Variational Bayesian Inference-Based Maximum Correntropy Kalman Filtering for Visual Tracking With Unknown Process and Measurement Noise

Robust unscented Kalman filter with adaptation of process and measurement noise covariances

This paper presents an extended Kalman filter for pose estimation using noise covariance matrices based on sensor output. Compact and lightweight nine-axis motion sensors are used for motion analysis in widely various fields such as medical welfare and sports. A nine-axis motion sensor includes a three-axis gyroscope, a three-axis accelerometer, and a three-axis magnetometer. Information obtained from the three sensors is useful for estimating joint angles using the Kalman filter. The extended Kalman filter is used widely for state estimation because it can estimate the status with a small computational load. However, determining the process and observation noise covariance matrices in the extended Kalman filter is complicated. The noise covariance matrices in the extended Kalman filter were found for this study based on the sensor output. Postural change appears in the gyroscope output because the rotational motion of the joints produces human movement. Therefore, the process noise covariance matrix was determined based on the gyroscope output. An observation noise covariance matrix was determined based on the accelerometer and magnetometer output because the two sensors’ outputs were used as observation values. During a laboratory experiment, the lower limb joint angles of three participants were measured using an optical 3D motion analysis system and nine-axis motion sensors while participants were walking. The lower limb joint angles estimated using the extended Kalman filter with noise covariance matrices based on sensor output were generally consistent with results obtained from the optical 3D motion analysis system. Furthermore, the lower limb joint angles were measured using nine-axis motion sensors while participants were running in place for about 100 s. The experiment results demonstrated the effectiveness of the proposed method for human pose estimation.

The widely used traditional Kalman filter-type power system dynamic state estimator is unable to address the unknown and non-Gaussian system process and measurement noise as well as dynamical model uncertainties. To this end, this paper proposes a decentralized H-infinity unscented Kalman filter that leverages the strength of the H-infinity criteria developed in robust control for handling system uncertainties with the advantage of the UKF for addressing strong model nonlinearities. Specifically, the statistical linerization approach is used to derive a linear-like batch-mode regression model similar to the linear Kalman filter. This allows us to resort to the linear H-infinity Kalman filter framework for the development of the proposed H-infinity UKF in the Krein space. An analytical form is also derived to tune the parameter of the H-infinity criterion. Two decoupled models are presented to enable the decentralized implementation of the H-infinity UKF using the local PMU measurements. Extensive simulation results carried out on the IEEE 39-bus system show that the proposed H-infinity UKF is able to bound the influences of various types of measurement and model uncertainties while obtaining accurate state estimates.

The electrification of the transport sector increases the demand for a battery management system that allows the Li-ion battery to work in a sophisticated way to reach its maximum. The main focus of the battery management system is the estimation of the battery’s state of charge (SOC) which is an indicator to determine the driving range of an electric vehicle. However, battery modeling has a direct influence on SOC estimation. In this article, the equivalent circuit model (ECM) and extended Kalman filter (EKF) algorithm are combined for SOC estimation of the Li-ion battery. Since the performance of Kalman filter algorithms strictly depends on noise covariance matrices, incorrect values reduce the accuracy and make divergence in state estimation. Therefore, it is motivated to analyze the impact of process noise and measurement noise covariance matrix values on SOC estimation using Kalman filter algorithms. Ten different combinations of noise covariance matrices are employed to analyze the effect of these matrices on SOC estimation. As a result, the tuning of the filter is critical for improvement in state estimation regardless of the type of the battery model and filtering technique. The matrix values are chosen to take into account the convergence rate and estimation error. To validate the effectiveness of the chosen noise covariance matrices, the simulation results of the ECM based EKF estimation method is superimposed with the discharge curves available in the data sheet. The simulation results show minimal estimation error and a good convergence rate for tuned EKF.

Most existing localization schemes necessitate a priori statistical characteristic of measurement noise, which may be unrealistic in practical applications. This paper investigates the variational Bayesian adaptive unscented Kalman filtering (VBAUKF) for received signal strength indication (RSSI) based indoor localization under inaccurate process and measurement noise covariance matrices. First, an inaccurate and slowly varying measurement noise covariance matrix can be estimated by choosing appropriate conjugate prior distribution for an indoor localization model with inaccurate process and measurement noise covariance matrices. By choosing inverse Wishart priors distribution, the state, predicted error and measurement noise covariance matrices are inferred on each time separately. Second, a parameter optimization algorithm is designed to minimize the localization error of VBAUKF until it less than the threshold set in advance. Finally, experimental validation is presented to demonstrate the accuracy and effectiveness of the proposed filtering method for indoor localization.

Real-time state of charge estimation for electric vehicle power batteries using optimized filter

For autonomous vehicles, navigation systems must be accurate enough to provide lane-level localization. Highaccuracy sensors are available but not cost-effective for production use. Although prone to significant error in poor circumstances, even low-cost GPS systems are able to correct Inertial Navigation Systems (INS) to limit the effects of dead reckoning error over short periods between sufficiently accurate GPS updates. Kalman filters (KF) are a standard approach for GPS/INS integration, but require careful tuning in order to achieve quality results. This creates a motivation for a KF which is able to adapt to different sensors and circumstances on its own. Typically for adaptive filters, either the process (Q) or measurement (R) noise covariance matrix is adapted, and the other is fixed to values estimated a priori. We show that by adapting Q based on the state-correction sequence and R based on GPS receiver-reported standard deviation, our filter reduces GPS root-mean-squared error by 23% in comparison to raw GPS, with 15% from only adapting R.

