www.pudn.com > trackingdemos.zip > plot_2d_pda1.m
% plot_2d_pda1.m
%
% Kalman filter with 2-D assignment for tracking multiple targets with possibly unresolved measurements,
% assuming the resolvability indicator is known.
% See also: gene_2d_scn.m, gene_2d_meas.m
function fig = plot_2d_pda1(target, measurement)
fig = figure;
hold on;
plot(target(1).state(1,:), target(1).state(3,:), '.');
plot(target(2).state(1,:), target(2).state(3,:), '.');
axis([100e3,130e3,147e3,151e3]);
% define SNR
SNRdb = 10;
SNR = 10^(SNRdb/10);
% detection threshold
threshold = 2.55;
% calc. the probability of detection and false alarm per cell
% according to certain model (currently Swerling-I)
Pfa = exp(-threshold*threshold/2);
Pd = exp(-threshold*threshold/2/(1+SNR));
% measurement std, cell size
C_r = 50;
C_b = 2e-3;
% track initiation
track(1).time(1) = 1;
track(2).time(1) = 1;
track(1).est(:,1) = target(1).state(:,1);
track(2).est(:,1) = target(2).state(:,1);
track(1).P(:,:,1) = 1e4.* [9, 0, -6, 0;
0, .2, 0, 0;
-6 0, 5, 0;
0, 0, 0, .2];
track(2).P(:,:,1) = 1e4.* [9, 0, -6, 0;
0, .2, 0, 0;
-6 0, 5, 0;
0, 0, 0, .2];
q = .05; % process noise
H = [1, 0, 0, 0; 0, 0, 1, 0];
vm = zeros(2,1);
wm = zeros(2,1);
Ik = eye(2);
Qk = q.*Ik;
lambda = 1e-7;
numScan = length(target(1).time);
for i=1:numScan
T = measurement(i).time - track(1).time(i);
F = [1, T, 0, 0;
0, 1, 0, 0;
0, 0, 1, T;
0, 0, 0, 1];
G = [T*T/2, 0;
T, 0;
0, T*T/2;
0, T];
z = [];
R = [];
cost = [];
assign = [];
ind = length(measurement(i).flag);
if ind == 0
[track(1).est(:,i+1), track(1).P(:,:,i+1)] = prekalman(track(1).est(:,i), track(1).P(:,:,i),vm,Qk,F,G);
[track(2).est(:,i+1), track(2).P(:,:,i+1)] = prekalman(track(2).est(:,i), track(2).P(:,:,i),vm,Qk,F,G);
else
k = 1;
cost(1,1) = 0;
cost(2,1) = 0;
for j=1:ind
if measurement(i).flag(j) == 0
[z(1,k), z(2,k), R(:,:,k)] = CalcMeasCov2(measurement(i).range(j), measurement(i).bearing(j), measurement(i).pos(1), measurement(i).pos(2), C_r, C_b);
plot(z(1,k), z(2,k), 'k*');
k = k + 1;
[z(1,k), z(2,k), R(:,:,k)] = CalcMeasCov2(measurement(i).range(j), measurement(i).bearing(j), measurement(i).pos(1), measurement(i).pos(2), C_r, C_b);
k = k + 1;
else
[z(1,k), z(2,k), R(:,:,k)] = CalcMeasCov2(measurement(i).range(j), measurement(i).bearing(j), measurement(i).pos(1), measurement(i).pos(2), C_r/sqrt(12), C_b/sqrt(12));
plot(z(1,k), z(2,k), 'c*');
k = k + 1;
end
end
for j=1:k-1
cost(1,j+1) = lr_kalman(track(1).est(:,i), track(1).P(:,:,i), z(:,j), Qk, R(:,:,j), vm, wm, F, G, H, Ik, Pd, lambda);
cost(2,j+1) = lr_kalman(track(2).est(:,i), track(2).P(:,:,i), z(:,j), Qk, R(:,:,j), vm, wm, F, G, H, Ik, Pd, lambda);
end
% LP solution of the 2-D assignment problem
associate_prob = myLinProg(-cost);
if isempty(associate_prob)
[track(1).est(:,i+1), track(1).P(:,:,i+1)] = prekalman(track(1).est(:,i), track(1).P(:,:,i),vm,Qk,F,G);
[track(2).est(:,i+1), track(2).P(:,:,i+1)] = prekalman(track(2).est(:,i), track(2).P(:,:,i),vm,Qk,F,G);
else
% update tracks
[track(1).est(:,i+1), track(1).P(:,:,i+1)] = pdakalman(track(1).est(:,i), track(1).P(:,:,i),...
z, R, associate_prob(1,:), Qk, vm, wm, F, G, H, Ik);
[track(2).est(:,i+1), track(2).P(:,:,i+1)] = pdakalman(track(2).est(:,i), track(2).P(:,:,i),...
z, R, associate_prob(2,:), Qk, vm, wm, F, G, H, Ik);
end
end
plot(track(1).est(1, i+1), track(1).est(3, i+1), 'g.');
plot(track(2).est(1, i+1), track(2).est(3, i+1), 'g.');
center1 = [track(1).est(1,i+1), track(1).est(3, i+1)];
covariance1 = [track(1).P(1,1,i+1), track(1).P(1,3,i+1); track(1).P(3,1,i+1), track(1).P(3,3,i+1)];
[X1, Y1] = get_ellipsoid_gate(center1, covariance1, 1.96);
plot(X1, Y1, 'm');
center2 = [track(2).est(1,i+1), track(2).est(3, i+1)];
covariance2 = [track(2).P(1,1,i+1), track(2).P(1,3,i+1); track(2).P(3,1,i+1), track(2).P(3,3,i+1)];
[X2, Y2] = get_ellipsoid_gate(center2, covariance2, 1.96);
plot(X2, Y2, 'm');
axis([100e3,130e3,147e3,151e3]);
pause(.5);
track(1).time(i+1) = measurement(i).time;
track(2).time(i+1) = measurement(i).time;
end
xlabel('x position (m)');
ylabel('y position (m)');
title('2-D soft assignment, sensor 1&2');
hold off;