kalman_intro.mht

来自「本人写的用MATLAB实现卡尔曼滤波」· MHT 代码 · 共 93 行

MHT

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<BODY><PRE>% Kalman filter example demo in Matlab

% This M code is modified from Andrew D. Straw's Python=20
% implementation of Kalman filter algorithm.
% The original code is here:
% http://www.scipy.org/Cookbook/KalmanFiltering
% Below is the Python version's comments:

        % Kalman filter example demo in Python

        % A Python implementation of the example given in pages 11-15 of =
"An
        % Introduction to the Kalman Filter" by Greg Welch and Gary =
Bishop,
        % University of North Carolina at Chapel Hill, Department of =
Computer
        % Science, TR 95-041,
        % http://www.cs.unc.edu/~welch/kalman/kalmanIntro.html

        % by Andrew D. Straw

% by Xuchen Yao
       =20
clear all;
close all;


% intial parameters
n_iter =3D 50;
sz =3D [n_iter, 1]; % size of array
x =3D -0.37727; % truth value (typo in example at top of p. 13 calls =
this z)
z =3D x + sqrt(0.1)*randn(sz); % observations (normal about x, =
sigma=3D0.1)

Q =3D 1e-5; % process variance

% allocate space for arrays
xhat=3Dzeros(sz);      % a posteri estimate of x
P=3Dzeros(sz);         % a posteri error estimate
xhatminus=3Dzeros(sz); % a priori estimate of x
Pminus=3Dzeros(sz);    % a priori error estimate
K=3Dzeros(sz);         % gain or blending factor

R =3D 0.01; % estimate of measurement variance, change to see effect

% intial guesses
xhat(1) =3D 0.0;
P(1) =3D 1.0;

for k =3D 2:n_iter
    % time update
    xhatminus(k) =3D xhat(k-1);
    Pminus(k) =3D P(k-1)+Q;

    % measurement update
    K(k) =3D Pminus(k)/( Pminus(k)+R );
    xhat(k) =3D xhatminus(k)+K(k)*(z(k)-xhatminus(k));
    P(k) =3D (1-K(k))*Pminus(k);
end
figure();
plot(z,'k+');
hold on;
plot(xhat,'b-')
hold on;
plot(x*ones(sz),'g-');
legend('noisy measurements', 'a posteri estimate', 'truth value');
xlabel('Iteration');
ylabel('Voltage');
hold off;

figure();
valid_iter =3D [2:n_iter]; % Pminus not valid at step 1
plot(valid_iter,Pminus([valid_iter]));
legend('a priori error estimate');
xlabel('Iteration');
ylabel('$(Voltage)^2$');
ylim([0,.01]);</PRE></BODY></HTML>

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