INS / GPS data fusion using Kalman filter - need help for tuning

Hi there,
I'm working on a low cost integrated INS/GPS navigation system (for
automotive applications).I use only 1 2D accelerometer and a GPS
receiver.
This is my system model (2D movement):
x(k) = Ax(k) + Bu(k) + w
z(k) = Hx(k) + v

Where: 
x(k)=[sx sy vx vy] (sx = position along x axis, sy = position along y
axis, vx = velocity along x axis, vy = velocity along y axis).

u(k)=[ax ay] (ax = acceleration along x axis, ay = acceleration along y
axis), this is the output of the gyros. 

z(k)= GPS measurements (position along x and y).

A=[1 0 T 0; 0 1 0 T; 0 0 1 0; 0 0 0 1];
B=[T^2/2 0; 0 T^2/2; T 0; 0 T];
H=[1 0 0 0; 0 1 0 0];

T= sampling time;

I've some problems in filter tuning, do you have some suggestions on how
can I evaluate Q and R matrix?

Thanks and sorry for my english ^_^

mayonnaise wrote:
> Hi there,
> I'm working on a low cost integrated INS/GPS navigation system (for
> automotive applications).I use only 1 2D accelerometer and a GPS
> receiver.
> This is my system model (2D movement):
> x(k) = Ax(k) + Bu(k) + w
> z(k) = Hx(k) + v
> 
> Where: 
> x(k)=[sx sy vx vy] (sx = position along x axis, sy = position along y
> axis, vx = velocity along x axis, vy = velocity along y axis).
> 
> u(k)=[ax ay] (ax = acceleration along x axis, ay = acceleration along y
> axis), this is the output of the gyros. 
> 
> z(k)= GPS measurements (position along x and y).
> 
> A=[1 0 T 0; 0 1 0 T; 0 0 1 0; 0 0 0 1];
> B=[T^2/2 0; 0 T^2/2; T 0; 0 T];
> H=[1 0 0 0; 0 1 0 0];
> 
> T= sampling time;
> 
> I've some problems in filter tuning, do you have some suggestions on how
> can I evaluate Q and R matrix?
> 
> Thanks and sorry for my english ^_^
> 
> 

You might also wish to ask on sci.geo.satellite-nav

This would be the place for the math.

sci.geo.satellite-nav has some developers who read the group. It has a 
strong end user emphasis now, but it's original intent was to serve 
developers.

I know little of either field, but am fascinated by both.

BTW, your English is fine. I know many high school and college 
instructors that wish their native English speaking students were as fluent.

For perspective, ~50 years ago while vacationing in northern Ontario, 
Canada [a predominately French speaking area], our host asked me to 
borrow something from a neighbor. I tried out my French. I was asked to 
speak English as it was much more recognizable than my French ;\