我在 Matlab 中实现了 EKF（扩展卡尔曼滤波器），用于视觉跟踪对象的3D轨迹，但是，我给了它的实际轨迹的位置和速度分别为in1和in2。在经常与实际轨迹相反的一些点之后，我面临着错误的预测。我认为，这可能是一些初步的假设问题，因为我多次检查方程但无法找到错误。如何解决我的初步假设或避免任何其他猜测？给出样品位置和速度。
我们欢迎任何改进我的方法的建议。
我的代码：
function EKF(in1,in2)
ind=0; % indicator function. Used for unwrapping of tan
[H] = [];
[K] = [];
[Z] = [];
Q=[0 0 0 0 0 0;
0 0 0 0 0 0;
0 0 0 0 0 0;
0 0 0 0.01 0 0;
0 0 0 0 0.01 0;
0 0 0 0 0 0.01];% Covarience matrix of process noise
M=[0.001 0 0; 0 0.001 0; 0 0 0.001]; % Covarience matrix of measurment noise
A=[1 0 0 0.1 0 0;
0 1 0 0 0.1 0;
0 0 1 0 0 0.1;
0 0 0 1 0 0;
0 0 0 0 1 0;
0 0 0 0 0 1]; % System Dynamics
in = cat(2,in1,in2);
X(:,1)=in(1,:)'; % Actual initial conditions
Z(:,1)=X(1:3,:);% initial observation
Xh(:,1)=X(:,1);%Assumed initial conditions
P(:,:,1)=[0.1 0 0 0 0 0;
0 0.1 0 0 0 0;
0 0 0.1 0 0 0;
0 0 0 0.1 0 0;
0 0 0 0 0.1 0;
0 0 0 0 0 0.1]; %inital value of covarience of estimation error
% plots
subplot(3,3,1)
xlabel('time')
ylabel('X')
title('X possition')
hold on
subplot(3,3,4)
xlabel('time')
ylabel('Y')
title('Y possition')
hold on
subplot(3,3,7)
xlabel('time')
ylabel('Z')
title('Z possition')
hold on
subplot(2,2,2)
xlabel('time')
title('Minimum MSE')
hold on
subplot(2,2,4)
plot3(0,0,0)
title('3-D trajectory ')
xlabel('X')
ylabel('Y')
zlabel('Z')
hold on
for n=1:100
%% PROCESS AND OBSERVATION PROCESS WITH GAUSSINA NOISE
X(:,n+1)=A*X(:,n)+[0;0;0;sqrt(Q(4,4))*randn(1);sqrt(Q(5,5))*randn(1);sqrt(Q(6,6))*randn(1)]; % State process % w generating process noise
Z(:,n+1)=[sqrt(X(1,n)^2+X(2,n)^2);arctang(X(2,n),X(1,n),ind);X(3,n)]+[sqrt(M(1,1))*randn(1);sqrt(M(1,1))*randn(1);sqrt(M(1,1))*randn(1)]; %generating & observation observation noise
%% prediction of next state
Xh(:,n+1)=A*Xh(:,n);% ESTIMATE
P(:,:,n+1)=A*P(:,:,n)*A'+Q;% PRIORY ERROR COVARIENCE
%% CORRECTION EQUTIONS
H(:,:,n+1)=[Xh(1,n+1)/(sqrt(Xh(1,n+1)^2+Xh(2,n+1)^2)), Xh(2,n+1)/(sqrt(Xh(1,n+1)^2+Xh(2,n+1)^2)),0,0,0,0; ...
-Xh(2,n+1)/(sqrt(Xh(1,n+1)^2+Xh(2,n+1)^2)), Xh(1,n+1)/(sqrt(Xh(1,n+1)^2+Xh(2,n+1)^2)),0,0,0,0; ...
