-
Notifications
You must be signed in to change notification settings - Fork 0
/
fTracker.m
392 lines (342 loc) · 10.1 KB
/
fTracker.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
% ftracker - kalman filter cv/ca
T=2; % 采样间隔
Tsim=60; % 仿真时间
Nt=Tsim/T;% 仿真总采样点数
n1=1; % 循环次数
filter=1; % 0-CV,1- CA
q1=1;%20 目标1过程噪声标准偏差 m
q=3;%20 % 滤波器设置的过程噪声标准偏差 m
rd1=150; % 传感器1距离测量噪声实际标准偏差 m
rbeita1=0.9*pi/180;% 传感器1方位角测量噪声实际标准偏差 角度
rebuxinon1=0.9*pi/180;% 传感器1高低角测量噪声实际标准偏差 角度
rmd1=150; % 传感器1距离测量噪声模型标准偏差
rmbeita1=0.9*pi/180;% 传感器1方位角测量噪声模型标准偏差
rmebuxinon1=0.9*pi/180;% 传感器1高低角测量噪声模型标准偏差
rmdf1=rmd1^2; % 传感器1距离测量噪声模型方差
rmbeitaf1=rmbeita1^2;% 传感器1方位角测量噪声模型方差
rmebuxinonf1=rmebuxinon1^2; % 传感器1高低角测量噪声模型方差
for n=1:n1
%%%% 航迹生成-直角坐标 %%%%
%pi=3.1415926;
x1=zeros(1,Nt); % 目标1
y1=zeros(1,Nt);
z1=zeros(1,Nt);
Vx=zeros(1,Nt); % 目标1
Vy=zeros(1,Nt);
Vz=zeros(1,Nt);
Ax=zeros(1,Nt); % 目标1
Ay=zeros(1,Nt);
Az=zeros(1,Nt);
x1(1,1)=10000;
y1(1,1)=10000;
z1(1,1)=2000;
Vx(1,1)=-100;
Vy(1,1)=-100;
Vz(1,1)=0;
for k=1:10
Ax(1,k)=0;
Ay(1,k)=0;
Az(1,k)=0;
end
for k=11:18
Ax(1,k)=-20;
Ay(1,k)=-10;
Az(1,k)=0;
end
for k=19:30
Ax(1,k)=0;
Ay(1,k)=0;
Az(1,k)=0;
end
for k=1:29 % 匀速
x1(1,k+1)=x1(1,k)+Vx(1,k)*T+0.5*Ax(1,k)*T^2+normrnd(0,q1);
y1(1,k+1)=y1(1,k)+Vy(1,k)*T+0.5*Ay(1,k)*T^2+normrnd(0,q1);
z1(1,k+1)=z1(1,k)+Vz(1,k)*T+0.5*Az(1,k)*T^2+normrnd(0,0.5*q1);
Vx(1,k+1)=Vx(1,k)+Ax(1,k)*T;
Vy(1,k+1)=Vy(1,k)+Ay(1,k)*T;
Vz(1,k+1)=Vz(1,k)+Az(1,k)*T;
end
%%%% 量测生成 %%%%%%%%%%
%% 直/球坐标变换
beita1=zeros(1,Nt);
ebuxinon1=zeros(1,Nt);
D1=zeros(1,Nt);
beita1c=zeros(1,Nt);
ebuxinon1c=zeros(1,Nt);
D1c=zeros(1,Nt);
for k=1:Nt % 航迹真值生成—球坐标
beita1(1,k)=atan2(y1(1,k),x1(1,k)); % atan2四象限反正切
ebuxinon1(1,k)=atan2(z1(1,k),(x1(1,k)^2+y1(1,k)^2)^0.5);
D1(1,k)=(x1(1,k)^2+y1(1,k)^2+z1(1,k)^2)^0.5;
end
for k=1:Nt % 测量噪声—球坐标
beita1c(1,k)=beita1(1,k)+normrnd(0,rbeita1);
