A recursive total least squares algorithm for deconvolution problems

Deconvolution problems are encountered in signal processing applications where an unknown input signal can only be observed after propagation through one or more noise corrupted FIR channels. The first step in recovering the input usually entails an estimation of the FIR channels through training based or blind algorithms. The 'standard' procedure then uses least squares estimation to recover the input. A recursive implementation with constant computational cost is based on the Kalman filter. In this paper we focus on a total least squares based approach, which is more appropriate if errors are expected both on the output samples and the estimates of the FIR channels. We will develop a recursive total least squares algorithm (RTLS) which closely approximates the performance of the non-recursive TLS algorithm and this at a much lower computational cost.