plot_3d_pda1.m

一个目标跟踪系统的MATLAB 源程序包

% plot_3d_pda1.m
%
% Kalman filter with 3-D PDA using LP 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_3d_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];
% sufficient stat. at the rear end of the frozen window 
track(1).X = track(1).est(:,1);
track(1).Cov = track(1).P(:,:,1);
track(2).X = track(2).est(:,1);
track(2).Cov = track(2).P(:,:,1);
frozen_time = track(1).time(1);

q = .01; % 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-1
        T = measurement(i).time - frozen_time;
        T2 = measurement(i+1).time - measurement(i).time;
        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];
        F2 = [1, T2, 0, 0;
            0, 1, 0, 0;
            0, 0, 1, T2;
            0, 0, 0, 1];
        G2 = [T2*T2/2, 0;
            T2, 0;
            0, T2*T2/2;
            0, T2];
        z = []; z1 = []; z2 = [];
        R = []; R1 = []; R2 = [];
        cost = [];
        assign = [];
        ind00 = length(measurement(i).flag);
        ind01 = length(measurement(i+1).flag);
        if ind00 == 0
            [track(1).X, track(1).Cov] = prekalman(track(1).X, track(1).Cov,vm,Qk,F,G);
            [track(2).X, track(2).Cov] = prekalman(track(2).X, track(2).Cov,vm,Qk,F,G);
            if ind01 == 0
                [track(1).est(:,i+1), track(1).P(:,:,i+1)] = prekalman(track(1).X, track(1).Cov,vm,Qk,F2,G2);
                [track(2).est(:,i+1), track(2).P(:,:,i+1)] = prekalman(track(2).X, track(2).Cov,vm,Qk,F2,G2);
            else
                k1 = 1;
                for j=1:ind01
                    if measurement(i+1).flag(j) == 0
                        [z(1,k1), z(2,k1), R(:,:,k1)] = CalcMeasCov2(measurement(i+1).range(j), measurement(i+1).bearing(j), ...
                        measurement(i+1).pos(1), measurement(i+1).pos(2), C_r, C_b);
                        plot(z(1,k1), z(2,k1), 'k*');                    
                        k1 = k1 + 1;
                        [z(1,k1), z(2,k1), R(:,:,k1)] = CalcMeasCov2(measurement(i+1).range(j), measurement(i+1).bearing(j), ...
                        measurement(i+1).pos(1), measurement(i+1).pos(2), C_r, C_b);
                        k1 = k1 + 1;
                    else
                        [z(1,k1), z(2,k1), R(:,:,k1)] = CalcMeasCov2(measurement(i+1).range(j), measurement(i+1).bearing(j), ...
                        measurement(i+1).pos(1), measurement(i+1).pos(2), C_r/sqrt(12), C_b/sqrt(12));
                        plot(z(1,k1), z(2,k1), 'c*');                    
                        k1 = k1 + 1;
                    end                        
                end
                cost = zeros(2, k1);
                for j=1:k1-1
                    % form the cost function for 2-D assignment
                    cost(1,j+1) = lr_kalman(track(1).X, track(1).Cov, z(:,j), Qk, R(:,:,j), vm, wm, F2, G2, H, Ik, Pd, lambda);
                    cost(2,j+1) = lr_kalman(track(2).X, track(2).Cov, z(:,j), Qk, R(:,:,j), vm, wm, F2, G2, H, Ik, Pd, lambda);            
