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Kalman Filter

  • 04-01-2010 3:48pm
    #1
    Webmonkey
    Registered Users, Registered Users 2 Posts: 9,579 ✭✭✭


    Hi There,

    I've successfully implemented a Kalman Filter implementation in C#. It assumes an object is travelling 5 meters per second with an acceleration standard deviation of 0.5 meters.

    So from this I've specified my matrices, with process variance of 0.25 and a gaussian distributed measurement with standard deviation of 5 meters thus my measurement variance of 25 meters.

    I simulated noisy measurements of a vehicle traveling 5 meters per second and obtained a distance traveled. This worked lovely, and the Kalman filter's estimated converged to the real distance.


    Now the problem is, I'm going to be receiving data from systems that report an object's x,y z with a standard deviation to signify the quality of the measurement. From this, I have to calculate the velocity and heading/angle using delta T between measurements.

    To me this does not seem like a linear system. I don't have anyway of specifying the A matrix to represent the dynamic of the system. So basically, the measurement will be the state (x,y,z) with the additional angle and velocity determined.

    Can a Kalman filter work with this data, or do I need to use the Extended Kalman Filter for non linear systems?

    Thanks very much.


Comments

  • #2
    CathalMc
    Registered Users, Registered Users 2 Posts: 225 ✭✭CathalMc


    In the absence of more knowledgeable people chipping in here, I'd seem to recall all my course material on adaptive filtering being determined in terms of vector variables. If you re-examine the formal definitions of the Kalman Filter you've been using, they are probably in generalized vector notation that you've been parsing (correctly) for the 1-D scalar case.
    http://www.swarthmore.edu/NatSci/echeeve1/Ref/Kalman/MatrixKalman.html looks like it has the vector definition for instance.

    Apologies for not tackling the meat of your problem more directly, but I don't trust my cloudy memory on the subject.


  • #3
    Webmonkey
    Registered Users, Registered Users 2 Posts: 9,579 ✭✭✭Webmonkey


    Hey thanks for the reply.

    I looked at that page and that's the exact set of equations I'm using. I've a 4 state vector as well (Well a 4x1 matrix). This works fine but i'm not sure what to do if I cannot specify the A matrix as there's no linerality in a object moving randomly on a 2d plane.

    I believe it's the Extended Kalman I should focus my research into, but that's a bit daunting as this whole electronic engineering business is quite new to me :)

    Thanks anyways. I wonder if the mathematic guys would have any idea over there.


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