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On the Steady State Performance of the Kalman Filter Applied to Acoustical Systems
IEEE Signal Processing Letters ( IF 3.9 ) Pub Date : 2020-01-01 , DOI: 10.1109/lsp.2020.3029703
Johannes Fabry , Stefan Kuhl , Peter Jax

The identification of transversal filters is important for numerous applications. In acoustical applications a first order Markov model is often used to describe the time-variant nature of transversal filters. The Kalman filter is the optimal unbiased estimator for such a Markov model. It inherently calculates the uncertainty of the current state estimate by its state error covariance matrix. In contrast to the broadband Kalman filter the covariance matrix of the exact Kalman filter depends on properties of the input signal. The single step covariance update of the exact Kalman filter is a discrete-time algebraic Riccati equation. We propose a solution for the steady state covariance matrix, which depends on the process parameters of the Markov model as well as properties of the input signal. It is derived based on the eigendecomposition of the covariance matrix and the autocorrelation matrix of the input signal. The proposed algorithm converges in few iterations and gives accurate results. We show how this result can be used to predict the steady state performance of the Kalman filter for system identification through numerical examples.

中文翻译:

卡尔曼滤波器应用于声学系统的稳态性能研究

横向过滤器的识别对于许多应用都很重要。在声学应用中,通常使用一阶马尔可夫模型来描述横向滤波器的时变特性。卡尔曼滤波器是这种马尔可夫模型的最佳无偏估计器。它固有地通过其状态误差协方差矩阵计算当前状态估计的不确定性。与宽带卡尔曼滤波器相比,精确卡尔曼滤波器的协方差矩阵取决于输入信号的特性。精确卡尔曼滤波器的单步协方差更新是离散时间代数 Riccati 方程。我们提出了稳态协方差矩阵的解决方案,它取决于马尔可夫模型的过程参数以及输入信号的属性。它是根据输入信号的协方差矩阵和自相关矩阵的特征分解推导出来的。所提出的算法在几次迭代中收敛并给出准确的结果。我们通过数值例子展示了如何使用该结果来预测卡尔曼滤波器的稳态性能以进行系统识别。
更新日期:2020-01-01
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