Effect of Faults on Kalman Filter of State Vectors in Linear Systems

Abstract

Kalman filter (KF) is composed of a set of recursion algorithms which can be used to estimate the optimal state of the linear system, and widely used in the control system, signal processing and other fields. In the practical application of the KF, it is an unavoidable problem that how faults or anomalies are infectious to the estimation value of state vectors in the linear system, which must be paid much attention to and solved down. In this paper, the effect of sensor faults and control input anomalies on the Kalman filtering values of state vectors is discussed, the transmission relationship is established to analyze the estimation deviation of state vectors which comes from pulse or step faults/anomalies, and a sufficient condition is deduced for the convergence of the estimation deviation of state vectors; Four different system models with 3-dimension state vector and 2-dimension observation vector are selected for simulation calculation and comparative analysis, simulation results show that sensor faults and control input anomalies in linear systems may cause significant deviations in the estimation value of state vectors for a long time, and there are distinct differences in the estimation value of state vectors. The research results provide a certain theoretical reference for us to analyze system fault types and to identify fault.