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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Recursive Maximum Likelihood Algorithm for Dependent Observations
 IEEE transactions on signal processing 67 (2019), No.5, pp.13661381 ISSN: 00963518 ISSN: 00189278 ISSN: 00961620 ISSN: 1053587X ISSN: 19410476 

 English 
 Journal Article 
 Fraunhofer IIS () 
Abstract
A recursive maximumlikelihood algorithm (RML) is proposed that can be used when both the observations and the hidden data have continuous values and are statistically dependent between different time samples. The algorithm recursively approximates the probability density functions of the observed and hidden data by analytically computing the integrals with respect to the state variables, where the parameters are updated using gradient steps. A full convergence proof is given, based on the ordinary differential equation approach, which shows that the algorithm converges to a local minimum of the KullbackLeibler divergence between the true and the estimated parametric probability density functionsa result that is useful even for a missspecified parametric model. Compared to other RML algorithms proposed in the literature, this contribution extends the statespace model and provides a theoretical analysis in a nontrivial statistical model that was not analyzed so far. We further extend the RML analysis to constrained parameter estimation problems. Two examples, including nonlinear statespace models, are given to highlight this contribution.