卡尔曼滤波器Matlab初始化的假设

时间:2014-05-09 22:17:59

标签: matlab signal-processing kalman-filter

我正在Matlab中设计一个卡尔曼滤波器,但我想设置初始值。我已经设置了以下矩阵并找到了设置初始化观察的方法。

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
P=[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

我想设置初始观察,因为我在Matrix X中有实际初始条件,观察矩阵和其余假设的假设初始化是什么。

编辑1: 我在Matlab中实现了EKF(扩展卡尔曼滤波器),用于对象的3D轨迹的视觉跟踪,但是,我将实际轨迹的位置和速度分别设为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。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

样本位置矩阵in1:

 -191.2442  187.7193    1.0000
 -188.3010  184.5880    1.0880
 -185.7538  181.3845    1.1760
 -183.5429  178.1301    1.2640
 -181.6158  174.8440    1.3520
 -179.9268  171.5442    1.4400
 -178.4357  168.2469    1.5280
 -177.1073  164.9674    1.6160
 -175.9110  161.7195    1.7040
 -174.8199  158.5160    1.7920
 -173.8109  155.3688    1.8800
 -172.8634  152.2884    1.9680
 -171.9599  149.2849    2.0560
 -171.0849  146.3669    2.1440
 -170.2251  143.5427    2.2320
 -169.3691  140.8192    2.3200
 -168.5068  138.2028    2.4080
 -167.6298  135.6988    2.4960
 -166.7307  133.3120    2.5840
 -165.8035  131.0459    2.6720
 -164.8429  128.9038    2.7600
 -163.8447  126.8877    2.8480
 -162.8053  124.9991    2.9360
 -161.7219  123.2387    3.0240
 -160.5925  121.6065    3.1120
 -159.4156  120.1018    3.2000
 -158.1900  118.7233    3.2879
 -156.9155  117.4689    3.3759
 -155.5919  116.3360    3.4639
 -154.2197  115.3214    3.5518
 -152.7997  114.4215    3.6398
 -151.3331  113.6319    3.7277
 -149.8214  112.9480    3.8156
 -148.2665  112.3647    3.9035
 -146.6706  111.8764    3.9913
 -145.0360  111.4775    4.0791
 -143.3655  111.1617    4.1669
 -141.6619  110.9226    4.2546
 -139.9283  110.7537    4.3422
 -138.1681  110.6481    4.4298
 -136.3846  110.5991    4.5173
 -134.5815  110.5995    4.6047
 -132.7624  110.6424    4.6919
 -130.9310  110.7206    4.7791
 -129.0913  110.8272    4.8661
 -127.2472  110.9553    4.9529
 -125.4024  111.0978    5.0395
 -123.5610  111.2482    5.1260
 -121.7268  111.3998    5.2121
 -119.9036  111.5463    5.2981
 -118.0952  111.6816    5.3837
 -116.3052  111.7997    5.4690
 -114.5371  111.8949    5.5539
 -112.7944  111.9621    5.6384
 -111.0803  111.9962    5.7225
 -109.3980  111.9924    5.8062
 -107.7502  111.9465    5.8893
 -106.1398  111.8546    5.9718
 -104.5691  111.7130    6.0537
 -103.0406  111.5185    6.1350
 -101.5561  111.2684    6.2156
 -100.1174  110.9602    6.2954
  -98.7262  110.5919    6.3744
  -97.3835  110.1619    6.4525
  -96.0906  109.6691    6.5297
  -94.8480  109.1126    6.6059
  -93.6563  108.4921    6.6810
  -92.5156  107.8075    6.7551
  -91.4259  107.0592    6.8279
  -90.3868  106.2479    6.8996
  -89.3979  105.3748    6.9699
  -88.4582  104.4414    7.0389
  -87.5667  103.4493    7.1064
  -86.7222  102.4007    7.1724
  -85.9230  101.2981    7.2369
  -85.1674  100.1441    7.2998
  -84.4536   98.9417    7.3609
  -83.7795   97.6940    7.4203
  -83.1427   96.4047    7.4779
  -82.5409   95.0772    7.5336
  -81.9715   93.7154    7.5874
  -81.4318   92.3234    7.6392
  -80.9191   90.9052    7.6889
  -80.4304   89.4650    7.7365
  -79.9629   88.0072    7.7819
  -79.5136   86.5363    7.8251
  -79.0794   85.0565    7.8660
  -78.6574   83.5725    7.9047
  -78.2444   82.0885    7.9409
  -77.8375   80.6092    7.9748
  -77.4337   79.1388    8.0062
  -77.0299   77.6817    8.0352
  -76.6235   76.2420    8.0616
  -76.2114   74.8239    8.0855
  -75.7912   73.4314    8.1068
  -75.3600   72.0681    8.1256
  -74.9155   70.7379    8.1418
  -74.4552   69.4440    8.1553
  -73.9769   68.1898    8.1662
  -73.4786   66.9783    8.1745
  -72.9582   65.8121    8.1802
  -72.4140   64.6940    8.1832
  -71.8445   63.6260    8.1836
  -71.2480   62.6103    8.1813
  -70.6234   61.6485    8.1764
  -69.9696   60.7420    8.1690
  -69.2856   59.8920    8.1590
  -68.5707   59.0994    8.1464
  -67.8243   58.3645    8.1313
  -67.0460   57.6878    8.1137
  -66.2356   57.0691    8.0936
  -65.3931   56.5080    8.0711
  -64.5185   56.0039    8.0462
  -63.6122   55.5557    8.0189
  -62.6745   55.1624    7.9894
  -61.7061   54.8223    7.9576
  -60.7076   54.5336    7.9236
  -59.6799   54.2943    7.8875
