I have a linear discrete time-varying State-Space model, I am trying to estimate the slow-varying parameters (delta variation of parameters for K+1,K is around 10^-10). normal KF wouldn't work for parameter estimation but EKF and recursive methods would.
So my question which of these method would detect and estimate this small variation of my parameters (keeping in mind that i have more than 1 parameter and 3 states).
Thank you
Recursive Least-Squares and Kalman Filter (steady-state gain) are basically the same thing. I would go with EKF with a careful tuning of weights.
Bruno Martins Lima Thank you, yes in fact, EKF works but with some modifications due to the negligible variations of parameters. And I also tried the DKF method which gives acceptable results.
You can see each update step of the EKF as one iteration of the Gaus-Newton algorithm involved in the solution of the least-squares problems (unfortunately I do not have present anymore the reference in which I read this).
However, you can expect much more robustness from the batch estimator. If correctly initialized, it is easier to configure it than the EKF, in which the (in my opinion) non-intuitive tuning of the process and measurement noises, the initial covariance matrices and even the sampling rate makes it difficult to prevent it from diverging from the true values of the parameters/states, depending on the model.
If you have the computational power, I would suggest to use Moving-Horizon Estimation. As long as the arrival cost is reasonably tuned, you have a very robust joint state- and parameter estimation scheme.
Good luck.
Roberto Lemoine-Nava Thank you for the helpful information.
Regards
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