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.本MATLAB代码文件配套以下发表论文：Kulikova M.V.、Tsyganova J.V.（2015）《面向基于梯度自适应滤波的数值稳定型卡尔曼滤波算法构建》，刊载于《国际自适应控制与信号处理期刊》（International Journal of Adaptive Control and Signal Processing），第29卷第11期，页码1411-1426，DOI：http://dx.doi.org/10.1002/acs.2552。 该论文聚焦于面向状态与参数联合估计（例如采用极大似然估计法）的自适应滤波（Adaptive Filtering, AF）技术的数值特性问题。本文证明，各类平方根自适应滤波方案仅可通过两项核心理论结论推导得到。这些简洁优雅的计算技术，替代了基于传统卡尔曼滤波（Kalman Filter, KF）方程直接求导的标准方法——该传统方法存在固有的数值不稳定性——转而采用先进的平方根滤波（及其衍生算法）。 此处提供的代码仅用于教学演示用途。本代码已经过细致测试，但不保证完全无错误，因此不可仅依靠本代码作为解决问题的唯一依据。若您在研究中使用本代码，请引用上述对应论文。