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67 Detection: Determining the Number of Sources

The processing of signals received by sensor arrays generally can be separated into two problems: (1) detecting the number of sources and (2) isolating and analyzing the signal produced by each source. | Williams D.B. Detection Determining the Number of Sources Digital Signal Processing Handbook Ed. Vijay K. Madisetti and Douglas B. Williams Boca Raton CRC Press LLC 1999 1999 by CRC Press LLC 67 Detection Determining the Number of Sources Douglas B. Williams Georgia Institute of Technology 67.1 Formulation of the Problem 67.2 Information Theoretic Approaches AIC and MDL EDC 67.3 Decision Theoretic Approaches The Sphericity Test Multiple Hypothesis Testing 67.4 For More Information References The processing of signals received by sensor arrays generally can be separated into two problems 1 detecting the number of sources and 2 isolating and analyzing the signal produced by each source. We make this distinction because many of the algorithms for separating and processing array signals make the assumption that the number of sources is known a priori and may give misleading results if the wrong number of sources is used 3 . A good example are the errors produced by many high resolution bearing estimation algorithms e.g. MUSIC when the wrong number of sources is assumed. Because in general it is easier to determine how many signals are present than to estimate the bearings of those signals signal detection algorithms typically can correctly determine the number of signals present even when bearing estimation algorithms cannot resolve them. In fact the capability of an array to resolve two closely spaced sources could be said to be limited by its ability to detect that there are actually two sources present. If we have a reliable method of determining the number of sources not only can we correctly use high resolution bearing estimation algorithms but we can also use this knowledge to utilize more effectively the information obtained from the bearing estimation algorithms. If the bearing estimation algorithm gives fewer source directions than we know there are sources then we know that there is more than one source in at least one of those directions and have thus .