Suboptimal Filter for Multisensor Linear Discrete-Time Systems with Observation Uncertainties

Abstract - The focus of this paper is the problem of recursive estimation for uncertain multisensor linear discrete-time systems. We herein propose a new suboptimal filtering algorithm. The basis of the proposed algorithm is the fusion formula for an arbitrary number of local Kalman filters. The proposed suboptimal filter fuses each local Kalman filter by weighted sum with scalar weights. This filter can be implemented in real time because the scalar weights do not depend on current observations in distinction to the optimal adaptive filter. The examples given, demonstrate the effectiveness and high precision of proposed filter. IndexTerms- Linear discrete-time system, multisensor, Kalman filter, fusion formula I. INTRODUCTION The consideration focused herein is the estimation of the state of a linear system with multisensor environment with uncertainties. Though there are many methods available for such kind of systems in the structure adaptation [1]-[3], we chose, for this paper, the partition method and Lainiotis-Kalman filter (LKF). It is composed of segregation of the original nonlinear filter into a collection of much simpler local Kalman filters (KF’s), where each local filter uses its own system model corresponding to each possible parameter value [1],[4]. The weighted sum of the local KF’s provides the optimal fusion estimate of the state of LKF. The problem with the LKF is that the optimal scalar weights depend on sensor observations which complicates the implementation of the LKF in real-time, knowing that the dimension of state vector and the number of sensors are large.