MatLab: Maximum likelihood estimation via the extended covariance and combined square-root filters
Description
These MATLAB files accompany the following publication: Kulikova M. (2009) "Maximum likelihood estimation via the extended covariance and combined square-root filters", Mathematics and Computers in Simulation 79(5):1641-1657. DOI: http://dx.doi.org/10.1016/j.matcom.2008.08.004 The paper addresses the numerical aspects of the maximum likelihood estimation by gradient-based adaptive Kalman filtering (KF) techniques (for simultaneous state and parameters estimation). Here, we derive a stable square-root method for the log LF and its gradient evaluation that replaces the standard methodology based on direct differentiation of the conventional KF equations (with their inherent numerical instability). The method is based on the extended square-root covariance KF implementation (P.Park and T.Kailath, 1995). The differentiated combined square-root algorithm is not presented here. The codes have been presented here for their instructional value only. They have been tested with care but are not guaranteed to be free of error and, hence, they should not be relied on as the sole basis to solve problems. If you use these codes in your research, please, cite to the corresponding article.
Files
Steps to reproduce
This archive includes the following files. •[run_test_score] compares two methods for the score evaluation (Diff_KF_conventional and Diff_KF_eSRCF) •[Diff_KF_conventional] is the differentiated KF (conventional approach) •[Diff_KF_eSRCF] is the differentiated extended square-root KF (the new method developed in the paper) Please provide proper acknowledgment of all uses of this code, i.e. cite to the corresponding article.