Constructing numerically stable Kalman filter-based algorithms for gradient-based adaptive filtering
These MATLAB files accompany the following publication: Kulikova M.V., Tsyganova J.V. (2015) "Constructing numerically stable Kalman filter-based algorithms for gradient-based adaptive filtering", International Journal of Adaptive Control and Signal Processing, 29(11):1411-1426. DOI http://dx.doi.org/10.1002/acs.2552 The paper addresses the numerical aspects of adaptive filtering (AF) techniques for simultaneous state and parameters estimation (e.g. by the method of maximum likelihood). Here, we show that various square-root AF schemes can be derived from only two main theoretical results. These elegant and simple computational techniques replace the standard methodology based on direct differentiation of the conventional KF equations (with their inherent numerical instability) by advanced square-root filters (and its derivatives as well). 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.
Steps to reproduce
This archive includes the following files. - [run_demo_example1] produces the results in Example 1 (see the cited paper) - [run_demo_example2] produces the results in Example 2 (see the cited paper) - [run_test_score] compares two methods for the score evaluation (Diff_KF_conventional and Diff_KF_SRCF) - [Diff_QR] illustrates the computational scheme from Lemma 2 - [Diff_QL] illustrates the computational scheme from Lemma 1 - [Diff_KF_conventional] is the differentiated KF (conventional approach) - [Diff_KF_SRCF] is the differentiated square-root KF (illustrates how Lemma 2 can be used in practice for the score evaluation) Please provide proper acknowledgment of all uses of this code, i.e. cite to the corresponding article.