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I am implementing a Kalman filter for GPS/INS data, but I do not have data that can be considered "true" (i.e. a deterministic state). The only data I have for the problem is the collection of measurements available to me, which are naturally corrupted. I wish to test that my filter error is zero mean and passes the consistency, containment, and NEES tests from Bar-Shalom et al. However, these tests require a deterministic truth, from which one computes the error based on the difference between estimated state and true state, leaving (ideally) a white process.

How can I test the efficacy of my filter without a deterministic truth?

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  • $\begingroup$ This may have been a dumb question...my apologies if so. en.wikipedia.org/wiki/… $\endgroup$
    – Matt
    Dec 26 '20 at 20:15
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    $\begingroup$ Usually, if you need to test your model and need “true” state and noisy data that represents it, you simulate it by yourself by creating the true state data and adding noise to it. How you do it depends on what exactly are the properties of the model & simulation you want to achieve. $\endgroup$
    – Tim
    Dec 27 '20 at 9:40
  • $\begingroup$ @Tim thank you for the reply. I totally thought about the filter the wrong way and this helped. Thanks. $\endgroup$
    – Matt
    Jan 3 at 19:15
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To my understanding you can use the Normalized Innovation Error Squared (NIS) Metric which is similar to NEES, but instead of using P it uses S which is the innovation covariance. And instead of using the ground truth, NIS uses the residuals (measured - predicted). These two sources helped me. Weak in the NEES?: Auto-tuning Kalman Filters with Bayesian Optimization Wikipedia for Kalman Filters

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  • $\begingroup$ Much appreciated! This will be an interesting paper for me to read this weekend. $\endgroup$
    – Matt
    May 21 at 19:04

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