Time-Varying Autoregressive (TVAR) Models for Multiple Radar Observations

We consider the adaptive radar problem where the properties of the (nonstationary) clutter signals can be estimated using multiple observations of radar returns from a number of sufficiently homogeneous range/azimuth resolution cells. We derive a method for approximating an arbitrary Hermitian covariance matrix by a time-varying autoregressive model of order m, TVAR(m), that is based on the Dym-Gohberg band-matrix extension technique which gives the unique TVAR(m) model for any nondegenerate covariance matrix. We demonstrate that the Dym-Gohberg transformation of the sample covariance matrix gives the maximum-likelihood (ML) estimate of the TVAR(m) covariance matrix. We introduce an example of TVAR(m) clutter modeling for high-frequency over-the-horizon radar that demonstrates its practical importance