This paper describes a new adaptive filtering approach for nonlinear systems with additive noise. Based on Square-Root Unscented Kalman Filter (SRUKF), the traditional Maybeck’s estimator is modified and extended to the nonlinear systems, the estimation of square root of the process noise covariance matrix Q or measurement noise covariance matrix R is obtained straightforwardly. Then the positive semi-definiteness of Q or R is guaranteed, some shortcomings of traditional Maybeck’s algorithm are overcome, so the stability and accuracy of the filter is improved greatly.

In this paper, after reviewing the traditional Kalman filter formulation, a development of a fuzzy logic-based adaptive Kalman filter is outlined. The adaptation is in the sense of adaptively tuning, on-line, the measurement noise covariance matrix R or the process noise covariance matrix Q. This improves the Kalman filter performance and prevents filter divergence when R or Q are uncertain. Based on the whiteness of the filter innovation sequence and employing the covariance-matching technique the tuning process is carried out by a fuzzy inference system. If a statistical analysis of the innovation sequence shows discrepancies with its expected statistics then a fuzzy inference system adjusts a factor through which the matrices R or Q are tuned on line. This fuzzy logic-based adaptive Kalman filter is tested on a numerical example. The results are compared with these obtained using a conventional Kalman filter and a traditionally adapted Kalman filter. The fuzzy logic-based adaptive Kalman filter showed better results than its traditional counterparts.

Kalman filter tracking in a Cherenkov neutrino telescope

Real-time reconstruction of the time-dependent heat flux and temperature distribution in participating media by using the Kalman filtering technique

The satellite clock plays a key role in the global navigation satellite system (GNSS). The accuracy of GNSS and its applications depend on the quality of the satellite clock. Therefore, precisely estimating and predicting the satellite clock is an important issue in the fields of GNSS and its application. As an optimal estimation algorithm, Kalman filter has been used to estimate and predict the satellite clock. However, in a conventional Kalman filter algorithm, the noise covariance matrices of satellite clock need to be predetermined, which restricts its further applications since the noise covariance matrices, especially the process noise covariance matrix, are usually unknown in the real cases. With inappropriate noise covariance matrices, the state estimation of conventional Kalman filter is suboptimal. To cope with this problem, a new noise covariance matrix estimation method of Kalman filter is proposed, and then we apply it to the problem of satellite clock estimation and prediction. Considering the fact that the process noise covariance matrix depends on the unknown noise parameters, the problem of estimating process noise covariance matrix can be solved by estimating the unknown noise parameters. First, the correlation between the Kalman innovations is used to establish a linear relationship with the unknown noise parameters. Then the unknown parameters can be estimated by least-squares estimation. Finally, the satellite clock can be estimated and predicted with the estimated noise parameters. In the new method, no prior information about the noise parameters is needed. Even with some extreme prior noise parameters, the new method can also work very well and has good convergence properties. For comparison, we conduct two experiments using the new method and the adaptively robust Kalman filter with classified adaptive factors based on opening windows separately, both results are consistent with each other very well, which verifies the correctness and effectiveness of this new method.

The accuracy of state estimators using the Kalman Filter (KF) is largely influenced by the measurement and the process noise covariance matrices. The former can be directly inferred from the available measurement devices whilst the latter needs to be assessed, as a function of the process model, in order to maximize the KF performances. In this paper we present different approaches that allow assessing the optimal values of the elements composing the process noise covariance matrix within the context of the State Estimation (SE) of Active Distribution Networks (ADNs). In particular, the paper considers a linear SE process based on the availability of synchrophasors measurements. The assessment of the process noise covariance matrix, related to a process model represented by the ARIMA [0,1,0] one, is based either on the knowledge of the probabilistic behavior of nodal network injections/absorptions or on the a-posteriori knowledge of the estimated states and their accuracies. Numerical simulations demonstrating the improvements of the KF-SE accuracy achieved by using the calculated matrix Q are included in the paper. A comparison with the Weighted Least Squares (WLS) method is also given for validation purposes.

A KALMAN FILTER-BASED STABLE DYNAMIC INVERSION FOR DISCRETE-TIME, LINEAR, TIME-VARYING SYSTEMS

The integration of distributed renewable energy sources into distribution networks is a key approach to achieving sustainable and low-carbon power systems. However, high renewable penetration significantly increases the volatility and uncertainty of distribution systems, posing challenges to renewable energy accommodation and reliable operation. To address these challenges, active control of distribution networks is required, which in turn relies on accurate system states. In practice, the limited number and accuracy of measurement devices in distribution networks make dynamic state estimation a critical technology for sustainable distribution systems. In this paper, a novel dynamic state estimation method for sustainable distribution systems is proposed, incorporating spatiotemporal data correlation and adaptiveness to process and measurement noise. A CNN-BiGRU-Attention model is developed to reconstruct high-accuracy real-time pseudo-measurements, compensating for insufficient sensing infrastructure. Furthermore, a noise adaptive dynamic state estimation method is proposed based on an improved unscented Kalman filter. An amplitude modulation factor (AMF) is applied to track time-varying process noise, while an evaluation method based on robust Mahalanobis distance (RMD) is embedded to deal with non-Gaussian measurement noise. Finally, simulation studies on the IEEE 33-bus three-phase unbalanced distribution network demonstrate the effectiveness and robustness of the proposed method.