  -58.6240   54.1020    7.8493
  -57.5409   53.9543    7.8090
  -56.4319   53.8484    7.7668
  -55.2982   53.7812    7.7227
  -54.1413   53.7497    7.6768
  -52.9624   53.7505    7.6291
  -51.7632   53.7800    7.5797
  -50.5453   53.8347    7.5287
  -49.3101   53.9108    7.4761
  -48.0594   54.0044    7.4221
  -46.7947   54.1115    7.3667
  -45.5178   54.2283    7.3099
  -44.2303   54.3506    7.2520
  -42.9339   54.4743    7.1928
  -41.6301   54.5954    7.1326
  -40.3206   54.7098    7.0714
  -39.0069   54.8135    7.0094
  -37.6904   54.9026    6.9464
  -36.3727   54.9731    6.8828
  -35.0551   55.0213    6.8185
  -33.7388   55.0436    6.7537
  -32.4252   55.0364    6.6883
  -31.1153   54.9963    6.6226
  -29.8101   54.9201    6.5566
  -28.5106   54.8048    6.4904
  -27.2175   54.6475    6.4241
  -25.9318   54.4456    6.3577
  -24.6538   54.1968    6.2914
  -23.3842   53.8988    6.2252
  -22.1233   53.5496    6.1592
  -20.8714   53.1477    6.0936
  -19.6287   52.6916    6.0284
  -18.3953   52.1802    5.9636
  -17.1710   51.6124    5.8995
  -15.9558   50.9878    5.8360
  -14.7494   50.3059    5.7733
  -13.5515   49.5667    5.7114
  -12.3616   48.7704    5.6504
  -11.1793   47.9173    5.5904
  -10.0039   47.0083    5.5315
   -8.8348   46.0443    5.4738
   -7.6713   45.0265    5.4172
   -6.5127   43.9565    5.3620
   -5.3581   42.8359    5.3082
   -4.2066   41.6666    5.2559
   -3.0576   40.4510    5.2050
   -1.9100   39.1912    5.1558
   -0.7631   37.8900    5.1082
    0.3839   36.5499    5.0623
    1.5320   35.1740    5.0181
    2.6817   33.7654    4.9758
    3.8339   32.3272    4.9354
    4.9891   30.8627    4.8969
    6.1479   29.3755    4.8603
    7.3108   27.8690    4.8257
    8.4781   26.3468    4.7932
    9.6500   24.8128    4.7627
   10.8267   23.2704    4.7342
   12.0081   21.7236    4.7078
   13.1940   20.1761    4.6835
   14.3840   18.6316    4.6613
   15.5776   17.0940    4.6411
   16.7741   15.5669    4.6231
   17.9726   14.0540    4.6070
   19.1719   12.5590    4.5929
   20.3707   11.0854    4.5809
   21.5675    9.6367    4.5707
   22.7606    8.2163    4.5624
   23.9480    6.8275    4.5560
   25.1275    5.4734    4.5512
   26.2967    4.1571    4.5482
   27.4529    2.8815    4.5467
   28.5935    1.6494    4.5466
   29.7153    0.4634    4.5480
   30.8151   -0.6739    4.5506
   31.8895   -1.7604    4.5543
   32.9349   -2.7938    4.5591
   33.9476   -3.7721    4.5647
   34.9236   -4.6935    4.5711
   35.8589   -5.5565    4.5780
   36.7494   -6.3596    4.5853
   37.5908   -7.1015    4.5928
   38.3789   -7.7812    4.6004
   39.1092   -8.3978    4.6079
   39.7775   -8.9506    4.6151
   40.3795   -9.4393    4.6218
   40.9107   -9.8634    4.6278
   41.3672  -10.2231    4.6330
   41.7448  -10.5184    4.6370
   42.0396  -10.7497    4.6398
   42.2479  -10.9178    4.6410
   42.3663  -11.0232    4.6406
   42.3917  -11.0673    4.6384
   42.3211  -11.0511    4.6340
   42.1522  -10.9764    4.6273
   41.8829  -10.8447    4.6182
   41.5116  -10.6582    4.6065
   41.0374  -10.4190    4.5919
   40.4598  -10.1297    4.5743
   39.7789   -9.7931    4.5535
   38.9955   -9.4121    4.5295
   38.1111   -8.9900    4.5020
   37.1279   -8.5302    4.4709
   36.0491   -8.0365    4.4361
   34.8783   -7.5129    4.3975
   33.6204   -6.9635    4.3550
   32.2809   -6.3928    4.3085
   30.8663   -5.8052    4.2580
   29.3839   -5.2056    4.2035
   27.8420   -4.5989    4.1448
   26.2499   -3.9901    4.0821
   24.6175   -3.3843    4.0153
   22.9558   -2.7866    3.9444
   21.2765   -2.2021    3.8695
   19.5922   -1.6360    3.7908
   17.9157   -1.0932    3.7082
   16.2608   -0.5785    3.6220
   14.6415   -0.0964    3.5323
   13.0719    0.3489    3.4392
   11.5663    0.7537    3.3430
   10.1385    1.1146    3.2439
    8.8020    1.4292    3.1423
    7.5692    1.6953    3.0384
    6.4513    1.9120    2.9327
    5.4576    2.0791    2.8256
    4.5952    2.1974    2.7177
    3.8682    2.2689    2.6094
    3.2769    2.2970    2.5015
    2.8173    2.2862    2.3948
    2.4798    2.2427    2.2901
    2.2484    2.1741    2.1886
    2.0994    2.0895    2.0914
    2.0000    2.0000    2.0000

