Time-varying Noise Covariance Research Articles

A novel residual-based Bayesian expectation–maximization adaptive Kalman filter with inaccurate and time-varying noise covariances

In this study, we introduce a novel residual-based Bayesian expectation–maximization adaptive Kalman filter (RBEMAKF) for dynamic state estimation with inaccurate and time-varying noise covariance matrices. The proposed scheme presents a novel maximum a-posteriori (MAP) estimator for characterizing process and measurement noises, leveraging the residual information derived from the Kalman filter. Simultaneously, the MAP is addressed through the application of the expectation–maximization (EM) algorithm. Subsequently, the standard Kalman filter is executed based on the estimated posterior of process and measurement noises (PMNs) to correct the dynamic state in real-time. Additionally, RBEMAKF is extended to propose Laplacian-RBEMAKF (L-RBEMAKF) and Student’s t-RBEMAKF (ST-RBEMAKF) to accommodate outlier environments. These methods assume Laplacian and Student’s t distributions for the prior of PMNs in RBEMAKF, respectively. Extensive simulations and real-world results demonstrate the effectiveness of the proposed RBEMAKF and its extensions (L-RBEMAKF and ST-RBEMAKF) in dynamic state estimation. The availability of our codes can be found at https://github.com/Gaitxh/RBEMAKF.

A generalized data assimilation architecture of digital twin for complex process industrial systems

As one of the critical cores of digital twin (DT), data assimilation (DA) can maintain consistency and synchronization between DT and physical system. Kalman filtering is a common DA method, but its estimation performance is deteriorated by factors such as model inaccuracy and time-varying noise covariance in practical applications. The errors caused by these multiple uncertainties are all coupled to the measurements, which augments the difficulty for DT to obtain physical system information. In order to tackle the DA problem with multiple uncertainties, this paper proposes a generalized DA architecture for DT in sophisticated process industry. First, by combining Stein variational gradient descent and nonlinear Bayesian filtering paradigm, a recursive estimation framework is established, which has higher accuracy in estimating the noise covariance compared to traditional methods. Second, to effectively deal with model inaccuracy by using filtering residuals containing time-varying noise, we propose a neural network and modified wavelet-based model error compensation (NNMW-MEC) block. Based on the modified wavelet technique, the filtering residual denoising built in NNMW-MEC can better cope with time-varying noise compared to existing wavelets, and extract the low-frequency signal involving model error information from noisy residual smoothly. In addition, because of the neural network-based state-compensation subblock, NNMW-MEC has more outstanding ability in compensating the state deviations with large changing range. Finally, we take the boiler system in a coal-fired power plant as an example to verify the effectiveness of our architecture. Experimental results show that the DA architecture proposed in this paper can improve the estimation performance of DT under inaccurate models and uncertain noise statistics.

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.

Adaptive robust unscented Kalman filter-based state-of-charge estimation for lithium-ion batteries with multi-parameter updating

State-of-charge (SOC) estimation is one of the key technologies for the development and application of battery management system (BMS). To achieve high accuracy in SOC estimation, which can adapt to any conditions, an adaptive robust unscented Kalman filter (ARUKF) based on multi-parameter update is proposed herein. First, the DP battery model is applied to replicate the dynamic behavior of lithium-ion batteries, and the model parameters are identified online by the improved forgetting factor recursive least square (IFFRLS). Then, the Institute of Geodesy and Geophysics (IGGIII) weight function is introduced into unscented Kalman filter (UKF) as the form of a robust factor to adjust the weights of observation residuals, and receding horizon based adaptive filter tuning is employed to obtain the time-varying noise covariance. Subsequently, joint estimation of battery model parameters and SOC with capacity updating is implemented which can suppress the system disturbance caused by outliers, mistuning, unknown initial value, and aging. Finally, the superior performance of accuracy and convergence is verified by cycle and aging tests. The maximum absolute error of SOC estimation under the proposed method is kept within 2%. The convergence speed of SOC estimation utilizing ARUKF is nearly 80 s faster than that of robust UKF (RUKF) and UKF under a 20% SOC initial error.

