Globally Optimal Distributed Kalman Filtering for Multisensor Systems with Unknown Inputs.

Yali Ruan,Yingting Luo,Yunmin Zhu

doi:10.3390/s18092976

Abstract

In this paper, the state estimation for dynamic system with unknown inputs modeled as an autoregressive AR (1) process is considered. We propose an optimal algorithm in mean square error sense by using difference method to eliminate the unknown inputs. Moreover, we consider the state estimation for multisensor dynamic systems with unknown inputs. It is proved that the distributed fused state estimate is equivalent to the centralized Kalman filtering using all sensor measurement; therefore, it achieves the best performance. The computation complexity of the traditional augmented state algorithm increases with the augmented state dimension. While, the new algorithm shows good performance with much less computations compared to that of the traditional augmented state algorithms. Moreover, numerical examples show that the performances of the traditional algorithms greatly depend on the initial value of the unknown inputs, if the estimation of initial value of the unknown input is largely biased, the performances of the traditional algorithms become quite worse. However, the new algorithm still works well because it is independent of the initial value of the unknown input.

Highlights

The classic Kalman filtering (KF) [1] requires the model of the dynamic system is accurate.in many realistic situations, the model may contain unknown inputs in process or measurement equations
Its computational cost increases due to the augmented state dimension. It is proposed by Friedland [2] in 1969 a two-stage Kalman filtering (TSKF) to reduce the computation complexity of the augmented state Kalman filtering (ASKF), which is optimal for the situation of a constant unknown input
The main contributions are: (1) A novel optimal algorithm for dynamic system with unknown inputs in the mean square error (MSE) sense is proposed by differential method

Summary

Introduction

The classic Kalman filtering (KF) [1] requires the model of the dynamic system is accurate. One widely adopted approach is to consider the unknown inputs as part of the system state and estimate both of them This leads to an augmented state Kalman filtering (ASKF). Its computational cost increases due to the augmented state dimension It is proposed by Friedland [2] in 1969 a two-stage Kalman filtering (TSKF) to reduce the computation complexity of the ASKF, which is optimal for the situation of a constant unknown input. Kalman filtering (CKF) can be accomplished, and the resulting state estimates are optimal in the MSE.

Problem Formulation

Optimal Estimation for the Remodeled System

Multisensor Fusion

Numerical Examples

Conclusions