样本速度矩阵in2:

    2.9432   -3.1313    0.0880
    2.5472   -3.2035    0.0880
    2.2109   -3.2545    0.0880
    1.9270   -3.2861    0.0880
    1.6890   -3.2998    0.0880
    1.4912   -3.2972    0.0880
    1.3284   -3.2795    0.0880
    1.1963   -3.2479    0.0880
    1.0910   -3.2035    0.0880
    1.0091   -3.1473    0.0880
    0.9475   -3.0803    0.0880
    0.9035   -3.0036    0.0880
    0.8750   -2.9179    0.0880
    0.8598   -2.8243    0.0880
    0.8561   -2.7235    0.0880
    0.8623   -2.6164    0.0880
    0.8770   -2.5040    0.0880
    0.8990   -2.3869    0.0880
    0.9272   -2.2660    0.0880
    0.9606   -2.1422    0.0880
    0.9983   -2.0161    0.0880
    1.0394   -1.8886    0.0880
    1.0833   -1.7604    0.0880
    1.1294   -1.6322    0.0880
    1.1770   -1.5047    0.0880
    1.2255   -1.3785    0.0880
    1.2746   -1.2544    0.0880
    1.3236   -1.1329    0.0880
    1.3722   -1.0146    0.0880
    1.4200   -0.9000    0.0879
    1.4666   -0.7896    0.0879
    1.5117   -0.6839    0.0879
    1.5549   -0.5833    0.0879
    1.5959   -0.4882    0.0878
    1.6346   -0.3990    0.0878
    1.6705   -0.3158    0.0878
    1.7036   -0.2391    0.0877
    1.7336   -0.1689    0.0876
    1.7602   -0.1055    0.0876
    1.7835   -0.0491    0.0875
    1.8031    0.0004    0.0874
    1.8191    0.0429    0.0873
    1.8313    0.0783    0.0871
    1.8397    0.1066    0.0870
    1.8442    0.1280    0.0868
    1.8447    0.1426    0.0866
    1.8414    0.1504    0.0864
    1.8342    0.1516    0.0862
    1.8232    0.1465    0.0859
    1.8084    0.1352    0.0856
    1.7900    0.1181    0.0853
    1.7681    0.0953    0.0849
    1.7427    0.0672    0.0845
    1.7141    0.0340    0.0841
    1.6824   -0.0037    0.0836
    1.6478   -0.0459    0.0831
    1.6104   -0.0920    0.0825
    1.5706   -0.1416    0.0819
    1.5286   -0.1945    0.0813
    1.4845   -0.2501    0.0806
    1.4386   -0.3082    0.0798
    1.3913   -0.3683    0.0790
    1.3426   -0.4299    0.0781
    1.2930   -0.4928    0.0772
    1.2426   -0.5565    0.0762
    1.1917   -0.6205    0.0751
    1.1407   -0.6846    0.0740
    1.0897   -0.7483    0.0729
    1.0390   -0.8113    0.0716
    0.9889   -0.8731    0.0703
    0.9397   -0.9335    0.0690
    0.8915   -0.9921    0.0675
    0.8446   -1.0486    0.0660
    0.7992   -1.1026    0.0645
    0.7555   -1.1540    0.0629
    0.7138   -1.2024    0.0612
    0.6741   -1.2476    0.0594
    0.6368   -1.2894    0.0576
    0.6018   -1.3275    0.0557
    0.5694   -1.3618    0.0538
    0.5397   -1.3921    0.0518
    0.5127   -1.4182    0.0497
    0.4886   -1.4402    0.0476
    0.4675   -1.4578    0.0454
    0.4493   -1.4710    0.0432
    0.4342   -1.4797    0.0409
    0.4221   -1.4841    0.0386
