MatLab: On efficient parametric identification methods for linear discrete stochastic systems

These MATLAB files accompany the following publication: Tsyganova Yu.V., Kulikova M.V. (2012) "On efficient parametric identification methods for linear discrete stochastic systems", Automation and Remote Control, 73(6): 962-975. DOI: http://dx.doi.org/10.1134/S0005117912060033 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 array square-root covariance KF implementation (Kaminski, 1971). 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.

本配套MATLAB文件对应如下发表成果：Tsyganova Yu.V.、Kulikova M.V.（2012）《线性离散随机系统的高效参数辨识方法研究》，载于《自动化与遥控》（Automation and Remote Control）73卷第6期，第962-975页。DOI：http://dx.doi.org/10.1134/S0005117912060033。
本文围绕基于梯度的自适应卡尔曼滤波（Kalman Filtering, KF）技术实现最大似然估计的数值相关问题展开论述，该技术可同时完成状态与参数的联合估计。文中推导了一种针对对数似然函数及其梯度计算的稳定平方根方法，用以替代基于传统卡尔曼滤波方程直接求导的标准范式——该传统方法存在固有数值不稳定性。本方法基于阵列平方根协方差卡尔曼滤波的实现思路（Kaminski, 1971）。
此处提供的代码仅用于教学演示用途。尽管已经过严谨测试，但无法保证其完全无错误，因此不可将其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。