Analysis of discrete-time Kalman filtering under incorrect noise covariances

Sangsuk-Iam S.; Bullock T.E.

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Analysis of discrete-time Kalman filtering under incorrect noise covariances

机译：不正确的噪声协方差下的离散时间卡尔曼滤波分析

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Analysis tools are developed that can be effectively used to study the performance degradation of a filter when incorrect models of the state and measurement noise covariances are used. For a linear time-variant system with stationary noise processes, it is shown that under certain stability conditions on the system model, the one-step prediction error covariance matrix will converge to a steady-state solution even when the filter gain is not optimal. On the other hand, if the state transition matrix has an unreachable mode outside a unit circle, then the modeling errors in the noise covariances may cause the filter to diverge. Bounds on the asymptotic filter performance are computed when the range of errors in the noise covariance matrices are known. Using simple examples, insights into the behavior of a Kalman filter under nonideal conditions are provided.

机译：开发了分析工具，当使用状态和测量噪声协方差的错误模型时，可以有效地用于研究滤波器的性能下降。对于具有平稳噪声过程的线性时变系统，表明在系统模型上的某些稳定性条件下，即使滤波器增益不是最佳的，单步预测误差协方差矩阵也会收敛到稳态解。另一方面，如果状态转移矩阵在单位圆之外具有不可到达的模式，则噪声协方差中的建模误差可能导致滤波器发散。当已知噪声协方差矩阵的误差范围时，计算渐近滤波器性能的界限。使用简单的示例，可以洞悉非理想条件下卡尔曼滤波器的行为。

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《IEEE Transactions on Automatic Control》 |1990年第12期|P.1304-1309|共6页
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Sangsuk-Iam S.; Bullock T.E.;
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1. Comparative Study between the Discrete-Frequency Kalman Filtering and the Discrete-Time Kalman Filtering with Application in Noise Reduction in Speech Signals [J] . Leandro Aureliano da Silva, Gilberto Arantes Carrijo, Eduardo Silva Vasconcelos, Journal of electrical and computer engineering . 2018,第PTa1期

机译：离散频率卡尔曼滤波与离散时间卡尔曼滤波在语音信号降噪中的比较研究
2. Optimal Distributed Kalman Filtering Fusion With Singular Covariances of Filtering Errors and Measurement Noises [J] . Song E., Xu J., Zhu Y. IEEE Transactions on Automatic Control . 2014,第5期

机译：具有滤波误差和测量噪声奇异方差的最优分布式卡尔曼滤波融合
3. Robust Kalman-Type Filter for Non-Gaussian Noise: Performance Analysis With Unknown Noise Covariances [J] . Fakoorian Seyed, Mohammadi Alireza, Azimi Vahid, Journal of Dynamic Systems, Measurement, and Control . 2019,第9期

机译：用于非高斯噪声的强大卡尔曼型过滤器：具有未知噪声CoviRA的性能分析
4. Divergence Of The Discrete-time Kalman Filter Under Incorrect Noise Covariances For Linear Periodic Systems [C] . Sangsuk-Iam, S. . 2001

机译：线性周期系统在不正确的噪声协方差下的离散时间卡尔曼滤波器的发散
5. Determination of noise covariances for extended Kalman filter parameter estimators to account for modeling errors. [D] . Garcia-Velo, Juan Bautista. 1997

机译：确定扩展卡尔曼滤波器参数估计器的噪声协方差，以解决建模误差。
6. Adaptive Unscented Kalman Filter for Target Tracking with Unknown Time-Varying Noise Covariance [O] . Baoshuang Ge, Hai Zhang, Liuyang Jiang, 2019

机译：具有未知时变噪声协方差的目标跟踪的自适应无味卡尔曼滤波器
7. Comparative Study between the Discrete-Frequency Kalman Filtering and the Discrete-Time Kalman Filtering with Application in Noise Reduction in Speech Signals [O] . Leandro Aureliano da Silva, Gilberto Arantes Carrijo, Eduardo Silva Vasconcelos, 2018

机译：不同频率卡尔曼滤波与分立时Kalman滤波的比较研究，在语音信号中的噪声减少中的应用

Analysis of discrete-time Kalman filtering under incorrect noise covariances

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