0,0,1,0,0,0]; % Jacobian matrix
K(:,:,n+1)=P(:,:,n+1)*H(:,:,n+1)'*(M+H(:,:,n+1)*P(:,:,n+1)*H(:,:,n+1)')^(-1); % Kalman Gain
Inov=Z(:,n+1)-[sqrt(Xh(1,n+1)^2+Xh(2,n+1)^2);arctang(Xh(2,n+1),Xh(1,n+1),ind);Xh(3,n+1)];% INNOVATION
Xh(:,n+1)=Xh(:,n+1)+ K(:,:,n+1)*Inov; %computes final estimate
P(:,:,n+1)=(eye(6)-K(:,:,n+1)*H(:,:,n+1))*P(:,:,n+1);% %computes covarience of estimation error
%% unwrapping the tan function
theta1=arctang(Xh(1,n+1),Xh(2,n+1),0);
theta=arctang(Xh(1,n),Xh(2,n),0);
if abs(theta1-theta)>=pi
if ind==1
ind=0;
else
ind=1;
end
end
%% Some Plots
subplot(3,3,1)
line([n,n+1],[X(1,n),X(1,n+1)])
hold on
drawnow
subplot(3,3,4)
line([n,n+1],[X(2,n),X(2,n+1)])
hold on
drawnow
subplot(3,3,7)
line([n,n+1],[X(3,n),X(3,n+1)])
hold on
drawnow
subplot(2,2,4)
line([Xh(1,n) Xh(1,n+1)],[Xh(2,n) Xh(2,n+1)],[Xh(3,n) Xh(3,n+1)],'Color','r')
hold on
drawnow
line([X(1,n) X(1,n+1)],[X(2,n) X(2,n+1)],[X(3,n) X(3,n+1)])
hold on
drawnow
subplot(2,2,2)
line([n,n+1],[(X(1,n)-Xh(1,n))^2,(X(1,n+1)-Xh(1,n+1))^2])
hold on
drawnow
line([n,n+1],[(X(2,n)-Xh(2,n))^2,(X(2,n+1)-Xh(2,n+1))^2],'Color','r')
hold on
drawnow
line([n,n+1],[(X(3,n)-Xh(3,n))^2,(X(3,n+1)-Xh(3,n+1))^2],'Color','c')
hold on
drawnow
legend('X-MSE','Y-MSE','Z-MSE')
subplot(3,3,1)
line([n,n+1],[Xh(1,n),Xh(1,n+1)],'Color','r')
hold on
drawnow
subplot(3,3,4)
line([n,n+1],[Xh(2,n),Xh(2,n+1)],'Color','r')
hold on
drawnow
subplot(3,3,7)
line([n,n+1],[Xh(3,n),Xh(3,n+1)],'Color','r')
hold on
drawnow
end
%% arctang
function [ARG]=arctang(A,B,ind)
if B<0 && A>0 % PLACING IN THE RIGHT QUADRANT
ARG=abs(atan(A/B))+pi/2;
elseif B<0 && A<0
ARG=abs(atan(A/B))+pi;
elseif B>0 && A<0
ARG=abs(atan(A/B))+3*pi/2;
else
ARG=atan(A/B);
end
if ind==-1 % UNWARPPING PART
ARG=ARG-2*pi;
else
if ind==1;
ARG=ARG+2*pi;
end
end
end
end
in1 - 对象的位置
-21.8318 19.2251 -16.0000
-21.4604 18.9727 -15.8555
-21.0925 18.7208 -15.7102
-20.7281 18.4693 -15.5639
-20.3671 18.2182 -15.4169
-20.0093 17.9676 -15.2692
-19.6547 17.7173 -15.1208
-19.3031 17.4674 -14.9717
-18.9545 17.2178 -14.8221
-18.6088 16.9687 -14.6719
-18.2658 16.7198 -14.5213
-17.9255 16.4714 -14.3702
-17.5879 16.2232 -14.2187
-17.2528 15.9755 -14.0669
-16.9203 15.7281 -13.9147
-16.5901 15.4811 -13.7623
-16.2623 15.2345 -13.6097
-15.9368 14.9883 -13.4569
-15.6135 14.7425 -13.3040
-15.2925 14.4971 -13.1509
-14.9735 14.2522 -12.9978
-14.6567 14.0078 -12.8446
-14.3420 13.7638 -12.6914
-14.0292 13.5204 -12.5383
-13.7185 13.2776 -12.3852
-13.4097 13.0353 -12.2322
-13.1028 12.7936 -12.0793
-12.7979 12.5525 -11.9266
-12.4948 12.3122 -11.7741
-12.1935 12.0725 -11.6218
-11.8941 11.8336 -11.4697
-11.5965 11.5954 -11.3179
