Demonstrate UKF parameter estimation with a nonlinear spring example.

------------------------------------------------------------------------
See also Plot2D, RK4, UKFP
------------------------------------------------------------------------

Contents

%--------------------------------------------------------------------------
%   Copyright 2006 Princeton Satellite Systems, Inc.
%   All rights reserved.
%--------------------------------------------------------------------------

nSim          = 1500;
dRHS.u        = 1; % Step disturbance
dRHS.w        = 4; % Spring constant
sigY          = 0.0001;%0.05;
xP            = zeros(5,nSim);
x             = 0;
dT            = 0.001;

Estimation parameters

%----------------------
d             = struct;
d.x           = 0;
d.p           = 0.4;
d.int         = @RK4;
d.rHSFun      = @RHSUKF;
d.measFun     = @GXUKF;
d.measFunData = [];
d.alpha       = 1;
d.kappa       = 2;
d.beta        = 2;
d.dY          = 1;
d.dT          = dT;
d.rHSFunData  = dRHS;
d.rP          = 0.0001*dRHS.u;
d.rY          = 0.000001*dRHS.u;
t             = 0;
y             = 0;
d.w           = dRHS.w/2;
d             = UKFP('initialize', d );

for k = 1:nSim

  % Plotting
  %---------
  d.x     = x;
  xP(:,k) = [y; x; d.w; d.dY; d.p];

  % Update the RHS
  %---------------
  x       = RK4( @RHSUKF, x, dT, 0, dRHS );

  % Measurement
  %------------
  y       = x + sigY*randn;
  t       = t + dT;

  % Kalman Filter
  %--------------
  d.t     = t;
  d       = UKFP( 'update', d, y );
end

t = (0:(nSim-1))*dT;
xL = {'Meas' 'State' 'Param' 'Residual' 'Covariance'};
Plot2D( t, xP, 'Time (sec)', xL, 'Nonlinear Spring Parameter estimation' );


%--------------------------------------
% $Date$
% $Id: 4f0a128c70a0643600fd157ef9ac96f34413be03 $

Published with MATLAB® R2021b