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 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.