Estimating number and parameters of signal components in presence of noise
Abstract
An algorithm is constructed for extimating the number and parameters of signal components in a signal noise mixture based on a minimum average risk criterion with special choice of cost function and a simplifying assumption on apriori distribution. Intuitively the number of signal components is expected to be the minimum most likely number not including false noise components. A cost function asymmetric with respect to the true number and parameter values is selected consisting of a principal part, a simple function of the number and signal component amplitudes and parameters and an additional term which is a constant multiplied by the sum of decision rules for a possible larger number of components. An increase of the probability of correct detection when the estimated number of signal components is increased by one is the measure of likelihood. The minimum average risk function is maximized by maximumlikelihood extimates and by a reasonable assumption of quasiuniform apriori distribution. Protection against overestimates is built into this algorithm since each addition of one to the estimated number of signal components increases the number of alternatives for selection of parameters while the error penalty for their number and values is assumed the same.
 Publication:

USSR Rept Electron Elec Eng JPRS UEE
 Pub Date:
 April 1985
 Bibcode:
 1985RpEEE....S...4K
 Keywords:

 Algorithms;
 Continuous Noise;
 Discrimination;
 Estimating;
 Parameter Identification;
 Signal Analysis;
 Signal Detection;
 Amplitudes;
 Inequalities;
 Maximum Likelihood Estimates;
 Probability Distribution Functions;
 Reliability;
 Signal To Noise Ratios;
 Communications and Radar