                end
                associate_prob = myLinProg(-cost);
                if isempty(associate_prob)
                    [track(1).est(:,i+1), track(1).P(:,:,i+1)] = prekalman(track(1).X, track(1).Cov,vm,Qk,F2,G2);
                    [track(2).est(:,i+1), track(2).P(:,:,i+1)] = prekalman(track(2).X, track(2).Cov,vm,Qk,F2,G2);
                else
                    [track(1).est(:,i+1), track(1).P(:,:,i+1)] = pdakalman(track(1).X, track(1).Cov,...
                            z, R, associate_prob(1,:), Qk, vm, wm, F2, G2, H, Ik);
                    [track(2).est(:,i+1), track(2).P(:,:,i+1)] = pdakalman(track(2).X, track(2).Cov,...
                            z, R, associate_prob(2,:), Qk, vm, wm, F2, G2, H, Ik);
                end
            end
        else         % ind00~=0
            if ind01 == 0
                k1 = 1;
                for j=1:ind00
                    if measurement(i).flag(j) == 0
                        [z(1,k1), z(2,k1), R(:,:,k1)] = CalcMeasCov2(measurement(i).range(j), measurement(i).bearing(j), ...
                        measurement(i).pos(1), measurement(i).pos(2), C_r, C_b);
                        plot(z(1,k1), z(2,k1), 'k*');
                        k1 = k1 + 1;
                        [z(1,k1), z(2,k1), R(:,:,k1)] = CalcMeasCov2(measurement(i).range(j), measurement(i).bearing(j), ...
                        measurement(i).pos(1), measurement(i).pos(2), C_r, C_b);
                        k1 = k1 + 1;
                    else
                        [z(1,k1), z(2,k1), R(:,:,k1)] = 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,k1), z(2,k1), 'c*');
                        k1 = k1 + 1;
                    end                        
                end
                cost = zeros(2, k1);
                for j=1:k1-1
                    % form the cost function for 2-D assignment
                    cost(1,j+1) = lr_kalman(track(1).X, track(1).Cov, z(:,j), Qk, R(:,:,j), vm, wm, F, G, H, Ik, Pd, lambda);
                    cost(2,j+1) = lr_kalman(track(2).X, track(2).Cov, z(:,j), Qk, R(:,:,j), vm, wm, F, G, H, Ik, Pd, lambda);            
                end
                associate_prob = myLinProg(-cost);
                if isempty(associate_prob)
                    [track(1).X, track(1).Cov] = prekalman(track(1).X, track(1).Cov,vm,Qk,F,G);
                    [track(2).X, track(2).Cov] = prekalman(track(2).X, track(2).Cov,vm,Qk,F,G);
                else
                    [track(1).X, track(1).Cov] = pdakalman(track(1).X, track(1).Cov,...
                            z, R, associate_prob(1,:), Qk, vm, wm, F, G, H, Ik);
                    [track(2).X, track(2).Cov] = pdakalman(track(2).X, track(2).Cov,...
                            z, R, associate_prob(2,:), Qk, vm, wm, F, G, H, Ik);
                end
                [track(1).est(:,i+1), track(1).P(:,:,i+1)] = prekalman(track(1).X, track(1).Cov,vm,Qk,F2,G2);
                [track(2).est(:,i+1), track(2).P(:,:,i+1)] = prekalman(track(2).X, track(2).Cov,vm,Qk,F2,G2);
                