ebuxinon1c(1,k)=ebuxinon1(1,k)+normrnd(0,rebuxinon1);
D1c(1,k)=D1(1,k)+normrnd(0,rd1);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 传感器1滤波%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 球/直坐标变换
zx1=zeros(1,Nt);
zy1=zeros(1,Nt);
zz1=zeros(1,Nt);
R1=zeros(3,3,Nt);
R2=zeros(3,3,Nt);
for k=1:Nt % 测量量球/直坐标变换
zx1(1,k)=D1c(1,k)*cos(ebuxinon1c(1,k))*cos(beita1c(1,k));
zy1(1,k)=D1c(1,k)*cos(ebuxinon1c(1,k))*sin(beita1c(1,k));
zz1(1,k)=D1c(1,k)*sin(ebuxinon1c(1,k));
end
Z1=[zx1
zy1
zz1];
for k=1:Nt% 测量误差协方差球/直转换
R1(1,1,k)=rmdf1*cos(ebuxinon1c(1,k))^2*cos(beita1c(1,k))^2+D1c(1,k)^2*cos(ebuxinon1c(1,k))^2*sin(beita1c(1,k))^2*rmbeitaf1... % 测量误差协方差球/直转换
+D1c(1,k)^2*sin(ebuxinon1c(1,k))^2*cos(beita1c(1,k))^2*rmebuxinonf1;
R1(2,2,k)=rmdf1*cos(ebuxinon1c(1,k))^2*sin(beita1c(1,k))^2+D1c(1,k)^2*cos(ebuxinon1c(1,k))^2*cos(beita1c(1,k))^2*rmbeitaf1...
+D1c(1,k)^2*sin(ebuxinon1c(1,k))^2*cos(beita1c(1,k))^2*rmebuxinonf1;
R1(3,3,k)=rmdf1*sin(ebuxinon1c(1,k))^2+D1c(1,k)^2*cos(ebuxinon1c(1,k))^2*rmebuxinonf1;
R1(1,2,k)=0.5*sin(2*beita1c(1,k))*(rmdf1*cos(ebuxinon1c(1,k))^2-D1c(1,k)^2*cos(ebuxinon1c(1,k))^2*rmbeitaf1...
+D1c(1,k)^2*sin(ebuxinon1c(1,k))^2*rmebuxinonf1);
R1(2,3,k)=0.5*sin(2*ebuxinon1c(1,k))*(rmdf1-D1c(1,k)^2*rmebuxinonf1)*sin(beita1c(1,k));
R1(1,3,k)=0.5*sin(2*ebuxinon1c(1,k))*(rmdf1-D1c(1,k)^2*rmebuxinonf1)*cos(beita1c(1,k));
R1(2,1,k)=R1(1,2,k)';
R1(3,2,k)=R1(2,3,k)';
R1(3,1,k)=R1(1,3,k)';
end
%% 滤波初始化及参数设置%%%
if filter==0 % % 0-CV,1- CA
%% -CV- %%%
%% 滤波初始化及参数设置%%%
Xg1=zeros(6,Nt);
P1=zeros(6,6,Nt);
F1=[1 T 0 0 0 0
0 1 0 0 0 0
0 0 1 T 0 0
0 0 0 1 0 0
0 0 0 0 1 T
0 0 0 0 0 1];
G1=[1/2*T^2 T 0 0 0 0
0 0 1/2*T^2 T 0 0
0 0 0 0 1/2*T^2 T]';
B1=[1/2*T^2 T 1/2*T^2 T 1/2*T^2 T]';
H1=[1 0 0 0 0 0
0 0 1 0 0 0
0 0 0 0 1 0];
Q1=q^2*[1 0 0
0 1 0
0 0 1];
Xg1(:,2)=[zx1(1,2)
(zx1(1,2)-zx1(1,1))/T
zy1(1,2)
