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小木虫论坛-学术科研互动平台 » 专业学科区 » 信息科学 » 控制工程 » 卡尔曼滤波的增益如何离线求出？
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xuh1991

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[求助] 卡尔曼滤波的增益如何离线求出？

卡尔曼滤波的增益表达式与观测数据无关，最终会收敛于一个定值，那么如何求解这个定值呢？是可以直接求得解析结果呢？还是利用数值求解方法求解？@mchen_6431
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1楼 2016-05-17 16:26:39
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messi01

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卡尔曼滤波分为时间更新和量测更新两部分，滤波增益的计算属于时间更新，它的具体计算不需要量测量，你可以看下增益的计算式子，就明白了

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2楼2016-05-19 23:37:59
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Sache

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For LTI Systems (this seems to be the case), the Kalman filter gain matrix can be computed off-line. To this end, a Riccati eq. should be solved. This is standard and can found in any textbook on the topic.
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3楼2016-05-20 13:06:40
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Sache

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4楼: Originally posted by xuh1991 at 2016-05-20 15:39:29
Can you recomand one textbook about how to solve the Riccati eq..I am puzzled by the problem for nearly one month and I want to know if there exist a closed-form expression for  the equation.Your va ...

In MATLAB, one can find standard solutions für Riccati eqs. There is no a simple closed-form (if solutions of eigenvalue-/-vector problems are not considred as a closed-form).

In most textbooks on robust control theory, solutions of Riccati eqs. can be found.
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xuh1991
5楼2016-05-20 19:36:28
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水灵小白菜

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你找本现代信号处理书，我记得有推导公式和算法
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10楼2016-05-24 11:22:51
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xuh1991

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3楼: Originally posted by Sache at 2016-05-20 13:06:40
For LTI Systems (this seems to be the case), the Kalman filter gain matrix can be computed off-line. To this end, a Riccati eq. should be solved. This is standard and can found in any textbook on the ...

Can you recomand one textbook about how to solve the Riccati eq..I am puzzled by the problem for nearly one month and I want to know if there exist a closed-form expression for  the equation.Your valuable advice will be highly appreciated and thank you！

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4楼2016-05-20 15:39:29
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xuh1991

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引用回帖:
5楼: Originally posted by Sache at 2016-05-20 19:36:28
In MATLAB, one can find standard solutions für Riccati eqs. There is no a simple closed-form (if solutions of eigenvalue-/-vector problems are not considred as a closed-form).

In most textbooks ...

Thank you!
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6楼2016-05-21 14:40:54
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xuh1991

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引用回帖:
5楼: Originally posted by Sache at 2016-05-20 19:36:28
In MATLAB, one can find standard solutions für Riccati eqs. There is no a simple closed-form (if solutions of eigenvalue-/-vector problems are not considred as a closed-form).

In most textbooks ...

I have one more question.Could you recomand some papers or textbooks about How the covariance matrices Q and R influence the performance of Kalman filter?
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7楼2016-05-22 21:23:23
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Sache

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7楼: Originally posted by xuh1991 at 2016-05-22 21:23:23
I have one more question.Could you recomand some papers or textbooks about How the covariance matrices Q and R influence the performance of Kalman filter?...

Sorry, I cannot, although there are definitively discussions on this topic. Q and R are co-variance matrices of the process and measurement noises. Uncertainty in R and Q would cause performance degradation. But, the estimation is still unbiased.
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8楼2016-05-23 12:30:27
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ShawJoe

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有没有资料？

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9楼2016-05-24 08:35:13
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