An adaptive parametric estimation of space-time deterministic signal against unknown Gaussian noise background

Parametric estimation technique for deterministic space-time signals on the output of linear sensor array in the presence of white Gaussian noise with unknown covariance matrix is considered. For this scenario, the derived maximum likelihood statistics become invariant with respect to the structure of noise covariance matrix, i.e., using of derived statistics corresponds exactly to adaptive array processing. It was found that in the simplest case of one source and factorized spatial and time components of deterministic signal, the statistic can be represented exactly as the combination of two trivial statistics: the first one corresponds to conventional time matched filtering and adaptive beamforming with the weight vector obtained from empirical covariance matrix of snapshots (i.e., from observed mixture of noise and deterministic component), and the second is the same statistic derived for unknown shape of steering vector. A stochastic numerical simulation showed that the statistic proposed eliminates some estimate bias appearing for the adaptive beamformer with inverse covariance matrix of snapshots.