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?