(zy1(1,2)-zy1(1,1))/T
zz1(1,2)
(zz1(1,2)-zz1(1,1))/T];
P1(:,:,2)=[R1(1,1,2) R1(1,1,2)/T R1(1,2,2) R1(1,2,2)/T R1(1,3,2) R1(1,3,2)/T
R1(1,1,2)/T 2*R1(1,1,2)/T^2 R1(1,2,2)/T 2*R1(1,2,2)/T^2 R1(1,3,2)/T 2*R1(1,3,2)/T^2
R1(1,2,2) R1(1,2,2)/T R1(2,2,2) R1(2,2,2)/T R1(2,3,2) R1(2,3,2)/T
R1(1,2,2)/T 2*R1(1,2,2)/T^2 R1(2,2,2)/T 2*R1(2,2,2)/T^2 R1(2,3,2)/T 2*R1(2,3,2)/T^2
R1(1,3,2) R1(1,3,2)/T R1(2,3,2) R1(2,3,2)/T R1(3,3,2) R1(3,3,2)/T
R1(1,3,2)/T 2*R1(1,3,2)/T^2 R1(2,3,2)/T 2*R1(2,3,2)/T^2 R1(3,3,2)/T 2*R1(3,3,2)/T^2];
%%%%%%% CV kalmnf %%%%%%
Xy1=zeros(6,Nt);
Zy1=zeros(3,Nt);
v1=zeros(3,Nt);
Py1=zeros(6,6,Nt);
S1=zeros(3,3,Nt);
K1=zeros(6,3,Nt);
for k=2:(Nt-1)
Xy1(:,k+1)=F1*Xg1(:,k);
Zy1(:,k+1)=H1*Xy1(:,k+1);
v1(:,k+1)=Z1(:,k+1)-Zy1(:,k+1);
Py1(:,:,k+1)=F1*P1(:,:,k)*F1'+G1*Q1*G1';
S1(:,:,k+1)=H1*Py1(:,:,k+1)*H1'+R1(:,:,k+1);
K1(:,:,k+1)=Py1(:,:,k+1)*H1'*inv(S1(:,:,k+1));
P1(:,:,k+1)=Py1(:,:,k+1)-K1(:,:,k+1)*S1(:,:,k+1)*K1(:,:,k+1)';
Xg1(:,k+1)=Xy1(:,k+1)+K1(:,:,k+1)*v1(:,k+1);
end
else
%% -CA- %%%
%% 滤波初始化及参数设置%%%
Xg1=zeros(9,Nt);
P1=zeros(9,9,Nt);
F1=[1 T 1/2*T^2 0 0 0 0 0 0
0 1 T 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0
0 0 0 1 T 1/2*T^2 0 0 0
0 0 0 0 1 T 0 0 0
0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 1 T 1/2*T^2
0 0 0 0 0 0 0 1 T
0 0 0 0 0 0 0 0 1];
G1=[1/2*T^2 T 1 0 0 0 0 0 0
0 0 0 1/2*T^2 T 1 0 0 0
0 0 0 0 0 0 1/2*T^2 T 1]';
%B1=[1/2*T^2 T 1/2*T^2 T 1/2*T^2 T]';
H1=[1 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 1 0 0];
Q1=q^2*[1 0 0
0 1 0
0 0 1];
Xg1(:,3)=[zx1(1,3)
(zx1(1,3)-zx1(1,2))/T
(zx1(1,3)-2*zx1(1,2)+zx1(1,1))/T^2
zy1(1,3)
(zy1(1,3)-zy1(1,2))/T
(zy1(1,3)-2*zy1(1,2)+zy1(1,1))/T^2
zz1(1,3)
(zz1(1,3)-zz1(1,2))/T
(zz1(1,3)-2*zz1(1,2)+zz1(1,1))/T^2];
%P1(:,:,2)=[R1(1,1,2) R1(1,1,2)/T R1(1,2,2) R1(1,2,2)/T R1(1,3,2) R1(1,3,2)/T
