This talk introduces my joint work with engineers at Air Force Research Laboratory, Radar Signal Processing Branch. The first problem involves a statistical signal detection procedure, which assumes homogeneous covariance matrix for all the secondary data. We deal with inhomogeneity by a partitioning procedure, which screens out dissimilar secondary data prior to any detection. The partitioning statistic and its distribution will be used to derive P(CP), the probability of a correct partition. The procedure parameters can be found from P(CP) and be used to perform simulation studies and in data analysis.
The second problem estimates the unknown number of signals, which can be formulated as the difference between the number of the components in data vector and the multiplicity of the smallest eigenvalue of the covariance matrix. We propose a selection procedure to estimate the multiplicity of the smallest eigenvalue. For both problems, simulation results and data analysis on US Air Force Multi-Channel Airborne Radar Measurement (MCARM) collected by Westinghouse (now Northrop Grumman) will be presented to illustrate our theory.