Estimation of multichannel TVAR parameters from noisy observations based on an evolutive method

The multichannel time-varying autoregressive (M-TVAR) model is used in various applications such as radar processing, mobile communications and econometric time series. In that case, the M-TVAR parameter matrices are usually estimated by extending the evolutive method, initially proposed by Grenier in the 80ies for the scalar case. In that case, the time-varying coefficients of each matrix are expressed as weighted combinations of pre-defined basis functions. However, the estimation of the M-TVAR parameter matrices from noisy observations is a still key issue to be addressed. In this paper, we propose an effective evolutive method to estimate M-TVAR matrices from noisy observations. We suggest viewing the weight estimation from noisy observations as an errors-in-variables issue. Despite its high computational cost, the approach has the advantage of also providing the covariance matrix of both the driving process and the additive noise. Simulation results point out the relevance of the approach.