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I have a nonlinear system, and I need to use the extended kalman filter to estimate it. I know I need the jacobian, but once I get that, is everything else the same as the normal kalman filter?

I currently have the state equations updating in a loop because everything is discrete, so for example

x(0) = 5
for k 2:100
x(k) = x(k-1) + 2
end

I am unsure how to get the jacobian from constants like this, I was considering by hand but some of the equations are a little complicated and I figured there would be an easier MATLAB solution I dont know. And once I get the jacobian, I am unsure where to go. I have some working code for the regular linear case kalman filter from an older project, can I somehow make that work?

Thanks for any help

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  • $\begingroup$ your state equation is linear and deterministic with a constant input. what does your measurement equation look like? $\endgroup$ – Stanley Pawlukiewicz Dec 13 '18 at 8:53
  • $\begingroup$ Hi! It' will be much appreciated if you supply mathematical details of your nonlinear system: it's process equation and its measurement equation. $\endgroup$ – Fat32 Dec 13 '18 at 10:52
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It's true that once the nonlinear system is linearized, things will be similar to a linear Kalman filter, except the fact that all the state dependent matrices will also be updated (according to previous / current state estimates) in the loop as well as the state estimates themselves.

You should better provide your systems's equations for a better answer.

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