Find likelihood from state space with Kalman filter

Hi everyone,

I'm struggeling to find the correct solution approach for my problem, despite screening the forum for an answer. I have a state space system with the respective A, B, C and D matrices and successfully used

state_space = ssm(A,B,C,D) ;

The respictive sizes of the matrices are:

>> size(A)

ans =

    27    27
    
>> size(B)

ans =

    27     9
    
>> size(C)

ans =

     9    27
     
>> size(D)

ans =

     9     9
     

There is also an observation matrix y which is a 155 x 9 matrix. Can anyone point me into the right direction how I can find the likelihood function of this system, using the Kalman filter. Or would I have to code this myself, as there's no command available? Many thanks for your help!

Rob

Answer 1

[Sam Chak]

Hi @Rob

Perhaps you are looking for the likelihood() function.

help likelihood

--- help for trackingEKF/likelihood ---

 LIKELIHOOD Calculate the likelihood of a measurement
   l = likelihood(EKF, Z) calculates the likelihood of a
   measurement, Z, given the object, EKF.
 
   l = likelihood(EKF, Z, measurementParams) allows you to
   define additional parameters that will be used by the
   EKF.MeasurementFcn. It should be specified as a cell array,
   e.g., {1, [2;3]}. If unspecified, it will be assumed to be
   an empty cell array.

    Documentation for trackingEKF/likelihood
       doc trackingEKF/likelihood

    Other uses of likelihood

       AlphaBetaFilter/likelihood
       ggiwphd/likelihood
       matlabshared.tracking.internal.AbstractTrackingFilter/likelihood

[Rob]

Thanks @Sam Chak let me give this a try and report back!

[Rob]

Hi @Sam Chak, your answer might go into the right direction but I am still in the process of working things out. Thanks for your help!