    0.4130   -1.4839    0.0363
    0.4069   -1.4793    0.0339
    0.4038   -1.4704    0.0314
    0.4037   -1.4571    0.0289
    0.4065   -1.4397    0.0264
    0.4120   -1.4181    0.0239
    0.4203   -1.3926    0.0213
    0.4312   -1.3632    0.0188
    0.4445   -1.3303    0.0162
    0.4603   -1.2939    0.0135
    0.4783   -1.2542    0.0109
    0.4983   -1.2116    0.0083
    0.5204   -1.1661    0.0056
    0.5442   -1.1182    0.0030
    0.5696   -1.0680    0.0004
    0.5964   -1.0157   -0.0022
    0.6246   -0.9618   -0.0049
    0.6538   -0.9065   -0.0075
    0.6840   -0.8500   -0.0100
    0.7149   -0.7927   -0.0126
    0.7464   -0.7348   -0.0151
    0.7783   -0.6767   -0.0176
    0.8104   -0.6187   -0.0201
    0.8425   -0.5611   -0.0225
    0.8746   -0.5041   -0.0249
    0.9063   -0.4481   -0.0272
    0.9377   -0.3934   -0.0295
    0.9684   -0.3401   -0.0318
    0.9985   -0.2887   -0.0340
    1.0277   -0.2393   -0.0361
    1.0559   -0.1922   -0.0382
    1.0831   -0.1477   -0.0402
    1.1090   -0.1059   -0.0422
    1.1337   -0.0672   -0.0441
    1.1570   -0.0315   -0.0459
    1.1788    0.0008   -0.0477
    1.1992    0.0295   -0.0494
    1.2180    0.0547   -0.0510
    1.2352    0.0761   -0.0526
    1.2507    0.0936   -0.0540
    1.2646    0.1072   -0.0554
    1.2769    0.1167   -0.0567
    1.2875    0.1223   -0.0580
    1.2964    0.1237   -0.0591
    1.3038    0.1211   -0.0602
    1.3095    0.1144   -0.0612
    1.3137    0.1037   -0.0621
    1.3164    0.0891   -0.0629
    1.3177    0.0705   -0.0636
    1.3176    0.0482   -0.0643
    1.3162    0.0223   -0.0649
    1.3136   -0.0072   -0.0653
    1.3099   -0.0401   -0.0657
    1.3052   -0.0762   -0.0660
    1.2995   -0.1153   -0.0662
    1.2930   -0.1573   -0.0663
    1.2858   -0.2019   -0.0664
    1.2780   -0.2489   -0.0663
    1.2696   -0.2980   -0.0662
    1.2609   -0.3491   -0.0659
    1.2519   -0.4019   -0.0656
    1.2427   -0.4561   -0.0652
    1.2335   -0.5115   -0.0647
    1.2242   -0.5677   -0.0641
    1.2152   -0.6246   -0.0635
    1.2064   -0.6819   -0.0627
    1.1979   -0.7392   -0.0619
    1.1899   -0.7964   -0.0610
    1.1823   -0.8530   -0.0600
    1.1754   -0.9090   -0.0589
    1.1691   -0.9640   -0.0577
    1.1635   -1.0178   -0.0565
    1.1587   -1.0700   -0.0552
    1.1546   -1.1206   -0.0538
    1.1514   -1.1692   -0.0524
    1.1491   -1.2157   -0.0508
    1.1476   -1.2598   -0.0493
    1.1469   -1.3013   -0.0476
    1.1471   -1.3400   -0.0459
    1.1480   -1.3759   -0.0441
    1.1497   -1.4087   -0.0423
    1.1522   -1.4382   -0.0404
    1.1552   -1.4645   -0.0385
    1.1588   -1.4872   -0.0366
    1.1629   -1.5065   -0.0346
    1.1673   -1.5221   -0.0326
    1.1719   -1.5341   -0.0305
    1.1767   -1.5423   -0.0285
