Multichannel AR parameter estimation from noisy observations as an errors-in-variables issue

In various applications from radar processing to mobile communication systems based on CDMA for instance, M-AR multichannel processes are often considered and may be combined with Kalman filtering. However, the estimations of the M-AR parameter matrices and the covariance matrices of the additive noise and the driving process from noisy observations are key issues to be addressed. In this paper, we propose to solve this problem as an errors-in-variables problem. Thus, the noisy observation autocorrelation matrix compensated by a specific diagonal block matrix and whose kernel is defined by the M-AR parameters matrices must be positive semi-definite. Hence, the parameter estimation consists of searching every diagonal block matrix that satisfies this property, of reiterating this search for a higher model order and then of extracting the solution that belongs to both sets. The proposed algorithm outperforms existing methods, especially for low signal-to-noise ratio and when the variances of the additive noise are not necessarily the same on each channel.