Wrong equation in the Kalman Filter document (AN5023) ?

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Wrong equation in the Kalman Filter document (AN5023) ?

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z258_14
Contributor I

Hi, I am trying to work out the math and possibly come up with a simpler update algorithm. My question is about the document named AN5023 v2p0.pdf which describes the EKF used for the Sensor Fusion. Equation (55), relates the a priori error in the angular speed to the apriori error in the gyrometer bias. The second equality does not seem correct, using equation (49), the w_{b,k} term in the final equation should be omitted. In any case, this may not matter much, as it only affects the covariance matrix (with a fixed scaling). But it would be good if it gets corrected.

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markpedley
NXP Employee
NXP Employee

I'm not sure I agree with you. Equation (49) follows algebraically from its predecessors and makes intuitive sense since it's the noise (change) in the gyro offset random walk from sample to sample that degrades the a priori estimate for iteration k from the a posteriori estimate from iteration k-1. Similarly the terms in equation (55) make physical sense. I would agree that in practice it's difficult to separate out some of the noise terms from each other. Zero mean white noise in the gyro offset is indistinguishable from zero mean gyro sensor noise for example in that the net result is also white.

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z258_14
Contributor I

Hi, thanks for the follow up. Maybe i was not clear. I am not debating on the interpretation of the equations and/or their physical meanings. You can follow the very simple algebra on those equations and you will see that the second part of equation 55 is not correct. I was just stating it out of courtesy because you have prepared a self-sufficient set of highly useful documents along with open source codes and it would be great to make them more complete and free of errors. In any case, thanks a lot for sharing your sensor fusion algorithms with the Internet community.

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michaelsmorto
Contributor IV

I know that this is an old post but I have been trying to find a copy of an5023 but haven't had any luck.  Can you please post a link or make it an attachment.

thanks 

mike

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michaelestanley
NXP Employee
NXP Employee

Mike,

AN5016 through AN5023 are bundled with the Sensor Fusion components of ISSDK included in K22F and K64F SDK builds at Welcome to MCUXpresso | MCUXpresso Config Tools .  The ISSDK option needs to be selected when you build an SDK.  To save you time, I'll post a copy to this space momentarily.

Regards,

Mike Stanley

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michaelsmorto
Contributor IV

Mike.  Thanks for posting the doc and pointing me to where they.  I did find them in the sensor fusion directory. The version I have is dated 2015

thanks

Mike

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