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I am looking for a way to combine data from a compass and gyro in order to determine attitude after the fact. I will be working with a complete data set in which the 3D compass and gyro readings have been recorded at regular intervals, but I want to recover an estimate of attitude in post-processing.

I've considered simply using a Kalman filter, since they are so well documented, but would rather use something more appropriate to a case where the complete data set is known. I have a feeling the solution is "simply" a least squares problem, but I'm hoping someone here can point me in the direction of a paper or two dealing with this problem (or problems like it).

At this point, I'm not even sure what this filter would be called, so I'm having a hard time finding useful search terms. Any help would be appreciated.

Thanks so much!

Michael Cooper
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  • Hi Michael! I am just curios, did you find anything useful for Kalman smoother? As it turns out, the nonlinear regression I use is not appropriate for our problems and I am also considering the Kalman smoother. – Ali Jul 01 '11 at 20:14
  • I am just curious, what did you implement in the end? – Ali Jun 06 '12 at 08:02

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If you understand the Kalman filter in details, you can also implement the so-called Kalman smoother which operates on the complete data set.

However, let me warn you about one thing. There is no such thing as Kalman Filter for programmers. Kalman filter is difficult to understand. You won't be able to implement and use it correctly if you do not understand it.

My implementation is almost what you are looking for. I used accelerometer and gyroscopes but no compasses. It is based on this manuscript, read it first. The most detailed description I have at the moment is slides 29-32 in my presentation on sensor fusion. It is an open source project, and I plan to release an updated version of the solver in the upcoming weeks.

Community
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Ali
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  • Thanks. I'll take a look at those links. The math isn't a problem at all. My background is in physics and pure mathematics so, while it's been a while since I used some of the math, it comes back to me quickly. – Michael Cooper May 16 '11 at 18:25
  • OK. If you need further information, you will find me here. Good luck! – Ali May 16 '11 at 20:04
  • Hmm... The DCM draft seems pretty heavy on explanations of basic math, but light on application. I've found [this paper](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.16.9049) which describes a quaternion-based Kalman filter for fusing magnetic, acceleration and gyro data. Ideally, what I'm looking for is an article directed at a similar audience, but discussing a Kalman smoother of any kind. – Michael Cooper May 17 '11 at 18:08
  • Yes, the Kalman smoother should do it. Please share the link if you find something useful on the Kalman smoother. – Ali May 17 '11 at 20:03