% R1(1,1,2)/T 2*R1(1,1,2)/T^2 R1(1,2,2)/T 2*R1(1,2,2)/T^2 R1(1,3,2)/T 2*R1(1,3,2)/T^2
% R1(1,2,2) R1(1,2,2)/T R1(2,2,2) R1(2,2,2)/T R1(2,3,2) R1(2,3,2)/T
% R1(1,2,2)/T 2*R1(1,2,2)/T^2 R1(2,2,2)/T 2*R1(2,2,2)/T^2 R1(2,3,2)/T 2*R1(2,3,2)/T^2
% R1(1,3,2) R1(1,3,2)/T R1(2,3,2) R1(2,3,2)/T R1(3,3,2) R1(3,3,2)/T
% R1(1,3,2)/T 2*R1(1,3,2)/T^2 R1(2,3,2)/T 2*R1(2,3,2)/T^2 R1(3,3,2)/T 2*R1(3,3,2)/T^2];
P1(:,:,3)=[R1(1,1,3) R1(1,1,3)/T R1(1,1,3)/T^2 R1(1,2,3) R1(1,2,3)/T R1(1,2,3)/T^2 R1(1,3,3) R1(1,3,3)/T R1(1,3,3)/T^2
R1(1,1,3)/T 2*R1(1,1,3)/T^2 3*R1(1,1,3)/T^3 R1(1,2,3)/T 2*R1(1,2,3)/T^2 3*R1(1,2,3)/T^3 R1(1,3,3)/T 2*R1(1,3,3)/T^2 3*R1(1,3,3)/T^3
R1(1,1,3)/T^2 3*R1(1,1,3)/T^3 6*R1(1,1,3)/T^4 R1(1,2,3)/T^2 3*R1(1,2,3)/T^3 6*R1(1,2,3)/T^4 R1(1,3,3)/T^2 3*R1(1,3,3)/T^3 6*R1(1,3,3)/T^4
R1(1,2,3) R1(1,2,3)/T R1(1,2,3)/T^2 R1(2,2,3) R1(2,2,3)/T R1(2,2,3)/T^2 R1(2,3,3) R1(2,3,3)/T R1(2,3,3)/T^2
R1(1,2,3)/T 2*R1(1,2,3)/T^2 3*R1(1,2,3)/T^3 R1(2,2,3)/T 2*R1(2,2,3)/T^2 3*R1(2,2,3)/T^3 R1(2,3,3)/T 2*R1(2,3,3)/T^2 3*R1(2,3,3)/T^3
R1(1,2,3)/T^2 3*R1(1,2,3)/T^3 6*R1(1,2,3)/T^4 R1(2,2,3)/T^2 3*R1(2,2,3)/T^3 6*R1(2,2,3)/T^4 R1(2,3,3)/T^2 3*R1(2,3,3)/T^3 6*R1(2,3,3)/T^4
R1(1,3,3) R1(1,3,3)/T R1(1,3,3)/T^2 R1(2,3,3) R1(2,3,3)/T R1(2,3,3)/T^2 R1(3,3,3) R1(3,3,3)/T R1(3,3,3)/T^2
R1(1,3,3)/T 2*R1(1,3,3)/T^2 3*R1(1,3,3)/T^3 R1(2,3,3)/T 2*R1(2,3,3)/T^2 3*R1(2,3,3)/T^3 R1(3,3,3)/T 2*R1(3,3,3)/T^2 3*R1(3,3,3)/T^3
R1(1,3,3)/T^2 3*R1(1,3,3)/T^3 6*R1(1,3,3)/T^4 R1(2,3,3)/T^2 3*R1(2,3,3)/T^3 6*R1(2,3,3)/T^4 R1(3,3,3)/T^2 3*R1(3,3,3)/T^3 6*R1(3,3,3)/T^4];
%%%%%%% CA kalmnf %%%%%%
Xy1=zeros(9,Nt);
Zy1=zeros(3,Nt);
v1=zeros(3,Nt);
Py1=zeros(9,9,Nt);
S1=zeros(3,3,Nt);
K1=zeros(9,3,Nt);
for k=3:(Nt-1)
Xy1(:,k+1)=F1*Xg1(:,k);
Zy1(:,k+1)=H1*Xy1(:,k+1);
v1(:,k+1)=Z1(:,k+1)-Zy1(:,k+1);
Py1(:,:,k+1)=F1*P1(:,:,k)*F1'+G1*Q1*G1';
S1(:,:,k+1)=H1*Py1(:,:,k+1)*H1'+R1(:,:,k+1);