A Compact Noise Covariance Matrix Model for MVDR Beamforming

Acoustic beamforming is routinely used to improve the SNR of the received signal in applications such as hearing aids, robot audition, augmented reality, teleconferencing, source localisation and source tracking. The beamformer can be made adaptive by using an estimate of the time-varying noise covariance matrix in the spectral domain to determine an optimised beam pattern in each frequency bin that is specific to the acoustic environment and that can respond to temporal changes in it. However, robust estimation of the noise covariance matrix remains a challenging task especially in non-stationary acoustic environments. This paper presents a compact model of the signal covariance matrix that is defined by a small number of parameters whose values can be reliably estimated. The model leads to a robust estimate of the noise covariance matrix which can, in turn, be used to construct a beamformer. The performance of beamformers designed using this approach is evaluated for a spherical microphone array under a range of conditions using both simulated and measured room impulse responses. The proposed approach demonstrates consistent gains in intelligibility and perceptual quality metrics compared to the static and adaptive beamformers used as baselines.

Variational Bayesian Based IMM Robust GPS Navigation Filter

This paper investigates the navigational performance of Global Positioning System (GPS) using the variational Bayesian (VB) based robust filter with interacting multiple model (IMM) adaptation as the navigation processor. The performance of the state estimation for GPS navigation processing using the family of Kalman filter (KF) may be degraded due to the fact that in practical situations the statistics of measurement noise might change. In the proposed algorithm, the adaptivity is achieved by estimating the time-varying noise covariance matrices based on VB learning using the probabilistic approach, where in each update step, both the system state and time-varying measurement noise were recognized as random variables to be estimated. The estimation is iterated recursively at each time to approximate the real joint posterior distribution of state using the VB learning. One of the two major classical adaptive Kalman filter (AKF) approaches that have been proposed for tuning the noise covariance matrices is the multiple model adaptive estimate (MMAE). The IMM algorithm uses two or more filters to process in parallel, where each filter corresponds to a different dynamic or measurement model. The robust Huber's M-estimation-based extended Kalman filter (HEKF) algorithm integrates both merits of the Huber M-estimation methodology and EKF. The robustness is enhanced by modifying the filter update based on Huber's M-estimation method in the filtering framework. The proposed algorithm, referred to as the interactive multi-model based variational Bayesian HEKF (IMM-VBHEKF), provides an effective way for effectively handling the errors with time-varying and outlying property of non-Gaussian interference errors, such as the multipath effect. Illustrative examples are given to demonstrate the navigation performance enhancement in terms of adaptivity and robustness at the expense of acceptable additional execution time.

Adaptive Unscented Kalman Filter for Target Tacking with Time-Varying Noise Covariance Based on Multi-Sensor Information Fusion

In this paper, an innovative optimal information fusion methodology based on adaptive and robust unscented Kalman filter (UKF) for multi-sensor nonlinear stochastic systems is proposed. Based on the linear minimum variance criterion, this multi-sensor information fusion method has a two-layer architecture: at the first layer, a new adaptive UKF scheme for the time-varying noise covariance is developed and serves as a local filter to improve the adaptability together with the estimated measurement noise covariance by applying the redundant measurement noise covariance estimation, which is isolated from the state estimation; the second layer is the fusion structure to calculate the optimal matrix weights and gives the final optimal state estimations. Based on the hypothesis testing theory with the Mahalanobis distance, the new adaptive UKF scheme utilizes both the innovation and the residual sequences to adapt the process noise covariance timely. The results of the target tracking simulations indicate that the proposed method is effective under the condition of time-varying process-error and measurement noise covariance.

Adaptive Unscented Kalman Filter for Tracking GPS signals in the Case of an Unknown and Time-Varying Noise Covariance

Adaptive Unscented Kalman Filter for Tracking GPS signals in the Case of an Unknown and Time-Varying Noise Covariance

Adaptive Unscented Kalman Filter for Target Tracking with Unknown Time-Varying Noise Covariance.