            else   % ind01~=0
                % form the cost for 3-D assignment
                k1 = 1;
                for j=1:ind00
                    if measurement(i).flag(j) == 0
                        [z1(1,k1), z1(2,k1), R1(:,:,k1)] = CalcMeasCov2(measurement(i).range(j), measurement(i).bearing(j), ...
                        measurement(i).pos(1), measurement(i).pos(2), C_r, C_b);
                        plot(z1(1,k1), z1(2,k1), 'k*');                    
                        k1 = k1 + 1;
                        [z1(1,k1), z1(2,k1), R1(:,:,k1)] = CalcMeasCov2(measurement(i).range(j), measurement(i).bearing(j), ...
                        measurement(i).pos(1), measurement(i).pos(2), C_r, C_b);
                        k1 = k1 + 1;
                    else
                        [z1(1,k1), z1(2,k1), R1(:,:,k1)] = 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(z1(1,k1), z1(2,k1), 'c*');                    
                        k1 = k1 + 1;
                    end                        
                end
                k2 = 1;
                for j=1:ind01
                    if measurement(i+1).flag(j) == 0
                        [z2(1,k2), z2(2,k2), R2(:,:,k2)] = CalcMeasCov2(measurement(i+1).range(j), measurement(i+1).bearing(j), ...
                        measurement(i+1).pos(1), measurement(i+1).pos(2), C_r, C_b);
                        plot(z2(1,k2), z2(2,k2), 'k*');                    
                        k2 = k2 + 1;
                        [z2(1,k2), z2(2,k2), R2(:,:,k2)] = CalcMeasCov2(measurement(i+1).range(j), measurement(i+1).bearing(j), ...
                        measurement(i+1).pos(1), measurement(i+1).pos(2), C_r, C_b);
                        k2 = k2 + 1;
                    else
                        [z2(1,k2), z2(2,k2), R2(:,:,k2)] = CalcMeasCov2(measurement(i+1).range(j), measurement(i+1).bearing(j), ...
                        measurement(i+1).pos(1), measurement(i+1).pos(2), C_r/sqrt(12), C_b/sqrt(12));
                        plot(z2(1,k2), z2(2,k2), 'c*');                    
                        k2 = k2 + 1;
                    end      
                end
                cost = zeros(2, k1, k2);
                for j=1:k1-1
                    cost(1,j+1,1) = lr_kalman(track(1).X, track(1).Cov, z1(:,j), Qk, R1(:,:,j), vm, wm, F, G, H, Ik, Pd, lambda);
                    cost(2,j+1,1) = lr_kalman(track(2).X, track(2).Cov, z1(:,j), Qk, R1(:,:,j), vm, wm, F, G, H, Ik, Pd, lambda);                    
                end
                [tmp1X, tmp1Cov] = prekalman(track(1).X, track(1).Cov,vm,Qk,F,G);
                [tmp2X, tmp2Cov] = prekalman(track(2).X, track(2).Cov,vm,Qk,F,G);
                for j=1:k2-1
                    cost(1,1,j+1) = lr_kalman(tmp1X, tmp1Cov, z2(:,j), Qk, R2(:,:,j), vm, wm, F2, G2, H, Ik, Pd, lambda);
                    cost(2,1,j+1) = lr_kalman(tmp2X, tmp2Cov, z2(:,j), Qk, R2(:,:,j), vm, wm, F2, G2, H, Ik, Pd, lambda);                    
                end                
                for j=1:k1-1
                    for k=1:k2-1
                        cost(1, j+1, k+1) = lr_3d_kalman(track(1).X, track(1).Cov, z1(:,j), R1(:,:,j), z2(:,k), R2(:,:,k), Qk, vm, wm, F, G, F2, G2, H, Ik, Pd, lambda);
                        cost(2, j+1, k+1) = lr_3d_kalman(track(2).X, track(2).Cov, z1(:,j), R1(:,:,j), z2(:,k), R2(:,:,k), Qk, vm, wm, F, G, F2, G2, H, Ik, Pd, lambda);                        
                    end
                end
                associate_prob = myLinProg(-cost);
                if isempty(associate_prob)
                    [track(1).X, track(1).Cov] = prekalman(track(1).X, track(1).Cov,vm,Qk,F,G);
                    [track(2).X, track(2).Cov] = prekalman(track(2).X, track(2).Cov,vm,Qk,F,G);
                    [track(1).est(:,i+1), track(1).P(:,:,i+1)] = prekalman(track(1).X, track(1).Cov,vm,Qk,F2,G2);
                    [track(2).est(:,i+1), track(2).P(:,:,i+1)] = prekalman(track(2).X, track(2).Cov,vm,Qk,F2,G2);
                else
                    prob1 = [];
                    prob2 = [];
                    prob3 = [];
                    prob4 = [];
                    % obtain the marginal pseudo-probabilities
                    for j=1:k1
                        prob1(j) = sum(associate_prob(1,j,:));
                        prob2(j) = sum(associate_prob(2,j,:));
                    end
                    for k=1:k2
                        prob3(k) = sum(associate_prob(1,:,k));
                        prob4(k) = sum(associate_prob(2,:,k));
                    end
                    % update tracks
                    [track(1).X, track(1).Cov] = pdakalman(track(1).X, track(1).Cov,...
                    z1, R1, prob1, Qk, vm, wm, F, G, H, Ik);
                    [track(2).X, track(2).Cov] = pdakalman(track(2).X, track(2).Cov,...
                    z1, R1, prob2, Qk, vm, wm, F, G, H, Ik);         

                    [track(1).est(:,i+1), track(1).P(:,:,i+1)] = pdakalman(track(1).X, track(1).Cov,...
                    z2, R2, prob3, Qk, vm, wm, F2, G2, H, Ik);
                    [track(2).est(:,i+1), track(2).P(:,:,i+1)] = pdakalman(track(2).X, track(2).Cov,...
                    z2, R2, prob4, Qk, vm, wm, F, G, H, Ik);                 
                end
            end % if ind00 == 0 ...
        end % for

        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);
        frozen_time = measurement(i).time;
        track(1).time(i+1) = measurement(i+1).time;
        track(2).time(i+1) = measurement(i+1).time;
    end
    
xlabel('x position (m)');
ylabel('y position (m)');
title('3-D soft assignment, sensor 1&2');
hold off;