a decentralized manner based on the constructed hierarchical Gaussian models using the variational Bayesian approach. Simulation and experimental results show that the proposed method has improved cooperative localization accuracy and estimation consistency but slightly heavier computational load than the existing recursive DCL method.

Multi-Fading Factor and Updated Monitoring Strategy Adaptive Kalman Filter-Based Variational Bayesian.

Aiming at the problem that the performance of adaptive Kalman filter estimation will be affected when the statistical characteristics of the process and measurement of the noise matrices are inaccurate and time-varying in the linear Gaussian state-space model, an algorithm of multi-fading factor and an updated monitoring strategy adaptive Kalman filter-based variational Bayesian is proposed. Inverse Wishart distribution is selected as the measurement noise model and the system state vector and measurement noise covariance matrix are estimated with the variational Bayesian method. The process noise covariance matrix is estimated by the maximum a posteriori principle, and the updated monitoring strategy with adjustment factors is used to maintain the positive semi-definite of the updated matrix. The above optimal estimation results are introduced as time-varying parameters into the multiple fading factors to improve the estimation accuracy of the one-step state predicted covariance matrix. The application of the proposed algorithm in target tracking is simulated. The results show that compared with the current filters, the proposed filtering algorithm has better accuracy and convergence performance, and realizes the simultaneous estimation of inaccurate time-varying process and measurement noise covariance matrices.

Bayesian step least mean squares algorithm for Gaussian signals

Selecting the step of the least mean squares (LMS) algorithm is an old problem. This study uses a new approach to address this problem resulting in a new algorithm with excellent system identification performance. The LMS algorithm, with time-varying step, size can be shown to be equivalent to the Kalman filter in some conditions. This is as long as the state noise of the Kalman filter and the step size of the LMS algorithm are chosen carefully. The Kalman filter is the optimum linear estimator (Bayesian) given the state and the measurement noise covariance matrices, but these matrices are not always known. This work considers the case where these matrices are not known, in the special cases that the Kalman filter reduces to the LMS. This results in an algorithm to select the step-size of the LMS algorithm with few priors. The optimum step size can be calculated using estimates of the probability density function (PDF) of the coefficient estimation error variance (qw ) and measurement noise variance (qv ). The PDFs can be estimated from the data using Bayes’ rule and assuming Gaussian reference and measurement noise signals. The resulting algorithm to determine qw and qv is a second small Kalman filter, and the outputs of this filter (means and covariances) are used to determine the expected value of the step.

A Comparative Study on Adaptive EKF Observers for State and Parameter Estimation of Induction Motor

In this article, conventional extended Kalman filter (EKF) and adaptive extended Kalman filters (AEKFs) based on adaptive fading, strong tracking, and innovation are compared for state and parameter estimation problem of induction motor (IM) by considering their estimation performances and computational burdens. The estimation performance of EKFs depends on the proper selection of system and measurement noise covariance matrices. However, it is hard to select optimum elements of those matrices using the trial-and-error method, and those are affected by the operating conditions of IM. Therefore, different AEKF approaches with the ability to update those matrices online according to the operating conditions have been proposed in the literature. However, to the best of the author's knowledge, no comparison has been yet reported as to which observer is more effective for real-time state and parameter estimation problem of IM. This paper focuses on the detailed comparison of those observers and provides useful results to the literature.

Variational Bayesian-Based Maximum Correntropy Cubature Kalman Filter With Both Adaptivity and Robustness

This paper focuses on solving the problems of unknown measurement noise covariance and measurement outliers, which occurs in the vision/dual-IMU integrated attitude determination system. Although many adaptive filters and robust filters have been proposed to deal with the unknown measurement noise covariance or measurement outliers, most of them cannot handle both the unknown noise covariance and outliers. The adaptive filters assume no outliers in measurements and the robust filters assume accurate measurement noise covariance matrices. In this paper, we propose an adaptive and robust cubature Kalman filter, which achieves the adaptivity by estimating the measurement noise covariance through the variational Bayesian (VB) method, and achieves the robustness by suppressing the outliers based on the maximum correntropy criterion (MCC). The robustness and adaptivity of the proposed filter are verified through a typical tracking simulation example. Furthermore, the experimental results show that the proposed filter can obtain higher estimation accuracy than other filters in the vision/dual-IMU integrated system.

