Analysis of the adaptive matched filter algorithm for cases with mismatched clutter statistics

In the majority of adaptive radar detection algorithms, the covariance matrix for the clutter plus noise is estimated using samples taken from range cells surrounding the test cell. In a nonhomogeneous environment, this can lead to a mismatch between the mean of the estimated covariance matrix and the true covariance matrix for the test cell. Closed-form expressions are provided, which give the performance for such cases when the popular adaptive matched filter algorithm is used. The expressions are exact in some cases and provide useful approximations in others. To simplify the analysis, the samples from the surrounding range cells are assumed to be independent and identically distributed (i.i.d.), and these samples are assumed to be independent from the sample taken from the test cell. The performance depends on a small number of important parameters. These parameters describe which types of mismatches are important and which are not. Numerical examples are provided to illustrate how performance varies with each of the important parameters. Monte Carlo simulations are included that closely match the predictions of our equations. An airborne radar example is provided that demonstrates that covariance matrix mismatch can have a significant effect on performance in some practical cases.