complete example of using kalman filter with autoregressive model

Hi I am trying to apply a kalman filter to a set of data. I know the basics, but I just need one complete example to follow. assume a data set,

 data = [143.850000000000  141.950000000000  141.450000000000  142.300000000000  140.600000000000  140  138.400000000000  137.100000000000  138.900000000000  139.850000000000  138.750000000000  139.850000000000  141.300000000000  139.450000000000  140.150000000000  140.800000000000  142.500000000000  143  142.350000000000  143  142.550000000000  140.500000000000  141.250000000000  140.550000000000  141.450000000000  142.050000000000]

(assume this is the real data, with no noise. so I guess I would need to add white Gaussian noise to it to verify the performance of the filter?)

Now I need to calculate the optimal AR order to determine the values for matrix A in the time update equations. 1) how do you determine the optimal order, using matlab functions? 2) once you find the order (lets say 5), I use aryule(data,5) to obtain the coeff. So is the matrix A these coefficients? 3)how to transform this linear model into the state space representation? 4) what is matrix H?

Basically I want to be able to see the result of the kalman filtering vs raw data, and to how it improves the result.

A simple and compete example is appreciated! :)