Toward security monitoring of industrial Cyber-Physical systems via hierarchically distributed intrusion detection

Industrial Cyber-physical systems (ICPSs), integrating communication, computation and control of industrial processes are referred to as a core technology to approach the Industry 4.0. Ensuring the ICPS security is of paramount importance in smart manufacturing. Considering the characteristics of large-scale, geographically-dispersed and multi-dimensional heterogeneous, federated and life-critical natures of ICPSs, this paper investigates a hierarchically distributed intrusion detection scheme that seeks to achieve the all-round safety protection of ICPSs according to the system structure and attacking types of each ICPS layer. For physical system-relevant perceptual executive layer, potential and covert attacks are detected by the clustered sensory system state residual anomaly monitoring based on a process noise and measurement noise-adaptive Kalman filter (PNMN-AKF). PNMN-AKF can perform a joint recursive estimation of dynamic system states, time-varying process and measurement noise covariance matrices by the variational Bayes approximation framework. In cyberspace, potential cyber-attacks are detected by the anomaly monitoring of the statistical distribution of the network transmission characteristics of data transmission layer by introducing a forgetting factor-induced recursive Gaussian mixture model (FF-RGMM). In the application control layer, a regularized sparse deep belief network model is introduced to characterize the misuse behavior for detecting potential attacks. Extensive validation and comparative experiments have been conducted on a numerical simulation system and a comprehensive ICPS simulation platform by using OPNET and a commonly-used benchmark simplified Tennessee Eastman process (STEP) based on Matlab/Simulink. Experimental results demonstrate that the proposed hierarchically distributed intrusion detection method can efficiently recognize potential and covert cyber-attacks in each ICPSs link with low false alarm rate and missing detection rate, which lays a foundation for the overall security monitoring of ICPSs.

Variational Adaptive Kalman Filter With Gaussian-Inverse-Wishart Mixture Distribution

In this article, a new variational adaptive Kalman filter with Gaussian-inverse-Wishart mixture distribution is proposed for a class of linear systems with both partially unknown state and measurement noise covariance matrices. The state transition and measurement likelihood probability density functions are described by a Gaussian-inverse-Wishart mixture distribution and a Gaussian-inverse-Wishart distribution, respectively. The system state vector together with the state noise covariance matrix and the measurement noise covariance matrix are jointly estimated based on the derived hierarchical Gaussian model. Examples are provided to demonstrate the effectiveness and potential of the developed new filtering design techniques.

A Slide Window Variational Adaptive Kalman Filter

A slide window variational adaptive Kalman filter is presented in this brief based on adaptive learning of inaccurate state and measurement noise covariance matrices, which is composed of the forward Kalman filtering, the backward Kalman smoothing, and the online estimates of noise covariance matrices. By imposing an approximation on the smoothing posterior distribution of slide window state vectors, the posterior distributions of noise covariance matrices can be analytically updated as inverse Wishart distributions by exploiting the variational Bayesian method, which avoids the fixed-point iterations and achieves good computational efficiency. Simulation comparisons demonstrate that the proposed method has better filtering accuracy and consistency than the existing cutting-edge method.

Collaborative Sequential State Estimation Under Unknown Heterogeneous Noise Covariance Matrices

We study the problem of distributed sequential estimation of common states and measurement noise covariance matrices of hidden Markov models by networks of collaborating nodes. We adopt a realistic assumption that the true covariance matrices are possibly different (heterogeneous) across the network. This setting is frequent in many distributed real-world systems where the sensors (e.g., radars) are deployed in a spatially anisotropic environment, or where the networks may consist of sensors with different measuring principles (e.g., using different wavelengths). Our solution is rooted in the variational Bayesian paradigm. In order to improve the estimation performance, the measurements and the posterior estimates are communicated among adjacent neighbors within one network hop distance using the information diffusion strategy. The resulting adaptive algorithm selects neighbors with compatible information to prevent degradation of estimates.

