-
Notifications
You must be signed in to change notification settings - Fork 4
/
J3Measurements.m
336 lines (266 loc) · 10 KB
/
J3Measurements.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
% Measurement Simulation
%%
clear all; close all; clc;
%% Constants
%Keplerian orbital elements
a = 10000; %semi-major axis, [km]
e = 0.001; %eccentricity
i = deg2rad(40); %inclination angle, [radians]
RAAN = deg2rad(80); %right ascension of ascending node, [radians]
w = deg2rad(40); %argument of periapsis [radians]
nu = deg2rad(0); %initial true anomaly [radians]
mu = 3.986004415e5; %Earth gravitational parameter, [km^4/s^2]
rE = 6378.136; %Earth radius, [km]
J2 = 0.0010826269; %Earth J2 parameter
J3 = -0.0000025323; %Earth j3 parameter
numOrbits = 15; %number of orbits to integrate
orbitPeriod = 2*pi*sqrt(a^3/mu); %orbital period, [s]
simTime = numOrbits*orbitPeriod; %total simulation time, [s]
tspan = 0:10:simTime; %10 second steps for measurements
spinRate = 7.2921158553e-5; %Earth spin rate, [rad/s]
params = [mu, J2, rE, J3];
%% Convert initial Keplerian constants to initial Cartesian state
p = a*(1-e^2); %semi-latus rectum, [km]
r = p/(1+e*cos(nu)); %orbit radius, [km]
rp = a*(1-e); %periapsis radius, [km]
h = sqrt(mu*a*(1-e^2)); %angular momentum
x = r*(cos(RAAN)*cos(w+nu) - sin(RAAN)*sin(w+nu)*cos(i)); %x-position, [km]
y = r*(sin(RAAN)*cos(w+nu) + cos(RAAN)*sin(w+nu)*cos(i)); %y-position, [km]
z = r*(sin(i)*sin(w+nu)); %z-position, [km]
xdot = x*h*e/(r*p)*sin(nu) - h/r*(cos(RAAN)*sin(w+nu) + sin(RAAN)*cos(w+nu)*cos(i)); %x-velocity, [km/s]
ydot = y*h*e/(r*p)*sin(nu) - h/r*(sin(RAAN)*sin(w+nu) - cos(RAAN)*cos(w+nu)*cos(i)); %y-velocity, [km/s]
zdot = z*h*e/(r*p)*sin(nu) + h/r*sin(i)*cos(w+nu);
X0 = [x y z xdot ydot zdot]'; %initial state vector
%% Compute reference trajectory (no perturbation)
%deltx0 = [1 0 0 0 10/1000 0]'; %[r v]'
deltx0 = [0 0 0 0 0 0 ]';
X0pert = X0 + deltx0;
options = odeset('RelTol', 1e-13, 'AbsTol', 1e-13);
[t, XJ3] = ode45(@(t,X) J3Dynamics(t, X, params), tspan, X0pert, options);
%% Plot trajectory
[xSph, ySph, zSph] = sphere;
figure(1)
surf(rE*xSph,rE*ySph,rE*zSph)
hold on
plot3(XJ3(:,1), XJ3(:,2), XJ3(:,3))
scatter3(X0(1), X0(2), X0(3))
view([50 30])
xlabel('Inertial X, [km]')
ylabel('Inertial Y, [km]')
zlabel('Inertial Z, [km]')
title('Trajectory in ECI frame')
%% Generate station states
theta0 = 122; %initial spin angle of Earth relative to ECI frame [degrees]
stationStatesLatLong = [rE -35.39833 148.981944; rE 40.427222 355.74944; rE 35.247164 243.205;];
% stationECEFPositions = [
% rE*cosd(stationStatesLatLong(1,2)*cosd(stationStatesLatLong(1,3) + theta), rE*cosd(stationStatesLatLong(1,2)*sind(stationStatesLatLong(1,3) + theta), rE*sind(stationStatesLatLong(1,2);
% rE*cosd(stationStatesLatLong(2,2)*cosd(stationStatesLatLong(2,3) + theta), rE*cosd(stationStatesLatLong(2,2)*sind(stationStatesLatLong(2,3) + theta), rE*sind(stationStatesLatLong(2,2);
% rE*cosd(stationStatesLatLong(3,2)*cosd(stationStatesLatLong(3,3) + theta), rE*cosd(stationStatesLatLong(3,2)*sind(stationStatesLatLong(3,3) + theta), rE*sind(stationStatesLatLong(3,2)];
stationStates = zeros(6, 3, length(tspan));
stationOmega = [0, 0, spinRate]';
stationOmegas = repmat(stationOmega, 1, 1, length(stationStates));
%station inertial states
for i=1:3
stationStates(1,i,:) = rE*sind(90 - stationStatesLatLong(i,2))*cos(spinRate*tspan + deg2rad(stationStatesLatLong(i,3) + theta0)); %station x
