Robust linearly constrained extended Kalman filter for mismatched nonlinear systems

Abstract

SummaryStandard state estimation techniques, ranging from the linear Kalman filter (KF) to nonlinear extended KF (EKF), sigma‐point or particle filters, assume a perfectly known system model, that is, process and measurement functions and system noise statistics (both the distribution and its parameters). This is a strong assumption which may not hold in practice, reason why several approaches have been proposed for robust filtering, mainly because the filter performance is particularly sensitive to different model mismatches. In the context of linear filtering, a solution to cope with possible system matrices mismatch is to use linear constraints. In this contribution we further explore the extension and use of recent results on linearly constrained KF for robust nonlinear filtering under both process and measurement model mismatch. We first investigate how linear equality constraints can be incorporated within the EKF and derive a new linearly constrained extended KF (LCEKF). Then we detail its use to mitigate parametric modeling errors in the nonlinear process and measurement functions. Numerical results are provided to show the performance improvement of the new LCEKF for robust vehicle navigation.

Robust LCEKF for Mismatched Nonlinear Systems with Non-Additive Noise/Inputs and Its Application to Robust Vehicle Navigation

“…Finally, if we consider nonlinear additive inputs of the form, , then and we recover the results in [ 20 ].…”

“…Once the general LCKF has been established, it is of interest to extend its use to more general nonlinear settings. A first attempt in the context of additive nonlinear systems was recently proposed by Hrustic et al [ 20 ], where a linearly constrained EKF (LCEKF) was introduced, together with its use to mitigate parametric misspecifications on both system functions. Notice that this approach is fundamentally different from state constrained solutions [ 21 , 22 ], where LCs are imposed on the state and not on the filter.…”

“…If we consider now an additive noise nonlinear discrete state–space model (NLDSSM), where and are the known system model (process and measurement) functions, and , ; a standard approach to derive a nonlinear filter of is to assume that Equations ( 6 ) and ( 7 ) can be linearised at the vicinity of a nominal trajectory [ 3 ] yielding the standard EKF, where is computed as in the unconstrained KF with . As has been recently proposed in [ 20 ], the corresponding LCEKF for additive noise systems is , where the constrained gain is computed as in the original LCKF but using the linearised matrices, as done in the EKF. Notice that the LCKF in [ 18 ] is not applicable to nonlinear systems, and the LCEKF in [ 20 ] is only valid for additive systems.…”

“…As has been recently proposed in [ 20 ], the corresponding LCEKF for additive noise systems is , where the constrained gain is computed as in the original LCKF but using the linearised matrices, as done in the EKF. Notice that the LCKF in [ 18 ] is not applicable to nonlinear systems, and the LCEKF in [ 20 ] is only valid for additive systems. The goal of this article is to further analyse these methods and extend their use to more general settings.…”

Modified particle filtering‐based robust estimation for a networked control system corrupted by impulsive noise

“…With the advent of the digital age and the prevalence of communication technologies, the network‐based modeling and control of the production processes have attracted the interests of many research communities, 1‐5 and the networked control systems (NCSs) have been widely applied in the engineering practice. Since the data information of controlled systems is exchanged in communication networks, the NCSs have the attractive properties such as low installation and operating costs and excellent reliability in contrast to the traditional point‐to‐point control systems 6 . A large number of advanced control schemes of NCSs have been reported for last decades, such as the event‐triggered control and iterative learning control 7,8 .…”