Identifying radar secondary data for signal detection

In signal detection, one is interested in the problem of detection of a given radar signal s which is a complex vector in the presence of noise in transmission. The signal may be a set of voltages that an EM wave from the selected search directions induces on a number of receiving elements. The actual observed data Y may be a pure noise vector n or the signal s plus a noise vector n. It is assumed that the noise follows a complex multivariate normal distribution with mean O and covariance matrix Σ. Statistically, the model can be described as Y=s+n where s is a specific signal and n is a noise random vector. The goal is to test the null hypothesis that Y=n versus the alternative hypothesis that Y=s+n. Reed et al. (1974) discussed an adaptive procedure for the above detection problem in which two sets of input data are used, which are called the primary and secondary data. A radar receives primary data Y₀ which may or may not contain a signal, and secondary data Y₁,Y₂,...,Y_n which are assumed to contain only noise, independent of and statistically identical to the noise components of the primary data. The goal is to test H₀:μ=O versus H₁:μ=s where μ is the population mean of Y₀. Kelly (1986) used the likelihood ratio principle to derive a test statistic for the above hypothesis testing problem. Chen and Wicks (1999) proposed a selection procedure which compares the covariance matrices of the secondary data with that of the primary data. It is used to identify and eliminate those observations that have a different covariance structure from the secondary data. It retains homogeneous radar data for further investigation. As described in Chen and Wicks (1999), this procedure can be applied prior to the step of estimating the covariance matrix of the secondary data in Kelly (1986). The selection procedure is discussed together with a simulation study.