I need to design 2d kalman filter in Matlab, however i've done the 1d filter before. The filter's inputs are the coordinate x and y from the image feature.
Hello
The KF equations are algebraically the same (in vector notation) between 1-D and 2-D. You just use matrices and vectors instead of scalars. BTW you haven't specified the problem precisely enough since you need to define the state and measurement dimensions, which do not have to be the same naturally. If you have 2-D state and 2-D measurement, you have 2x2 F and 2x2 Q with 1x2 H and scalar R. You initialise the state with two measurements to get a rate estimate. That's all there is to it.
We can use the x and y measurements to estimate the state respectively. But we should assure the x and y is decoupled, so the process model should be considered carefully. About the dynamic model, which is discussed detailly in the the paper" 1. Li X R , Jilkov V P. Survey of maneuvering target tracking 1: Dynamic models. IEEE Transactions on Aerospace and Electronic Systems, 2003, 39(4): 1333-1364". I wish it can help you.
Thank you very much for all of your advices.
@Graham so, is it better to use the 1D KF for my case?
Hello
Re-reading your question, you have a 2D position measurement. For constant velocity tracking you use a 4D state X=transpose(x, xdot, y ydot). The F matrix is [1 T 0 0; 0 1 0 0; 0 0 1 T; 0 0 0 1] (I think!). Take Q as [T^3/3, T^2/2; T^2/2, T]q where q is a scaling factor for process noise variance (eg 0.001 - 0.1). H = [1 0 1 0], R=[sigx^2 0; 0 sigy^2]. That's all assuming a linear model (best to start with this).
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