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The Schmidt–Kalman Filter is a modification of the Kalman filter for reducing the dimensionality of the state estimate, while still considering the effects of the additional state in the calculation of the covariance matrix and the Kalman gains. A common application is to account for the effects of nuisance parameters such as sensor biases without increasing the dimensionality of the state estimate. This ensures that the covariance matrix will accurately represent the distribution of the errors.

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  • Schmidt–Kalman filter (en)
  • 施密特-卡尔曼滤波器 (zh)
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  • 施密特-卡尔曼滤波器（Schmidt–Kalman Filter），是修改版的卡尔曼滤波，減少狀態估測的維度，不過仍有額外的狀態可以計算协方差矩阵及卡尔曼增益。常見的應用是考量像是傳感器誤差等的影響，但又不增加狀態估測的維度，因此可以確保协方差矩阵可以準確的呈現誤差的分析情形。 不增加狀態空間維度，而使用施密特-卡尔曼滤波器的主要好處是減少運算的複雜度。因此可以用在即時系統的濾波中。另外一個使用施密特-卡尔曼滤波器的場合是殘餘誤差無法觀測的情形下，也就是說，無法從量測資料中將誤差效果獨立出來的情形。此時，施密特-卡尔曼滤波器是強健性的濾波方式，不去估計偏差的大小，但在真實誤差分析中去追蹤偏差的影響。 若是非線性系統，可以在目前的平均值及协方差估計值附近，將觀測模型及狀態傳遞模型線性化，類似的作法。 (zh)
  • The Schmidt–Kalman Filter is a modification of the Kalman filter for reducing the dimensionality of the state estimate, while still considering the effects of the additional state in the calculation of the covariance matrix and the Kalman gains. A common application is to account for the effects of nuisance parameters such as sensor biases without increasing the dimensionality of the state estimate. This ensures that the covariance matrix will accurately represent the distribution of the errors. (en)
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  • The Schmidt–Kalman Filter is a modification of the Kalman filter for reducing the dimensionality of the state estimate, while still considering the effects of the additional state in the calculation of the covariance matrix and the Kalman gains. A common application is to account for the effects of nuisance parameters such as sensor biases without increasing the dimensionality of the state estimate. This ensures that the covariance matrix will accurately represent the distribution of the errors. The primary advantage of utilizing the Schmidt–Kalman filter instead of increasing the dimensionality of the state space is the reduction in computational complexity. This can enable the use of filtering in real-time systems. Another usage of Schmidt–Kalman is when residual biases are unobservable; that is, the effect of the bias cannot be separated out from the measurement. In this case, Schmidt–Kalman is a robust way to not try and estimate the value of the bias, but only keep track of the effect of the bias on the true error distribution. For use in non-linear systems, the observation and state transition models may be linearized around the current mean and covariance estimate in a method analogous to the extended Kalman filter. (en)
  • 施密特-卡尔曼滤波器（Schmidt–Kalman Filter），是修改版的卡尔曼滤波，減少狀態估測的維度，不過仍有額外的狀態可以計算协方差矩阵及卡尔曼增益。常見的應用是考量像是傳感器誤差等的影響，但又不增加狀態估測的維度，因此可以確保协方差矩阵可以準確的呈現誤差的分析情形。 不增加狀態空間維度，而使用施密特-卡尔曼滤波器的主要好處是減少運算的複雜度。因此可以用在即時系統的濾波中。另外一個使用施密特-卡尔曼滤波器的場合是殘餘誤差無法觀測的情形下，也就是說，無法從量測資料中將誤差效果獨立出來的情形。此時，施密特-卡尔曼滤波器是強健性的濾波方式，不去估計偏差的大小，但在真實誤差分析中去追蹤偏差的影響。 若是非線性系統，可以在目前的平均值及协方差估計值附近，將觀測模型及狀態傳遞模型線性化，類似的作法。 (zh)
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