Gaussian mixture modeling for bistatic measurements

Measurements from bistatic radar systems are known to become highly non-Gaussian in Cartesian coordinates as the target under track approaches the transmitter-receiver baseline. The distortion in the distribution is similar to the so-called contact-lens problem in monostatic radar, but the distortion is present for much shorter ranges and higher angle accuracies than in the typical monostatic case. In previous work, the authors demonstrated that a two-dimensional monostatic radar measurement can be modeled as a Gaussian mixture distribution with associated benefits in tracking performance. This paper extends the techniques used in the two-dimensional monostatic case to a two-dimensional bistatic radar system. A bistatic bias significance parameter is derived to describe classes of bistatic radar measurements whose true distribution exhibits equivalent Kullback-Leibler (KL) divergence from a single Gaussian approximation. The Expectation Maximization (EM) algorithm was applied to the problem of maximum-likelihood fitting a Gaussian mixture to the true distribution of a bistatic measurement. As in the monostatic radar case, this bias significance parameter can be used to build a lookup table that allows efficient mapping of the optimal Gaussian mixture approximation to the true distribution of a bistatic radar measurement.