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I would like to implement Kalman filter scheme with two different kind of sensors - say 9DOF IMU (gyro/accelerometer/magnetometer) and GPS sensor (position/velocity/altitude).

Problem is, as i understand, classic Kalman and Extended Kalman filter schemes require sensor measurements to be synchronized. But GPS sensor measurements could be obtained ones/two times a second, as opposed to gyro/accelerometer/magnetometer measurements which available 100 times a second.

So my question, how to fuse sensors with different sampling rates together?

HumpfreyJordan
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  • The usage of the tag "filters" is completely incorrect. Also, this is not mathematics. –  Feb 28 '14 at 23:32
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    Kalman filters are certainly part of applied math. For example, Gilbert Strang discusses them in his book Introduction to Applied Math. Related question: https://stats.stackexchange.com/questions/86332/how-to-handle-incomplete-data-in-kalman-filter – littleO Aug 04 '17 at 05:13

3 Answers3

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This is pretty much an engineering question, rather than a mathematics one. But fortunately, this is basically already solved in many books like Farrell or Titterton. Bad thing is, the answer is rather long.

To give you a heads up:

1-Magnetometer measurements are rarely used in practice for Aided Navigation, their quality is usually way too poor to fuse directly in a Kalman Filter. They may have other uses that you might want to analyze separately.

2-INS devices, you shouldn't require the user to provide you with estimated acceleration (either linear or angular). Instead, IMU measurements (angular rate and linear acceleration) are generally used directly for propagation of states, with Kalman corrections being used for GPS measurements to avoid divergence.

3-Normally, what you should do when the rate of sensors do not match, is that you should propagate states at a base sample rate (say 10Hz), and depending on your implementation you may propagate covariance only between measurements or all the time. Once a measurement arrives, you perform the Kalman correction, updating your covariance and your state.

Mefitico
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So, from my understanding in your motion model will have inputs from some sensors (gyro/accelerometer/magnetometers) and your observer will be only the GPS? The way I understand, the Kalman Filter should work in the frequency of the observer. In any other configuration you would be accumulating errors from your motion model and at some point your filter may diverge.

Daniel Lucena
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Well indeed, that's much more an engineering problem rather (or better, before) than mathematical.
Whatever manipulation you have to do on the data, first you must consider how much variable in time they are, how much noisy, and how many data of each you can memorize and work with.

That will determine the best trade-off among interpolating the slower sensor / filtering the quicker, in consideration of the advantage to get a more or less frequent output.

G Cab
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