A robust structural parameter estimation method using seismic response measurements

Although successful applications of data assimilation techniques such as Kalman filter to structural parameter identification problems exist in literature, they have been explored mostly via simulations because real-world application poses challenges. Current practice is to set the process and measurement noise covariance matrices by manual tuning and keeping them constant over the estimation period. However, when the matrices are not correct, Kalman filters are prone to suboptimal performance and/ or even divergence. In this paper, use of a stochastic approximation scheme along with the unscented Kalman filter is explored. The sensitivity of the initial filter parameter selection has been investigated through both simulations and full-scale laboratory experiments. Results show that by automatically updating the filter statistics, system states, including the structural parameters, are successfully estimated with a fast convergence rate, good accuracy, and trackability in a stable and objective manner. The method is further applied to in situ seismic response records of a box-girder bridge. The stiffness values of the rubber bearings are successfully identified.

Optimizing a Kalman filter with an evolutionary algorithm for nonlinear quadrotor attitude dynamics

Kalman filter is a linear minimum – mean square error estimator. However, process and measurement noise matrices of the Kalman filter must be known a priori to achieve this optimality condition. But in most cases, these parameters are guessed or tuned by trial and error approach both of which do not guarantee optimality and convergence. So in this work, an evolutionary algorithm is proposed to estimate the process and measurement noise covariance matrices of the Kalman filter to improve the performance of the sub – optimal filter. A fitness function is also proposed to achieve multi – dimensional optimization. Results are validated for both linear and nonlinear quadrotor attitude dynamics. Proposed method compared with optimization algorithms such as optimal Kalman filter, covariance – matrix adaptation evolution strategy and simulated annealing. Monte Carlo analysis showed that proposed algorithm is capable of tuning the state estimator better than the other algorithms. Thus, proposed algorithm reduces sensor errors and ensures efficient estimation of the quadrotor.

Doppler and bearing tracking using fuzzy adaptive unscented Kalman filter

The topic of Doppler and Bearing Tracking (DBT) problem is to achieve a target trajectory using the Doppler and Bearing measurements. The difficulty of DBT problem comes from the nonlinearity terms exposed in the measurement equations. Several techniques were studied to deal with this topic, such as the unscented Kalman filter. Nevertheless, the performance of the filter depends directly on the prior knowledge, involving the accurate model, sufficient information of the noise distribution and the suitable initialization. To address these problems, in this paper, a new adaptive factor together with a fuzzy logic system is proposed for online adjusting the process and the measurement noise covariance matrices simultaneously. In the core of the proposed algorithm, the fault detection procedure is also adopted to reduce the computational time. The theoretical developments are investigated by simulations, which indicate the effectiveness of the proposed filter in DBT problem.

Adaptive Extended Kalman Filter for Speed-Sensorless Control of Induction Motors

This paper presents an adaptive extended Kalman filter (AEKF) algorithm estimating the stator stationary axis components of stator currents, the stator stationary axis components of rotor fluxes, the rotor mechanical speed, and the load torque for speed-sensorless control applications of induction motors (IMs). The performance of a standard extended Kalman filter (SEKF) algorithm depends on the correct selection of system and measurement noise covariance matrices. In SEKF algorithms, these matrices are generally assumed as constant and determined by the trial-and-error method. However, they are affected by the operating conditions of IM and should be updated considering the operating conditions. For this purpose, instead of the time-consuming trial-and-error method for determining these matrices, an innovation-based adaptive estimation approach having the capability of online update is used in this paper. Finally, in order to verify the superiority of the AEKF algorithm, estimation performances of AEKF and SEKF algorithms are compared under challenging scenarios for a wide speed range considering computational burdens and parameter variations.

Adaptive Kalman Filter for Detectable Linear Time-Invariant Systems

A novel covariance matching technique is proposed for estimating the states and unknown entries of the process and measurement noise covariance matrices for additive white Gaussian noise elements in a linear Kalman filter. Under this assumption of detectability (that is, unobservable modes remain stable), the stability and convergence properties of the covariance matching Kalman filter are established. It is shown that the measurement covariance matrix cannot be unambiguously estimated if the measurement model contains linearly dependent measurements. Monte Carlo simulations evaluate the numerical properties of the proposed algorithm.