    1.1814   -1.5468   -0.0264
    1.1859   -1.5475   -0.0243
    1.1900   -1.5445   -0.0222
    1.1936   -1.5376   -0.0202
    1.1965   -1.5271   -0.0181
    1.1985   -1.5129   -0.0161
    1.1993   -1.4950   -0.0140
    1.1988   -1.4736   -0.0121
    1.1968   -1.4487   -0.0102
    1.1931   -1.4204   -0.0083
    1.1874   -1.3888   -0.0065
    1.1795   -1.3541   -0.0047
    1.1692   -1.3163   -0.0031
    1.1563   -1.2756   -0.0015
    1.1406   -1.2321   -0.0000
    1.1218   -1.1860    0.0014
    1.0998   -1.1374    0.0026
    1.0744   -1.0864    0.0037
    1.0454   -1.0334    0.0048
    1.0127   -0.9783    0.0056
    0.9760   -0.9215    0.0063
    0.9353   -0.8630    0.0069
    0.8905   -0.8031    0.0073
    0.8414   -0.7419    0.0075
    0.7881   -0.6797    0.0076
    0.7304   -0.6166    0.0075
    0.6683   -0.5528    0.0072
    0.6019   -0.4886    0.0067
    0.5313   -0.4242    0.0060
    0.4565   -0.3597    0.0051
    0.3776   -0.2953    0.0040
    0.2948   -0.2314    0.0028
    0.2083   -0.1680    0.0013
    0.1184   -0.1055   -0.0004
    0.0253   -0.0440   -0.0023
   -0.0706    0.0161   -0.0044
   -0.1689    0.0748   -0.0066
   -0.2693    0.1317   -0.0091
   -0.3712    0.1865   -0.0118
   -0.4742    0.2392   -0.0146
   -0.5776    0.2893   -0.0176
   -0.6809    0.3366   -0.0207
   -0.7834    0.3810   -0.0241
   -0.8844    0.4221   -0.0275
   -0.9831    0.4598   -0.0311
   -1.0789    0.4937   -0.0348
   -1.1707    0.5236   -0.0386
   -1.2579    0.5494   -0.0425
   -1.3395    0.5708   -0.0465
   -1.4146    0.5875   -0.0505
   -1.4824    0.5996   -0.0546
   -1.5419    0.6067   -0.0586
   -1.5922    0.6088   -0.0627
   -1.6324    0.6058   -0.0668
   -1.6617    0.5977   -0.0709
   -1.6793    0.5844   -0.0748
   -1.6844    0.5661   -0.0788
   -1.6764    0.5428   -0.0826
   -1.6549    0.5147   -0.0862
   -1.6193    0.4821   -0.0897
   -1.5696    0.4453   -0.0931
   -1.5056    0.4048   -0.0962
   -1.4278    0.3610   -0.0991
   -1.3365    0.3145   -0.1016
   -1.2328    0.2662   -0.1039
   -1.1179    0.2167   -0.1057
   -0.9937    0.1671   -0.1071
   -0.8624    0.1183   -0.1080
   -0.7270    0.0715   -0.1083
   -0.5913    0.0281   -0.1079
   -0.4596   -0.0108   -0.1067
   -0.3375   -0.0435   -0.1047
   -0.2314   -0.0686   -0.1015
   -0.1490   -0.0845   -0.0972
   -0.0994   -0.0895   -0.0914
    1.0000    1.0000    1.0000

1 个答案:

答案 0 :(得分:0)

观察矩阵H先验(预测)状态向量x1与测量向量z之间的“链接”,因此z=H*x1 。因此观察矩阵是滤波器的参数,通常它不会改变。我们不知道您在测量和过滤哪些数据,因此我们无法详细说明矩阵H的形式以及您提供的其他矩阵。

PS。矩阵A的形式表明你是恒定速度运动的动力学模型,测量周期为0.1秒。矩阵M的形式建议测量3个量,可能是3D空间中的位置。如果这是正确的,您的测量矩阵应如下所示:

H=[1 0 0 0 0 0; 0 1 0 0 0 0; 0 0 1 0 0 0];

假设x1z是列向量,它表示测量的预测只是由先验状态向量的前三个元素组成。

http://en.wikipedia.org/wiki/Kalman_filter#Update