stationStates(2,i,:) = rE*sind(90 - stationStatesLatLong(i,2))*sin(spinRate*tspan + deg2rad(stationStatesLatLong(i,3) + theta0)); %station y
stationStates(3,i,:) = rE*cosd(90 - stationStatesLatLong(i,2)); %station z
stationVel = cross(stationOmegas, stationStates(1:3,i,:), 1);
stationStates(4:6,i,:) = stationVel;
% stationStates(4,i,:) = -spinRate*rE*sind(90 - stationStatesLatLong(i,2))*sin(spinRate*tspan + deg2rad(stationStatesLatLong(i,3) + theta0)); %station xdot
% stationStates(5,i,:) = spinRate*rE*sind(90 - stationStatesLatLong(i,2))*cos(spinRate*tspan + deg2rad(stationStatesLatLong(i,3) + theta0)); %station xdot
% stationStates(6,i,:) = 0; %station zdot
end
%% Simulate measurements
elevationMask = 10; %station elevation mask, stations can only see spacecraft if it is at least 10 degrees above station horizon [degrees]
y = zeros(3, 2, length(tspan));
stationElevationAngles = zeros(3, 1, length(tspan));
meas_Aformat = [];
% Noise characteristics for measurements
sigmaRange = 0.001; % 1m [km]
sigmaRangeRate = 1e-6; % 1mm/s [km/s]
for i = 1:3
for j = 1:length(tspan)
%RStationSC projected onto RStation >= RStationSC*sin(10 degrees) for
%visibility <-- doesn't work, not sure why
rangeNoise = normrnd(0, sigmaRange);
rangeRateNoise = normrnd(0, sigmaRangeRate);
RStationSC = XJ3(j,1:3)' - stationStates(1:3,i,j); %vector from station to space station
RStationUnit = stationStates(1:3,i,j)/norm(stationStates(1:3,i,j)); %space station position unit vector
stationElevationAngles(i,1,j) = 90 - atan2d(norm(cross(RStationSC, stationStates(1:3,i,j))), dot(RStationSC, stationStates(1:3,i,j)));
if stationElevationAngles(i,1,j) >= 10
y(i,1,j) = norm(RStationSC) + rangeNoise; %range measurement
y(i,2,j) = dot(RStationSC',(XJ3(j,4:6)' - stationStates(4:6,i,j)))/norm(RStationSC) + rangeRateNoise; %range rate measurement
% Save Andrew format data
meas_Aformat = [meas_Aformat;
tspan(j), i, norm(RStationSC) + rangeNoise, ...
((RStationSC'*(XJ3(j,4:6)' - stationStates(4:6,i,j)))/norm(RStationSC)) + rangeRateNoise];
else
y(i,:,j) = NaN; %no measurement
end
end
end
%% Save out data
%Save out measurements with noise for hw3
sigmarange = 0.001; %sigma range is 1m
sigmarangerate = 1/(1e6); %sigma range rate is 1 mm/s
youtJ3 = zeros(size(y));
youtJ3(:,1,:) = y(:,1,:) + normrnd(0, sigmarange, 3, 1, length(tspan));
youtJ3(:,2,:) = y(:,2,:) + normrnd(0, sigmarangerate, 3, 1, length(tspan));
save('measurementsJ3_saiformat.mat', 'youtJ3');
% Convert measurements to Andrew's format
measAFormatSorted = sortrows(meas_Aformat,1);
save('measurements_A.mat', 'measAFormatSorted');
% Save out station state data
save('stationStates.mat', 'stationStates');
%Save out true orbit data for hw3
save('trueorbitdataJ3.mat', 'XJ3');
%% Plot measurements
figure
subplot(2,3,1)
plot(tspan, reshape(y(1,1,:), 1, []))
xlabel('Time [s]')
ylabel('Range [km]')
title('Station 1 Range')
subplot(2,3,2)
plot(tspan, reshape(y(2,1,:), 1, []))
xlabel('Time [s]')
ylabel('Range [km]')
title('Station 2 Range')
subplot(2,3,3)
plot(tspan, reshape(y(3,1,:), 1, []))
xlabel('Time [s]')
ylabel('Range [km]')
title('Station 3 Range')
subplot(2,3,4)
plot(tspan, reshape(y(1,2,:), 1, []))
xlabel('Time [s]')
ylabel('Range Rate [km/s]')
title('Station 1 Range Rate')
subplot(2,3,5)
plot(tspan, reshape(y(2,2,:), 1, []))
xlabel('Time [s]')
