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

© The Institution of Engineering and Technology
Received 29/11/2016, Accepted 11/08/2017, Revised 07/07/2017, Published 16/08/2017

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.

Inspec keywords: Gaussian processes; adaptive filters; FIR filters; random processes

Other keywords: linear prediction technique; input–output noises; least-squares error; computational complexity; forward-backward prediction error; coloured output noise; errors-in-variables system; finite impulse response filtering; statistical properties; adaptive EIV-FIR filtering; white Gaussian random processes

Subjects: Filtering methods in signal processing; Other topics in statistics

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