-11.3007 11.3581 -11.1663
-11.0067 11.1216 -11.0151
-10.7144 10.8860 -10.8642
-10.4240 10.6513 -10.7137
-10.1353 10.4176 -10.5635
-9.8483 10.1850 -10.4138
-9.5631 9.9533 -10.2644
-9.2797 9.7228 -10.1155
-8.9980 9.4934 -9.9671
-8.7181 9.2652 -9.8191
-8.4399 9.0382 -9.6717
-8.1636 8.8125 -9.5247
-7.8890 8.5882 -9.3783
-7.6162 8.3652 -9.2325
-7.3452 8.1436 -9.0872
-7.0760 7.9234 -8.9424
-6.8087 7.7048 -8.7983
-6.5432 7.4877 -8.6548
-6.2795 7.2723 -8.5119
-6.0178 7.0584 -8.3696
-5.7579 6.8463 -8.2280
-5.5000 6.6359 -8.0870
-5.2440 6.4273 -7.9467
-4.9899 6.2206 -7.8071
-4.7378 6.0157 -7.6681
-4.4878 5.8127 -7.5299
-4.2397 5.6118 -7.3923
-3.9938 5.4128 -7.2555
-3.7499 5.2159 -7.1194
-3.5080 5.0211 -6.9841
-3.2684 4.8285 -6.8495
-3.0308 4.6380 -6.7156
-2.7955 4.4498 -6.5825
-2.5624 4.2639 -6.4502
-2.3315 4.0803 -6.3187
-2.1028 3.8990 -6.1879
-1.8765 3.7202 -6.0579
-1.6525 3.5438 -5.9287
-1.4308 3.3699 -5.8004
-1.2115 3.1985 -5.6728
-0.9946 3.0297 -5.5460
-0.7801 2.8635 -5.4200
-0.5681 2.6999 -5.2949
-0.3586 2.5390 -5.1706
-0.1516 2.3807 -5.0471
0.0528 2.2253 -4.9245
0.2547 2.0725 -4.8027
0.4539 1.9226 -4.6817
0.6506 1.7755 -4.5616
0.8446 1.6313 -4.4423
1.0358 1.4899 -4.3239
1.2244 1.3514 -4.2063
1.4103 1.2159 -4.0897
1.5934 1.0833 -3.9738
1.7737 0.9538 -3.8589
1.9512 0.8272 -3.7448
2.1258 0.7036 -3.6315
2.2976 0.5831 -3.5192
2.4665 0.4657 -3.4077
2.6326 0.3513 -3.2971
2.7956 0.2400 -3.1874
2.9558 0.1318 -3.0786
3.1130 0.0268 -2.9707
3.2672 -0.0751 -2.8636
3.4184 -0.1739 -2.7575
3.5665 -0.2695 -2.6522
3.7117 -0.3620 -2.5479
3.8537 -0.4513 -2.4444
3.9927 -0.5374 -2.3419
4.1287 -0.6204 -2.2402
4.2615 -0.7002 -2.1395
4.3912 -0.7768 -2.0397
4.5178 -0.8503 -1.9408
4.6413 -0.9205 -1.8428
4.7616 -0.9876 -1.7457
4.8788 -1.0516 -1.6495
4.9928 -1.1124 -1.5542
5.1036 -1.1700 -1.4599
5.2113 -1.2246 -1.3665
5.3158 -1.2760 -1.2740
5.4171 -1.3242 -1.1825
5.5153 -1.3694 -1.0919
5.6102 -1.4115 -1.0022
5.7020 -1.4506 -0.9135
5.7906 -1.4866 -0.8257
5.8760 -1.5195 -0.7388
5.9583 -1.5495 -0.6529
6.0373 -1.5765 -0.5679
6.1132 -1.6005 -0.4839
6.1860 -1.6216 -0.4008
6.2555 -1.6398 -0.3187
6.3220 -1.6551 -0.2376
6.3853 -1.6675 -0.1574
6.4455 -1.6772 -0.0781
6.5026 -1.6840 0.0001
6.5565 -1.6882 0.0774
6.6074 -1.6896 0.1538
6.6553 -1.6883 0.2291
6.7000 -1.6844 0.3035
6.7418 -1.6779 0.3769
6.7805 -1.6688 0.4493
6.8163 -1.6572 0.5207
6.8491 -1.6431 0.5911
6.8789 -1.6266 0.6606
6.9058 -1.6077 0.7290
6.9298 -1.5865 0.7965
6.9510 -1.5630 0.8629
6.9693 -1.5373 0.9283
6.9847 -1.5093 0.9927
6.9974 -1.4792 1.0562
7.0074 -1.4470 1.1185
7.0146 -1.4128 1.1799
7.0191 -1.3766 1.2403
7.0210 -1.3385 1.2996
