function ParticleEx1
% Particle filter example, adapted from Gordon, Salmond, and Smith paper.
x = 0.1; % initial state
Q = 1; % process noise covariance
R = 1; % measurement noise covariance
tf = 50; % simulation length
N = 100; % number of particles in the particle filter
xhat = x;
P = 2;
xhatPart = x;
% Initialize the particle filter.
for i = 1 : N
xpart(i) = x + sqrt(P) * randn;
end
xArr = [x];
yArr = [x^2 / 20 + sqrt(R) * randn];
xhatArr = [x];
PArr = [P];
xhatPartArr = [xhatPart];
close all;
for k = 1 : tf
% System simulation
x = 0.5 * x + 25 * x / (1 + x^2) + 8 * cos(1.2*(k-1)) + sqrt(Q) *
randn;%状态方程
y = x^2 / 20 + sqrt(R) * randn;%观测方程
% Extended Kalman filter
F = 0.5 + 25 * (1 - xhat^2) / (1 + xhat^2)^2;
P = F * P * F' + Q;
H = xhat / 10;
K = P * H' * (H * P * H' + R)^(-1);
xhat = 0.5 * xhat + 25 * xhat / (1 + xhat^2) + 8 * cos(1.2*(k-1));%预测
xhat = xhat + K * (y - xhat^2 / 20);%更新
P = (1 - K * H) * P;
% Particle filter
for i = 1 : N
xpartminus(i) = 0.5 * xpart(i) + 25 * xpart(i) / (1 + xpart(i)^2) +
8 * cos(1.2*(k-1)) + sqrt(Q) * randn;
ypart = xpartminus(i)^2 / 20;
vhat = y - ypart;%观测和预测的差
q(i) = (1 / sqrt(R) / sqrt(2*pi)) * exp(-vhat^2 / 2 / R);
end
% Normalize the likelihood of each a priori estimate.
qsum = sum(q);
for i = 1 : N
q(i) = q(i) / qsum;%归一化权重
end
% Resample.
for i = 1 : N
u = rand; % uniform random number between 0 and 1
qtempsum = 0;
