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

Abstract

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.

SOC Estimation of a Rechargeable Li-Ion Battery Used in Fuel Cell Hybrid Electric Vehicles—Comparative Study of Accuracy and Robustness Performance Based on Statistical Criteria. Part II: SOC Estimators

“…The most popular nowadays, Kalman filter (KF) is the "optimum state estimator and intelligent tool for a linear system", beneficial for estimating the Li-ion battery dynamic states and parameters [8].…”

“…However, there are situations when some Li-ion battery models have a dynamic that is "extremely nonlinear" and therefore "the linearization error may occur due to the lack of precision in the extension of the first series Taylor series in extremely nonlinear conditions" [5]. The simplicity of the SOC EKF estimator design and real-time MATLAB implementation is among two main features that motivated many researchers to apply it to a variety of Li-ion battery models, as in [2,3,[6][7][8][9]. A new state of the art analysis on Li-ion BMSs is presented in [12], which includes a brief overview presentation of the most common adaptive filtration techniques for SOC estimation reported in the literature.…”

“…In recent years, the lithium-ion battery has proven to be an ideal safety battery for hybrid electric vehicles, with high discharge power, environmental protection, low pollution, and long life [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Some details about its features, modelling, and hybrid combinations with different power sources in a fuel cell electric vehicle (FCEV) and power distribution controlled and optimized by an energy management system (EMS) are shown in Part 1 [20].…”

“…Typically, the Kalman filter SOC estimators are model based, so both battery models-the linear RC equivalent electrical circuit (ECM) and the nonlinear Simscape generic model developed and analyzed in Part 1 [20] are beneficial for designing and implementing a high accuracy SOC estimator [1][2][3][4][5][6][7][8][9][10][12][13][14][15][16][17][18][19]. For better documentation and information for the reader, the diagrams of both models represented in Part 1 [20] are taken over and repeated in Appendix A.1, Figure A1a-c.…”

Adaptive Cubature Kalman Filter Based on the Expectation-Maximization Algorithm

“…The accurate and reliable state estimation of nonlinear systems plays a crucial role in numerous practical engineering systems such as navigation, environment monitoring, intelligent manufacturing, and target tracking [1]- [5]. Recently, an increasing number of researchers have been interested in the state estimation of nonlinear systems, and several nonlinear filtering algorithms have been developed [6]- [8], including extended Kalman filter (EKF) algorithms [9]- [11], unscented Kalman filter (UKF) algorithms [12]- [14], and cubature Kalman filter (CKF) algorithms [15]- [17]. The EKF based on the first-order linearization of a nonlinear system is a classical nonlinear filtering method.…”