Unbiased Finite Impluse Response Filtering: An Iterative Alternative to Kalman Filtering Ignoring Noise and Initial Conditions

If a system and its observation are both represented in state space with linear equations, the system noise and the measurement noise are white, Gaussian, and mutually uncorrelated, and the system and measurement noise statistics are known exactly; then, a Kalman filter (KF) [1] with the same order as the system provides optimal state estimates in a way that is simple and fast and uses little memory. Because such estimators are of interest for designers, numerous linear and nonlinear problems have been solved using the KF, and many articles about KF applications appear every year. However, the KF is an infinite impulse response (IIR) filter [2]. Therefore, the KF performance may be poor if operational conditions are far from ideal [3]. Researchers working in the field of statistical signal processing and control are aware of the numerous issues facing the use of the KF in practice: insufficient robustness against mismodeling [4] and temporary uncertainties [2], the strong effect of the initial values [1], and high vulnerability to errors in the noise statistics [5]-[7].