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kf_predict

PURPOSE ^

KF_PREDICT Perform Kalman Filter prediction step

SYNOPSIS ^

function [x,P] = kf_predict(x,P,A,Q,B,u)

DESCRIPTION ^

KF_PREDICT  Perform Kalman Filter prediction step

 Syntax:
   [X,P] = KF_PREDICT(X,P,A,Q,B,U)

 In:
   X - Nx1 mean state estimate of previous step
   P - NxN state covariance of previous step
   A - Transition matrix of discrete model (optional, default identity)
   Q - Process noise of discrete model     (optional, default zero)
   B - Input effect matrix                 (optional, default identity)
   U - Constant input                      (optional, default empty)

 Out:
   X - Predicted state mean
   P - Predicted state covariance
   
 Description:
   Perform Kalman Filter prediction step. The model is

     x[k] = A*x[k-1] + B*u[k-1] + q,  q ~ N(0,Q).
 
   The predicted state is distributed as follows:
   
     p(x[k] | x[k-1]) = N(x[k] | A*x[k-1] + B*u[k-1], Q[k-1])

   The predicted mean x-[k] and covariance P-[k] are calculated
   with the following equations:

     m-[k] = A*x[k-1] + B*u[k-1]
     P-[k] = A*P[k-1]*A' + Q.

   If there is no input u present then the first equation reduces to
     m-[k] = A*x[k-1]

 History:

   26.2.2007 JH Added the distribution model for the predicted state
                and equations for calculating the predicted state mean and
                covariance to the description section.
  
 See also:
   KF_UPDATE, LTI_DISC, EKF_PREDICT, EKF_UPDATE

CROSS-REFERENCE INFORMATION ^

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