Path: Common/Estimation
-------------------------------------------------------------------------- Mechanizes one step of a Kalman Filter with a forgetting factor x[k+1] = phi*x[k] + gamma*u[k] y[k] = x[k] + k[k]*(z - h*x[k]) The forgetting factor scales the covariance factor in the covariance update. If it were zero the covariance update would be the state covariance matrix q. p = s*phi*p*phi' + q; The function automatically forces symmetry on p by averaging p and p'. The function handles deterministic inputs as shown above. gamma is optional so it will also handle x[k+1] = phi*x[k] + u[k]. Note that the matrices are for a discrete time system. Since version 1. -------------------------------------------------------------------------- Form: [x, p, k, y, pY] = KFilter( r, phi, q, h, x, z, p, gamma, u, s ) -------------------------------------------------------------------------- ------ Inputs ------ r (m,m) Measurement Covariance phi (n,n) State transition matrix q (n,n) Process noise covariance h (m,n) Measurement matrix x (n) Previous value of the state z (m) Measurement vector p (n,n) Covariance of xold gamma (n,l) Input matrix u (n) Deterministic input s Forgetting factor 1 = don't, � = 1 stage filter ------- Outputs ------- x (n) Updated state this is at time k+1 p (n,n) Covariance of x k (n,m) Kalman Gain matrix y (m,1) Output at time k pY (n,n) Covariance after the measurement update --------------------------------------------------------------------------
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