The unscented Kalman filter (UKF) is widely used to address the nonlinear problems in target tracking. However, this standard UKF shows unstable performance whenever the noise covariance mismatches. Furthermore, in consideration of the deficiencies of the current adaptive UKF algorithm, this paper proposes a new adaptive UKF scheme for the time-varying noise covariance problems. First of all, the cross-correlation between the innovation and residual sequences is given and proven. On this basis, a linear matrix equation deduced from the innovation and residual sequences is applied to resolve the process noise covariance in real time. Using the redundant measurements, an improved measurement-based adaptive Kalman filtering algorithm is applied to estimate the measurement noise covariance, which is entirely immune to the state estimation. The results of the simulation indicate that under the condition of time-varying noise covariances, the proposed adaptive UKF outperforms the standard UKF and the current adaptive UKF algorithm, hence improving tracking accuracy and stability.

An Improved Strong Tracking Kalman Filter Algorithm for the Initial Alignment of the Shearer

The strap-down inertial navigation system (SINS) is a commonly used sensor for autonomous underground navigation, which can be used for shearer positioning under a coal mine. During the process of initial alignment, inaccurate or time-varying noise covariance matrices will significantly degrade the accuracy of the initial alignment of the shearer. To overcome the performance degradation of the existing initial alignment algorithm under complex underground environment, a novel adaptive filtering algorithm is proposed by the integration of the strong tracking Kalman filter and the sequential filter for the initial alignment of the shearer with complex underground environment. Compared with the traditional multiple fading factor strong tracking Kalman filter (MSTKF) method, the proposed MSTSKF algorithm integrates the advantage of strong tracking Kalman filter and sequential filter, and multiple fading factor and forgetting factor for east and north velocity measurement are designed in the algorithm, respectively, which can effectively weaken the coupling relationship between the different states and increase strong robustness against process uncertainties. The simulation and experiment results show that the proposed MSTSKF method has better initial alignment accuracy and robustness than existing strong tracking Kalman filter algorithm.

Prediction for human motion tracking failures

We propose a new and effective method of predicting tracking failures and apply it to the robust analysis of gait and human motion. We define a tracking failure as an event and describe its temporal characteristics using a hidden Markov model (HMM). We represent the human body using a three-dimensional, multicomponent structural model, where each component is designed to independently allow the extraction of certain gait variables. To enable a fault-tolerant tracking and feature extraction system, we introduce a single HMM for each element of the structural model, trained on previous examples of tracking failures. The algorithm derives vector observations for each Markov model using the time-varying noise covariance matrices of the structural model parameters. When transformed with a logarithmic function, the conditional output probability of each HMM is shown to have a causal relationship with imminent tracking failures. We demonstrate the effectiveness of the proposed approach on a variety of multiview video sequences of complex human motion.

State and Parameter Estimation Through Dynamic Bayesian Forecasting

Successful application of model based control depends on having good estimates for the system dynamic states and parameters. A multivariate dynamic linear model is developed for the estimation of the states from limited measurements in a non-linear system comprising model uncertainties. Since the noise statistics are rarely available a priori, the noise covariance matrix is treated as a tuning parameter and determined through repeated simulations. For non-linear, time varying processes, the assumption of a constant process noise covariance matrix does not realise accurate estimates. In this paper Monte Carlo simulations are used to obtain the time-varying noise covariance matrix. The methodology is demonstrated on a benchmark polymerisation process.

On the estimation of noise covariances in linear discrete-time systems

This paper is concerned with an approach for estimating or tracking the time-varying input and measurement noise covariances in time-varying discrete-time linear systems. The approach is firstly to introduce the estimators for the case where the noise co-variances are unknown constants. (The estimators are defined as the mean squares of the estimators of noises based on all the available measurement data.) They arc then transformed in sequential form, and are subsequently modified by incorporating a fading memory to yield estimates for time-varying noise covariances. The time-varying noise covariance estimates are evaluated as the fading mean squares of the estimates of noises based on all the measurement data up to present time. A numerical example for a simple system indicates acceptable performance of the proposed method.