Adaptive EIV-FIR filtering against coloured output noise by using linear prediction technique

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.