K1(:,:,k+1)=Py1(:,:,k+1)*H1'*inv(S1(:,:,k+1));
P1(:,:,k+1)=Py1(:,:,k+1)-K1(:,:,k+1)*S1(:,:,k+1)*K1(:,:,k+1)';
Xg1(:,k+1)=Xy1(:,k+1)+K1(:,:,k+1)*v1(:,k+1);
end
end % for filter=CV
end % for n=1:n1
%%%%%%%%%%%%%%%% 绘图 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% 航迹绘图 %%%%%%
trackplot=0;
if trackplot==1
k=1:Nt;
figure(20);
plot(k,x1);
hold on;
plot(k,zx1,'y');
hold off;
figure(21);
plot(k,y1);
hold on;
plot(k,zy1,'y');
hold off;
figure(22);
plot(k,z1);
hold on;
plot(k,zz1,'y');
hold off;
figure(23);
plot(x1,y1);
hold on;
plot(zx1,zy1,'y');
hold off;
end
%%%% 绘制误差曲线 %%%%%%
if filter==0
k=2:Nt;
figure (1)
plot(k,Xg1(1,k)-x1(1,k))
title ('egx1-b/elx1-r')
grid
hold on
plot(k,Z1(1,k)-x1(1,k),'r')
hold off
figure (2)
plot(k,Xg1(3,k)-y1(1,k))
title ('egy1-b/ely1-r')
grid
hold on
plot(k,Z1(2,k)-y1(1,k),'r')
hold off
figure (3)
plot(k,Xg1(5,k)-z1(1,k))
title ('egz1-b/elz1-r')
grid
hold on
plot(k,Z1(3,k)-z1(1,k),'r')
hold off
figure (4)
plot(k,Xg1(2,k))
title ('Vgx-b')
grid
hold off
figure (5)
plot(k,Xg1(4,k))
title ('Vgy-b')
grid
hold off
figure (6)
plot(k,Xg1(6,k))
title ('Vgz-b')
grid
hold off
else
k=3:Nt;
figure (11)
plot(k,Xg1(1,k)-x1(1,k))
title ('egx1-b/elx1-r')
grid
hold on
plot(k,Z1(1,k)-x1(1,k),'r')
hold off
figure (21)
plot(k,Xg1(4,k)-y1(1,k))
title ('egy1-b/ely1-r')
grid
hold on
plot(k,Z1(2,k)-y1(1,k),'r')
hold off
figure (31)
plot(k,Xg1(7,k)-z1(1,k))
title ('egz1-b/elz1-r')
grid
hold on
plot(k,Z1(3,k)-z1(1,k),'r')
hold off
figure (41)
plot(k,Xg1(2,k))
title ('Vgx-b')
grid
hold off
figure (51)
plot(k,Xg1(5,k))
title ('Vgy-b')
grid
hold off
figure (61)
plot(k,Xg1(8,k))
title ('Vgz-b')
grid
hold off
figure (71)
plot(k,Xg1(3,k))
title ('Agx-b')
grid
hold off
figure (81)
plot(k,Xg1(6,k))
title ('Agy-b')
grid
hold off
figure (91)
plot(k,Xg1(9,k))
title ('Agz-b')
grid
hold off
end % if filter==0