# How to input data in Particle Filter function

5 views (last 30 days)
my research is about the estimation of curing reaction of epoxy resin using particle filter. I had done simulation and also the experiment about curing reaction and plan to use particle filter to get the accurate curing reaction degree. For the ensemble member, I had done about 50 type of curing reaction simulation with different reaction distance and I understand that this data will act as particle. And the data from the experiment will act as the observation data? (correct me if I am wrong)
but I still confuse where I can input all the curing reaction degree data into the coding. I really really appreciate if you can help me. There is no one in my lab that understand the particle filter coding.
ThemeCopy
%% clear memory, screen, and close all figures
clear, clc, close all;
%% Process equation x[k] = sys(k, x[k-1], u[k]);
nx = 1; % number of states
sys = @(k, xkm1, uk) xkm1/2 + 25*xkm1/(1+xkm1^2) + 8*cos(1.2*k) + uk;
%% Observation equation y[k] = obs(k, x[k], v[k]);
ny = 1; % number of observations
obs = @(k, xk, vk) xk(1)+ vk; % (returns column vector)
%% PDF of process noise and noise generator function
nu = 1; % size of the vector of process noise
sigma_u = sqrt(10);
p_sys_noise = @(u) normpdf(u, 0, sigma_u);
gen_sys_noise = @(u) normrnd(0, sigma_u); % sample from p_sys_noise (returns column vector)
%% PDF of observation noise and noise generator function
nv = 1; % size of the vector of observation noise
sigma_v = sqrt(1);
p_obs_noise = @(v) normpdf(v, 0, sigma_v);
gen_obs_noise = @(v) normrnd(0, sigma_v); % sample from p_obs_noise (returns column vector)
%% Initial PDF
% p_x0 = @(x) normpdf(x, 0,sqrt(10)); % initial pdf
gen_x0 = @(x) normrnd(0, sqrt(10)); % sample from p_x0 (returns column vector)
%% Transition prior PDF p(x[k] | x[k-1])
% (under the suposition of additive process noise)
% p_xk_given_xkm1 = @(k, xk, xkm1) p_sys_noise(xk - sys(k, xkm1, 0));
%% Observation likelihood PDF p(y[k] | x[k])
% (under the suposition of additive process noise)
p_yk_given_xk = @(k, yk, xk) p_obs_noise(yk - obs(k, xk, 0));
%% Number of time steps
T = 40;
%% Separate memory space
x = zeros(nx,T); y = zeros(ny,T);
u = zeros(nu,T); v = zeros(nv,T);
%% Simulate system
xh0 = 0; % initial state (h, Vf)
u(:,1) = 0; % initial process noise
v(:,1) = gen_obs_noise(sigma_v); % initial observation noise
x(:,1) = xh0;
y(:,1) = obs(1, xh0, v(:,1));
for k = 2:T
% here we are basically sampling from p_xk_given_xkm1 and from p_yk_given_xk
u(:,k) = gen_sys_noise(); % simulate process noise
v(:,k) = gen_obs_noise(); % simulate observation noise
x(:,k) = sys(k, x(:,k-1), u(:,k)); % simulate state
y(:,k) = obs(k, x(:,k), v(:,k)); % simulate observation
end
fprintf('Finish simulate system \n')
%% Separate memory
xh = zeros(nx, T); xh(:,1) = xh0;
yh = zeros(ny, T); yh(:,1) = obs(1, xh0, 0);
pf.k = 1; % initial iteration number
pf.Ns = 10; % number of particles
pf.w = zeros(pf.Ns, T); % weights
pf.particles = zeros(nx, pf.Ns, T); % particles
pf.gen_x0 = gen_x0; % function for sampling from initial pdf p_x0
pf.p_yk_given_xk = p_yk_given_xk; % function of the observation likelihood PDF p(y[k] | x[k])
pf.gen_sys_noise = gen_sys_noise; % function for generating system noise
%pf.p_x0 = p_x0; % initial prior PDF p(x[0])
%pf.p_xk_given_ xkm1 = p_xk_given_xkm1; % transition prior PDF p(x[k] | x[k-1])
%% Estimate state
for k = 2:T
fprintf('Iteration = %d/%d\n',k,T);
% state estimation
pf.k = k;
%[xh(:,k), pf] = particle_filter(sys, y(:,k), pf, 'multinomial_resampling');
[xh(:,k), pf] = particle_filter(sys, y(:,k), pf, 'systematic_resampling');
% filtered observation
yh(:,k) = obs(k, xh(:,k), 0);
end
%% Make plots of the evolution of the density
Disp=3;%表示させたい状態変数（1:厚さ，2?6:Vf．6は表面）
figure
hold on;
xi = 1:T;
yi = -25:0.25:25; %変数としてDispを想定した領域に設定
[xx,yy] = meshgrid(xi,yi);
den = zeros(size(xx));
xhmode = zeros(size(xh));
for i = xi
% for each time step perform a kernel density estimation
den(:,i) = ksdensity(pf.particles(1,:,i), yi,'kernel','epanechnikov');
[~, idx] = max(den(:,i));
% estimate the mode of the density
xhmode(i) = yi(idx);
plot3(repmat(xi(i),length(yi),1), yi', den(:,i));
end
view(3);
box on;
title('Evolution of the state density','FontSize',14)
figure
mesh(xx,yy,den);
title('Evolution of the state density','FontSize',14)
%% plot of the state vs estimated state by the particle filter vs particle paths
figure
hold on;
h1 = plot(1:T,squeeze(pf.particles),'y');
h2 = plot(1:T,x,'b','LineWidth',4);
h3 = plot(1:T,xh,'r','LineWidth',4);
h4 = plot(1:T,xhmode,'g','LineWidth',4);
legend([h2 h3 h4 h1(1)],'state','mean of estimated state','particle paths');
title('State vs estimated state by the particle filter vs particle paths','FontSize',14);
%% plot of the observation vs filtered observation by the particle filter
figure
plot(1:T,y,'b', 1:T,yh,'r');
legend('observation','filtered observation');
title('Observation vs filtered observation by the particle filter','FontSize',14);
return;