Adaptive EIV‐FIR filtering against coloured output noise by using linear prediction technique. Issue 1 (1st February 2018) - Tang, Tang; Jia, Lijuan; Lou, Jian; Tao, Ran; Wang, Yue
Abstract : The problem of finite impulse response (FIR) filtering in errors‐in‐variables (EIV) system is studied. Due to the input noise, traditional recursive least‐squares (RLS) algorithms are biased in EIV system. Most existing bias‐compensated approaches are proposed in the case that both the input–output noises are white Gaussian random processes. However, taking account of the situation where the output is corrupted by coloured noise, there are rare existing algorithms work well. Two bias‐compensated RLS algorithms with acceptable computational complexity are proposed, which can obtain unbiased real‐time filtering in non‐stationary system when the input noise is white while the output noise is coloured. Under the assumption that the input signal is a coloured process, linear prediction technique is used to estimate the sample of the input signal. Exploiting the statistical properties of the cross‐correlation function between the least‐squares error and the forward/backward prediction error, the input noise variance can be estimated and the bias can be compensated. Simulation results illustrate the good performance of the proposed algorithms.