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.