Robust adaptive unscented Kalman filter for bearings-only tracking in three dimensional case

This paper proposes an improved version of Unscented Kalman Filter (UKF), namely Robust Adaptive UKF (RAUKF), with a special focus on Bearings-Only Target Tracking for three-dimensional case (3DBOT). The automatic tuning of the noise covariance matrices and the robust estimation of the target states form a critical point for the performance of the Kalman-type filtering algorithms, especially in the variable environmental conditions exposed in underwater. The key idea of the proposed filter is to combine robust aspects of UKF and adaption of the process and measurement noise covariance matrices with low computational complexity. The main contribution of this paper is to adjust these matrices by means of the steepest descent algorithm, and the H∞ technique is embedded to achieve superior performance in terms of accuracy and robustness against initial conditions and model uncertainties. Different experiments are performed to evaluate the performance of the proposed algorithm in the 3DBOT problem with a single moving observer. Simulations demonstrate that the proposed filter produce more accurate results with satisfactory computational burden in comparison with other methods.

Robust multi-target tracking under mismatches in both dynamic and measurement models

In multi-target tracking (MTT), it is hard to guarantee that the dynamic and measurement model mismatches are described by process and measurement noises with suitable covariance matrices (CMs). Meanwhile, model changes caused by target maneuvers and disturbance-corrupted measurements may coexist in a complex environment. Therefore, we propose the problem of MTT under mismatches in both dynamic and measurement models, where the uncertain state prediction error and measurement noise CMs are considered as random variables. Then, a robust generalized labeled multi-Bernoulli (RGLMB) filter framework is derived to recursively propagate the joint posterior density of the multi-target state and the random CMs. By modeling the random CMs as inverse Wishart distributions, on-line random CMs tuning and multi-target state estimation are unified via minimizing the Kullback–Leibler divergence. Simulation results show that the proposed RGLMB filter is robust to different target motion models and noisy radar measurements corrupted by step, sinusoidal and stochastic forms of bias.

A Novel Adaptive Kalman Filter With Inaccurate Process and Measurement Noise Covariance Matrices

In this paper, a novel variational Bayesian (VB)-based adaptive Kalman filter (VBAKF) for linear Gaussian state-space models with inaccurate process and measurement noise covariance matrices is proposed. By choosing inverse Wishart priors, the state together with the predicted error and measurement noise covariance matrices are inferred based on the VB approach. Simulation results for a target tracking example illustrate that the proposed VBAKF has better robustness to resist the uncertainties of process and measurement noise covariance matrices than existing state-of-the-art filters.

Design of measurement difference autocovariance method for estimation of process and measurement noise covariances

The paper deals with the estimation of the process and measurement noise covariance matrices of a system described by the linear time-varying state–space model. In particular, the stress is laid on the correlation methods and a novel method, the measurement difference autocovariance method, is designed. The proposed method is based on the statistical analysis of an augmented measurement prediction error leading to a system of linear matrix equations for the elements of the noise covariance matrices. Compared to other correlation methods, the proposed method provides unbiased estimates even for a finite number of measurements. The theoretical results are discussed and illustrated in a numerical example.

A Novel Adaptive Kalman Filter With Colored Measurement Noise

In this paper, a novel variational Bayesian-based adaptive Kalman filter (VBAKF) is proposed to solve the problem of a linear state-space model with colored measurement noise and inaccurate noise covariance matrices. The filter problem of a linear state-space model with colored measurement noise and inaccurate noise covariance matrices is transformed into the filtering problem of a linear state-space model with white measurement noise and inaccurate noise covariance matrices using measurement differencing method and state augmentation approach. The augmentation state vector, corresponding predicted error covariance matrix and covariance matrix of white measurement noise are jointly estimated based on the variational Bayesian approach. The ability of addressing the colored measurement and inaccurate noise covariance matrices is demonstrated in the simulation of a target tracking example.

Uniqueness Conditions for ALS Problems

Abstract Knowledge of the process, measurement, and cross noise covariance matrices (denoted Q, R, and S, respectively) is necessary for tasks such as state estimation and performance monitoring. Several different types of algorithms have been developed to estimate these parameters from plant output data. Chief among them are the so-called correlation methods, such as autocovariance least squares (ALS). Despite the advances in covariance estimation algorithms, relatively little attention has been given to the topic of parameter identifiability. This paper discusses the limitations of when Q, R, and S are identifiable from output data. In particular, it is shown that for stable, linear time-invariant systems, the Kalman predictor gain, but not Q, R, and S, can be uniquely identified from the steady-state output autocovariance. Constrained ALS problems and the extension of the ALS problem to nonlinear and linear time-varying systems are also discussed.