Adaptive divided difference filter for nonlinear systems with unknown noise

Abstract

An Adaptive Divided Difference filter has been proposed for joint estimation of parameter and states of nonlinear systems in situations with unknown process noise statistics. The proposed filter, which is based on the innovation sequence, ensures improved estimation performance adapting the unknown process noise covariance. The performance of the filter is assessed with a benchmark nonlinear problem. Simulation results demonstrate that the performance of the proposed filter is superior compared to a non adaptive Divided Difference filter when the process noise covariance is unknown.

Performance evaluation of a novel adaptive variable structure state estimator

“…Although adaptive state estimators for linear plants have been known for quite some time, 9,[19][20][21] adaptive state estimators for nonlinear systems have recently drawn the attention of researchers. 2,6,8 For both linear and nonlinear adaptive state estimators, the broad classifications constitute process noise adaptive (Q-adaptive), measurement noise adaptive (R-adaptive), 7,20,22 and a combination of Q and R adaptive (QR-adaptive) estimators. Almost all adaptive state estimators involve the estimation of covariance matrices.…”

“…In the present contribution, we confine our interest to nonlinear Q adaptive estimators. In the Q adaptive state estimators, two approaches 8,[20][21][22] are possible viz., scale-factor based and MLE based approaches. 8,[20][21][22] For adaptive nonlinear state estimators, out of several proposed versions the present work has employed the scale factor based variant of Adaptive Divided Difference Filter (ADDF) (contrasted with the MLE based variant of ADDF described in ref.…”

“…In the Q adaptive state estimators, two approaches 8,[20][21][22] are possible viz., scale-factor based and MLE based approaches. 8,[20][21][22] For adaptive nonlinear state estimators, out of several proposed versions the present work has employed the scale factor based variant of Adaptive Divided Difference Filter (ADDF) (contrasted with the MLE based variant of ADDF described in ref. 8) for primarily adaptive estimation of the Q matrix which is needed for defining the boundary zone of the SVSF-OBL as explained below.…”

“…Approximation in the process model is often represented by process noise covariance. Several nonlinear robust state estimators, [1][2][3][4][5] as well as adaptive state estimators, 2,[6][7][8][9] have been reported in the literature. Recently, a robust variable structure filter called Smooth Variable Structure Filter (SVSF) 4,[10][11][12][13] has been proposed and its application to air traffic control problems has been proposed in references.…”

Recursive Noise Adaptive Extended Object Tracking by Variational Bayesian Approximation

“…Adaptive filters are an appealing way to obtain the estimation of kinematic together with uncertain noise covariance, such as covariance matching [15], [16], maximum likelihood estimation [17], and state augmentation [18]. Additionally, iterative algorithms have been commonly employed to address joint state and parameter estimation problems.…”