How to improve the reliability of KF estimation? Sorry for boring you my dear friends. 

Rcently I'm taking advatage of the state estimates X, outcoming from a Kalman Filter, with the their statistical information, i.e. Matrix of covariance P, to implement other studies.

Theories and practical studies have shown that the quality of KF state estimates is severely depending on the 'correctness' of system modeling, while unfortunately the true situation is unknown. Generally, the KF is either too optimistic or too pessimistic about the state accuracy, i.e. the state covariance matrix P.

The question is therefore, is there any method to reflect the variation of state estimates or the reality on the state covariance matrx P?

Thank you in advance for taking a look!
For very long times, ive used the KF as a parametrized estimator, training the noise matrices, fitting them standard conditions. Just like a "neural net" on the covariance noises. And you have killer results ;).

And the method?... I've applied any standard nonlinear, gradient descent optimization algorithm, such as Newton Raphson, Levenberg Marquardt...

Sweet, simple, unexpected, and excelent results :). Though unpublishable xd.

If you have data, we can try them...