I have a filter that tracks a robot. I want it to use a 2D coordinated turn polar velocity motion model (from page 15 here):
But I want to expand on this motion model: I want an additional velocity state that is orthogonal to the heading, and I also want acceleration states for the two velocities.
How do I find the resulting discrete-time linearized model easily? I guess
I could someone smarter than me could find the find the continuous time differential equation by hand (by thinking really hard?), and then discretize/linearlize (or linearlize/discretize) it. But that seems like an awful amount of work. I think I can manage the "discretize/linearlize"-step, but I don't know how to start on the "find the continuous time model" step.
It would be nice if there were some program that takes my desired states as input and outputs a model. But my googling turns up nothing. Is it really hard to find motion models? Do I fail to see the gravity of the work if I feel like this could be done in an afternoon? What should my workflow look like? Where do I start?