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I'm trying to track an accelerating vehicle using a camera, an IMU, and a GPS. I use for the state space equation a constant acceleration model: state space equation. Ts is the sampling time, p the position, v the velocity, and a the acceleration. The states are the position, the velocity, and the acceleration of the vehicle in the x- and y-direction. No input is used. All the measurement equations are linear. I'm wondering if I should use a discrete normal Kalman filter, or a discrete extended Kalman filter. (i.e. is my process non linear?)

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  • $\begingroup$ @jsotola Thx for the heads-up! I improved the picture! $\endgroup$
    – Michael
    May 12 '18 at 6:40
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If you can write the dynamics with a matrix, which you have, then a normal kalman filter will be best.

However, your measurements will probably be nonlinear. You will find that you won't be able to write your measurements equations using matrices. You will almost certainly need an extended kalman filter because your measurements will be nonlinear.

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there is some error in your matrix I think. P(k+1)=V(k) And V(k+1)=A(k) so I don't kwon what is the A(k+1) maybe the jerk(jolt) of the vehicle.

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  • $\begingroup$ On Robotics we are fortunate enough to have MathJax support enabled, allowing you to easily create subscripts, superscripts, fractions, square roots, greek letters and more. This allows you to add both inline and block element mathematical expressions in robotics questions and answers. For a quick tutorial, take a look at How can I format mathematical expressions here, using MathJax? $\endgroup$
    – Ben
    Sep 1 at 19:15

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