Deciding on the covariance for a Kalman Filter matrixes

I am beginning to explore using probability in my robotics applications. My goal is to progress to full SLAM, but I am starting with a more simple Kalman Filter to work my way up.

I am using Extended Kalman Filter, with state as [X,Y,Theta]. I use control input [Distance, Vector], and I have an array of 76 laser ranges [Distance,Theta] as my measurement input.

I am having trouble knowing how to decide on the covariance to use in my Gaussian function. Because my measurements are uncertain (The laser is about 1cm accurate at < 1meter, but can be up to 5cm accurate at ranges higher) I do not know how to create the 'function' to estimate the probability of this. I know this function is supposed to 'linearize' to be used, but I'm not sure how to go about this.开发者_高级运维

I am reasonably confident on how to decide on the function for my state Gaussian, I am happy to use a plain old mean=0,variance=1 on this.. This should work no? I would appreciate some help from people understanding Kalman Filters, because I think I may be missing something.

This paper could be a good starting point for you, but you might just choose to manually tweak the values. That's probably good enough for your application.

For your laser scanner use a variance on the distance of 5cm. The 1cm accuracy below 1m is just tough luck. The Theta is probably very accurate, as this doesn't change, right? If so, take a variance on that of 1°. Assume independence (co-variance is 0).