Maximum-entropy spectral analysis of radar clutter

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

“…Even in conventional (single antenna beam) search radars, radar returns from adjacent range cells give multiple clutter observations (radar signal backscattered by terrain or sea surface) that are typically treated as independent observations of the same clutter process. Traditionally, clutter returns have been modeled as observations of a stationary process, then, after Burg's famous work [3], maximum-entropy spectral estimation methods (MEMs) were developed for clutter modeling and adaptive estimation [4], [5]. While the ergodicity of a stationary model theoretically allows spectral estimation with a conventional single observation (one range data train collected over the coherent integration time [CIT]), for a long time researchers have been using adjacent range cells for identifying the stationary AR clutter model [5].…”

“…Traditionally, clutter returns have been modeled as observations of a stationary process, then, after Burg's famous work [3], maximum-entropy spectral estimation methods (MEMs) were developed for clutter modeling and adaptive estimation [4], [5]. While the ergodicity of a stationary model theoretically allows spectral estimation with a conventional single observation (one range data train collected over the coherent integration time [CIT]), for a long time researchers have been using adjacent range cells for identifying the stationary AR clutter model [5]. According to Haykin et al [5], because of the discontinuity in time between the pertinent data segments, "the segments cannot be simply combined to produce one long data record to be used as input for the usual MEM algorithm," which made spatial averaging that "involves using data segments from adjacent resolution cells" [5] an important means to overcome the discontinuity problem.…”

“…While the ergodicity of a stationary model theoretically allows spectral estimation with a conventional single observation (one range data train collected over the coherent integration time [CIT]), for a long time researchers have been using adjacent range cells for identifying the stationary AR clutter model [5]. According to Haykin et al [5], because of the discontinuity in time between the pertinent data segments, "the segments cannot be simply combined to produce one long data record to be used as input for the usual MEM algorithm," which made spatial averaging that "involves using data segments from adjacent resolution cells" [5] an important means to overcome the discontinuity problem. Note that the combined spatial and temporal averaging suggested in [5] requires both stationarity (in time) and homogeneity (in space) for the clutter returns.…”

“…According to Haykin et al [5], because of the discontinuity in time between the pertinent data segments, "the segments cannot be simply combined to produce one long data record to be used as input for the usual MEM algorithm," which made spatial averaging that "involves using data segments from adjacent resolution cells" [5] an important means to overcome the discontinuity problem. Note that the combined spatial and temporal averaging suggested in [5] requires both stationarity (in time) and homogeneity (in space) for the clutter returns. Modern radar applications cannot guarantee both these assumptions.…”

“…It deals with (ML) covariance matrix estimation within the set of matrices, given the i.i.d. training samples (5) If such an estimate is available, then its quality in the adaptive filter (antenna) context is measured by the statistical properties of the random SNR loss factor with respect to the clairvoyant optimum filter (3) [8] (6) When the true covariance matrix is indeed a matrix, i.e. (7) then the loss factor accounts for only the losses associated with the finite sample support , since for any consistent estimate (8) and so (9) Whereas the ML covariance matrix estimate is traditionally used as a substitute for the unknown exact covariance matrix for both adaptive filters [8] and adaptive detectors [9], [10], it is a fact that (from their performance viewpoint) ML estimates have not been theoretically justified, especially for small i.i.d.…”