7.0203 -1.2985 1.3579
7.0170 -1.2567 1.4151
7.0111 -1.2132 1.4714
7.0027 -1.1679 1.5265
6.9919 -1.1210 1.5807
6.9786 -1.0726 1.6338
6.9629 -1.0226 1.6858
6.9449 -0.9712 1.7368
6.9246 -0.9184 1.7867
6.9020 -0.8642 1.8356
6.8773 -0.8088 1.8834
6.8503 -0.7522 1.9301
6.8212 -0.6945 1.9758
6.7901 -0.6357 2.0204
6.7569 -0.5759 2.0639
6.7218 -0.5152 2.1064
6.6847 -0.4536 2.1478
6.6458 -0.3912 2.1881
6.6050 -0.3280 2.2273
6.5625 -0.2643 2.2654
6.5183 -0.1999 2.3024
6.4723 -0.1350 2.3383
6.4248 -0.0696 2.3732
6.3757 -0.0039 2.4069
6.3251 0.0622 2.4396
6.2731 0.1285 2.4711
6.2197 0.1950 2.5016
6.1649 0.2616 2.5309
6.1089 0.3283 2.5592
6.0516 0.3949 2.5863
5.9932 0.4614 2.6124
5.9337 0.5278 2.6373
5.8731 0.5940 2.6611
5.8116 0.6598 2.6839
5.7491 0.7253 2.7055
5.6857 0.7904 2.7261
5.6216 0.8549 2.7455
5.5566 0.9189 2.7638
5.4910 0.9823 2.7811
5.4248 1.0450 2.7972
5.3579 1.1070 2.8122
5.2906 1.1681 2.8262
5.2228 1.2284 2.8391
5.1546 1.2877 2.8508
5.0860 1.3461 2.8615
5.0172 1.4034 2.8712
4.9481 1.4596 2.8797
4.8789 1.5146 2.8872
4.8096 1.5684 2.8936
4.7402 1.6210 2.8990
4.6708 1.6722 2.9033
4.6014 1.7221 2.9066
4.5322 1.7706 2.9088
4.4631 1.8176 2.9100
4.3943 1.8631 2.9102
4.3257 1.9070 2.9094
4.2574 1.9494 2.9076
4.1895 1.9901 2.9047
4.1221 2.0292 2.9009
4.0551 2.0666 2.8961
3.9886 2.1022 2.8904
3.9226 2.1361 2.8837
3.8573 2.1682 2.8761
3.7927 2.1985 2.8676
3.7287 2.2270 2.8581
3.6655 2.2536 2.8478
3.6030 2.2783 2.8365
3.5414 2.3011 2.8244
3.4806 2.3221 2.8115
3.4207 2.3411 2.7978
3.3618 2.3582 2.7832
3.3038 2.3734 2.7679
3.2467 2.3867 2.7517
3.1907 2.3980 2.7349
3.1357 2.4075 2.7173
3.0818 2.4150 2.6990
3.0290 2.4207 2.6800
2.9773 2.4245 2.6604
2.9267 2.4264 2.6401
2.8772 2.4266 2.6192
2.8289 2.4249 2.5978
2.7817 2.4215 2.5758
2.7358 2.4164 2.5533
2.6910 2.4095 2.5303
2.6474 2.4011 2.5068
2.6049 2.3910 2.4829
2.5637 2.3794 2.4587
2.5236 2.3664 2.4340
2.4846 2.3519 2.4091
2.4469 2.3361 2.3838
2.4102 2.3190 2.3584
2.3747 2.3008 2.3327
2.3403 2.2814 2.3068
2.3069 2.2610 2.2808
2.2746 2.2397 2.2548
2.2433 2.2175 2.2287
2.2130 2.1946 2.2026
2.1836 2.1711 2.1765
2.1551 2.1472 2.1506
2.1274 2.1228 2.1248
2.1006 2.0982 2.0992
2.0745 2.0735 2.0739
2.0491 2.0487 2.0489
2.0243 2.0242 2.0242
2.0000 2.0000 2.0000
in2 - 对象速度
0.3714 -0.2524 0.1445
0.3679 -0.2519 0.1454
0.3644 -0.2515 0.1462
0.3610 -0.2511 0.1470
0.3578 -0.2507 0.1477
0.3546 -0.2503 0.1484
0.3516 -0.2499 0.1491
0.3486 -0.2495 0.1496
0.3457 -0.2492 0.1502
0.3430 -0.2488 0.1506
0.3403 -0.2485 0.1511
0.3376 -0.2481 0.1515
0.3351 -0.2478 0.1518
0.3326 -0.2474 0.1521
0.3302 -0.2470 0.1524
0.3278 -0.2466 0.1526
0.3255 -0.2462 0.1528
