如何为扩展卡尔曼滤波器估计 R 中的参数

Question

Any one knows how to estimate parameters in R for extended KF? please educate me, thanks. I tried KF before but didn't work out for extended KF? is there existing package?

Specifically, my problem is: Y(t) = F(X(t)) + w1, X(t) = alpha + beta * X(t-1) + w2,

where F is a nonlinear function, w1 and w2 are assumed to be iid, how can we estimate the parameters alpha, beta, and the several paramters in function F() then.

Thanks a lot.

Answer 1

R depends on your measurements and the way you take them, not on the phisical model. Should be diagonal.

As part of your filter, you have to calculate innovation . Just have a look to the innovation (error of the expected measurement and the actual measurement). That order of error should be ok for your R matrix.

Another way of thinking is that R is diagonal of the (measurement noise)^2. If you are dealing with camera and it is well calibrated, error shoulden't be more than 2 pixels. Try to give values fromo 1 to 3.6. It should be experimental, but it is also important that you know what parameters mean.

Answer 2

Perhaps this >>http://www.stat.berkeley.edu/~brill/Stat248/kalmanfiltering.pdf >> can help you. It is an overview of r-packages for Kalman filter and there seems to be a part for the extended version of KF inside of sspir package.