ylabel('Range Rate [km/s]')
title('Station 2 Range Rate')
subplot(2,3,6)
plot(tspan, reshape(y(3,2,:), 1, []))
xlabel('Time [s]')
ylabel('Range Rate [km/s]')
title('Station 3 Range Rate')
% Plot elevation angles
figure
subplot(3,1,1)
hold on
plot(tspan, reshape(stationElevationAngles(1,1,:), 1, []))
plot([0, tspan(end)], [10, 10])
xlabel('Time [s]')
ylabel('Elevation Angle [degrees]')
title('Station 1 Elevation')
hold off
subplot(3,1,2)
hold on
plot(tspan, reshape(stationElevationAngles(2,1,:), 1, []))
plot([0, tspan(end)], [10, 10])
xlabel('Time [s]')
ylabel('Elevation Angle [degrees]')
title('Station 2 Elevation')
hold off
subplot(3,1,3)
hold on
plot(tspan, reshape(stationElevationAngles(3,1,:), 1, []))
plot([0, tspan(end)], [10, 10])
xlabel('Time [s]')
ylabel('Elevation Angle [degrees]')
title('Station 3 Elevation')
hold off
%% Real units
fref = 8.44; %reference transmit frequency [GHz]
c = 299792458/1000; %speed of light [km/s]
freqData = -2*y(:,2,:)/c*fref; %range rate converted to doppler shift freq data
rangeUnits = 221/749*y(:,1,:)/c*fref; %range converted to range units
%Plot new data
figure
subplot(2,3,1)
plot(tspan, reshape(rangeUnits(1,1,:), 1, []))
xlabel('Time [s]')
ylabel('Range [RU]')
title('Station 1 Range')
subplot(2,3,2)
plot(tspan, reshape(rangeUnits(2,1,:), 1, []))
xlabel('Time [s]')
ylabel('Range [RU]')
title('Station 2 Range')
subplot(2,3,3)
plot(tspan, reshape(rangeUnits(3,1,:), 1, []))
xlabel('Time [s]')
ylabel('Range [RU]')
title('Station 3 Range')
subplot(2,3,4)
plot(tspan, reshape(freqData(1,1,:), 1, []))
xlabel('Time [s]')
ylabel('Doppler Shift [GHz]')
title('Station 1 Range Rate')
subplot(2,3,5)
plot(tspan, reshape(freqData(2,1,:), 1, []))
xlabel('Time [s]')
ylabel('Doppler Shift [GHz]')
title('Station 2 Range Rate')
subplot(2,3,6)
plot(tspan, reshape(freqData(3,1,:), 1, []))
xlabel('Time [s]')
ylabel('Doppler Shift [GHz]')
title('Station 3 Range Rate')
%% Data with noise
sigma = 0.5/(1e6);
rangeRateNoise = normrnd(0, sigma, 3, 1, length(tspan));
noisyRangeRate = y(:,2,:) + rangeRateNoise;
% Plot noisy range rate data
figure
subplot(3,1,1)
hold on
plot(tspan, reshape(noisyRangeRate(1,1,:), 1, []))
plot(tspan, reshape(y(1,2,:), 1, []))
xlabel('Time [s]')
ylabel('Range Rate [km/s]')
title('Station 1 Range Rate')
legend('Noisy Range Rate Data', 'Original Range Rate Data')
hold off
subplot(3,1,2)
hold on
plot(tspan, reshape(noisyRangeRate(2,1,:), 1, []))
plot(tspan, reshape(y(2,2,:), 1, []))
xlabel('Time [s]')
ylabel('Range Rate [km/s]')
title('Station 2 Range Rate')
hold off
subplot(3,1,3)
hold on
plot(tspan, reshape(noisyRangeRate(3,1,:), 1, []))
plot(tspan, reshape(y(3,2,:), 1, []))
xlabel('Time [s]')
ylabel('Range Rate [km/s]')
title('Station 3 Range Rate')
hold off
%% Noisy minus original measurements
figure
subplot(3,1,1)
hold on
plot(tspan, reshape(noisyRangeRate(1,1,:)-y(1,2,:), 1, []))
xlabel('Time [s]')
ylabel('Range Rate [km/s]')
title('Station 1 Range Rate Difference')
legend('Noisy minus original range rates')
hold off
subplot(3,1,2)
hold on
plot(tspan, reshape(noisyRangeRate(2,1,:)-y(2,2,:), 1, []))
xlabel('Time [s]')
ylabel('Range Rate [km/s]')
title('Station 2 Range Rate Difference')
hold off
subplot(3,1,3)
hold on
plot(tspan, reshape(noisyRangeRate(3,1,:)-y(3,2,:), 1, []))
xlabel('Time [s]')
ylabel('Range Rate [km/s]')
title('Station 3 Range Rate Difference')
hold off