Recursive K-distribution parameter estimation

Recursive estimation of the parameter of the K-distribution is studied and tested. The probability density function (pdf) of the K-distribution is seen as a mixture pdf allowing the application of Titterington´s recursive expectation-maximization (EM) technique. Under mild conditions, the technique produces estimates that are strongly consistent and asymptotically normal. For the K-distribution, the complete data information matrix required by the recursive EM has an explicit form making the algorithm easy to implement. The algorithm is tested using K-distributed data with both constant and time-varying parameter. For the constant parameter case, recursive EM estimates are compared to numerical maximization of the likelihood. For the time-varying parameter case, recursive EM estimates are compared to estimates obtained using a fast routine from the literature and implemented by sliding a rectangular window over the observations.