Remote State Estimation With Enhanced Robustness in the Presence of Data Packet Dropouts

This article discusses the remote state estimation over unreliable links, where the packet dropouts occur from the sensor side to the filter, for discrete-time systems with both bounded-power disturbances and white Gaussian noises. A cascaded estimation scheme with enhanced robustness is proposed, driven by the residual signal related to the modeling mismatch. The estimation gains are characterized by two modified algebraic Riccati equations (MAREs), together with a complete and rigorous stability analysis in the mean square (MS) sense. Necessary and sufficient conditions for the MS stability of the corresponding error dynamics are then given in terms of the data arrival rate and unstable poles of the plant, i.e., the Mahler measure of the plant. Moreover, the filtering strategy is expanded into the case of distributed estimation over lossy sensor networks, where each sensor locally constructs an estimate based on its own observation and on those collected from its neighbors, and the solution is again derived by MAREs. The corresponding necessary and sufficient conditions to the MS stability in the distributed case are also characterized by relationships between data arrival rates and the Mahler measure of the plant. Finally, an example is presented to validate the current design method.

I. Introduction

State estimation has been widely employed in commercial and industrial areas for instance, motor drives [1], robotic vision [2], and fault estimation [3], [4], etc. The Kalman filter is one of the most popular optimal estimation designs that is applied to estimate the states of the system in the sense of achieving the minimum mean square (MS) estimation error when the process and measurement noises are Gaussian distributed. However, the design technique does not have guaranteed robustness as it is highly model dependent and may be very sensitive to parameter variation or other system uncertainty [5]. On the other hand, the technique, reaching a fairly mature state in the late 1980s, is capable of delivering good robustness against model uncertainties, but it is in general not able to effectively handle systems affected by stochastic noises, due to the nature of the worst case design [6], [7]. Thus it is not surprising to witness several multiobjective filtering methods [8]–[13], through Riccati-based or linear matrix inequality (LMI)-based approaches. Still, these existing multiobjective filtering methods suffer from some drawbacks and the most notable one is that all of these methods unavoidably pose the inherent conflict between the robustness and the optimality, which naturally leads to a tradeoff or conservative design. For example, when LMI-based approaches are used for multiobjective design, a common Lyapunov matrix is imposed on all equations to render the problem convex and this treatment inherently causes conservatism into the design procedure [14]. Although the extended LMIs with slack variables [15], [16] have been introduced to improve performance, conservatism still remains, together with extra computational costs. An ideal remedy of this drawback would call for “complementary control/filtering” framework, in which an linear quadratic Gaussian (LQG) control with extra regulation design as has been recently proposed in [17] . It is also worth noting that the guaranteed-cost design [18], the intrinsically Bayesian robust theory [19], and the divergence-based minimax approach [20], [21] have also been developed for deriving robust Kalman filters. Interested readers may refer to aforementioned references for a comprehensive discussion of these methods.