0.3233 -0.2458 0.1530
0.3211 -0.2454 0.1531
0.3189 -0.2449 0.1531
0.3168 -0.2444 0.1532
0.3148 -0.2439 0.1532
0.3127 -0.2434 0.1531
0.3107 -0.2429 0.1531
0.3088 -0.2423 0.1530
0.3069 -0.2417 0.1529
0.3050 -0.2410 0.1527
0.3031 -0.2404 0.1525
0.3012 -0.2397 0.1523
0.2994 -0.2389 0.1521
0.2976 -0.2382 0.1518
0.2958 -0.2373 0.1515
0.2940 -0.2365 0.1512
0.2922 -0.2356 0.1509
0.2905 -0.2347 0.1505
0.2887 -0.2337 0.1502
0.2870 -0.2327 0.1498
0.2852 -0.2316 0.1493
0.2834 -0.2305 0.1489
0.2817 -0.2294 0.1484
0.2799 -0.2282 0.1480
0.2781 -0.2270 0.1475
0.2764 -0.2257 0.1469
0.2746 -0.2244 0.1464
0.2728 -0.2230 0.1459
0.2710 -0.2216 0.1453
0.2692 -0.2201 0.1447
0.2673 -0.2186 0.1441
0.2655 -0.2171 0.1435
0.2636 -0.2155 0.1429
0.2618 -0.2138 0.1423
0.2599 -0.2121 0.1416
0.2579 -0.2104 0.1410
0.2560 -0.2086 0.1403
0.2540 -0.2068 0.1396
0.2521 -0.2049 0.1389
0.2501 -0.2030 0.1382
0.2480 -0.2010 0.1375
0.2460 -0.1990 0.1368
0.2439 -0.1969 0.1361
0.2418 -0.1948 0.1353
0.2397 -0.1926 0.1346
0.2375 -0.1904 0.1339
0.2353 -0.1882 0.1331
0.2331 -0.1859 0.1323
0.2309 -0.1836 0.1315
0.2286 -0.1812 0.1308
0.2263 -0.1788 0.1300
0.2240 -0.1764 0.1292
0.2217 -0.1739 0.1284
0.2193 -0.1714 0.1276
0.2169 -0.1688 0.1268
0.2145 -0.1662 0.1260
0.2120 -0.1636 0.1251
0.2095 -0.1609 0.1243
0.2070 -0.1582 0.1235
0.2044 -0.1555 0.1226
0.2019 -0.1527 0.1218
0.1993 -0.1499 0.1210
0.1966 -0.1471 0.1201
0.1940 -0.1442 0.1193
0.1913 -0.1414 0.1184
0.1886 -0.1385 0.1176
0.1858 -0.1355 0.1167
0.1831 -0.1326 0.1158
0.1803 -0.1296 0.1150
0.1775 -0.1266 0.1141
0.1747 -0.1236 0.1132
0.1718 -0.1205 0.1123
0.1689 -0.1175 0.1115
0.1660 -0.1144 0.1106
0.1631 -0.1113 0.1097
0.1601 -0.1082 0.1088
0.1572 -0.1051 0.1079
0.1542 -0.1019 0.1070
0.1512 -0.0988 0.1061
0.1482 -0.0956 0.1053
0.1451 -0.0925 0.1044
0.1421 -0.0893 0.1035
0.1390 -0.0861 0.1025
0.1359 -0.0830 0.1016
0.1328 -0.0798 0.1007
0.1297 -0.0766 0.0998
0.1266 -0.0734 0.0989
0.1235 -0.0703 0.0980
0.1203 -0.0671 0.0971
0.1172 -0.0640 0.0962
0.1140 -0.0608 0.0952
0.1108 -0.0577 0.0943
0.1077 -0.0545 0.0934
0.1045 -0.0514 0.0925
0.1013 -0.0483 0.0915
0.0981 -0.0452 0.0906
0.0950 -0.0421 0.0897
0.0918 -0.0390 0.0887
0.0886 -0.0360 0.0878
0.0854 -0.0330 0.0869
0.0822 -0.0300 0.0859
0.0791 -0.0270 0.0850
0.0759 -0.0240 0.0840
0.0727 -0.0211 0.0831
0.0696 -0.0182 0.0821
0.0664 -0.0153 0.0812
0.0633 -0.0125 0.0802
0.0602 -0.0096 0.0792
0.0571 -0.0069 0.0783
0.0540 -0.0041 0.0773
0.0509 -0.0014 0.0763
0.0478 0.0013 0.0754
0.0448 0.0039 0.0744
0.0417 0.0065 0.0734
0.0387 0.0091 0.0724
0.0357 0.0116 0.0714
0.0328 0.0141 0.0704
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