3 % Copyright (c) 2014 Samsung Electronics Co., Ltd.
\r
5 % Licensed under the Apache License, Version 2.0 (the "License");
\r
6 % you may not use this file except in compliance with the License.
\r
7 % You may obtain a copy of the License at
\r
9 % http://www.apache.org/licenses/LICENSE-2.0
\r
11 % Unless required by applicable law or agreed to in writing, software
\r
12 % distributed under the License is distributed on an "AS IS" BASIS,
\r
13 % WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
\r
14 % See the License for the specific language governing permissions and
\r
15 % limitations under the License.
\r
17 % Sensor Fusion Implementation - Orientation Estimation
\r
19 % - Orientation Estimation using Gyroscope as the driving system and Accelerometer+Geo-Magnetic Sensors as Aiding System.
\r
20 % - Quaternion based approach
\r
21 % - Estimation and correction of Euler errors and bias errors for gyroscope using Kalman filter
\r
26 LOW_PASS_FILTERING_ON = 1;
\r
28 Max_Range_Accel = 39.203407; Min_Range_Accel = -39.204006; Res_Accel = 0.000598;
\r
29 Max_Range_Gyro = 1146.862549; Min_Range_Gyro = -1146.880005; Res_Gyro = 0.017500;
\r
30 Max_Range_Magnetic = 1200; Min_Range_Magnetic = -1200; Res_Magnetic = 1;
\r
38 Bias_Az = 10.084 - GRAVITY;
\r
45 MOVING_AVERAGE_WINDOW_LENGTH = 20;
\r
46 RAD2DEG = 57.2957795;
\r
47 DEG2RAD = 0.0174532925;
\r
48 US2S = 1.0 / 1000000.0;
\r
51 % Systron-donner "Horizon"
\r
52 ZigmaW = 0.05 * DEG2RAD; %deg/s
\r
55 %ZigmaW = 0.05 * DEG2RAD; %deg/s
\r
57 %FOGs (KVH Autogyro and Crossbow DMU-FOG)
\r
58 %ZigmaW = 0; %deg/s
\r
60 % get accel x,y,z axis data from stored file
\r
61 Ax = (((dlmread("sensor_data/100ms/roll_pitch_yaw/accel.txt")(:,1))') - Bias_Ax)(1:BUFFER_SIZE);
\r
62 Ay = (((dlmread("sensor_data/100ms/roll_pitch_yaw/accel.txt")(:,2))') - Bias_Ay)(1:BUFFER_SIZE);
\r
63 Az = (((dlmread("sensor_data/100ms/roll_pitch_yaw/accel.txt")(:,3))') - Bias_Az)(1:BUFFER_SIZE);
\r
64 ATime = ((dlmread("sensor_data/100ms/roll_pitch_yaw/accel.txt")(:,4))');
\r
66 % get gyro x,y,z axis data from stored file
\r
67 Gx = (((dlmread("sensor_data/100ms/roll_pitch_yaw/gyro.txt")(:,1))') - Bias_Gx)(1:BUFFER_SIZE);
\r
68 Gy = (((dlmread("sensor_data/100ms/roll_pitch_yaw/gyro.txt")(:,2))') - Bias_Gy)(1:BUFFER_SIZE);
\r
69 Gz = (((dlmread("sensor_data/100ms/roll_pitch_yaw/gyro.txt")(:,3))') - Bias_Gz)(1:BUFFER_SIZE);
\r
70 GTime = ((dlmread("sensor_data/100ms/roll_pitch_yaw/gyro.txt")(:,4))');
\r
77 % get magnetometer x,y,z axis data from stored file
\r
78 Mx = (((dlmread("sensor_data/100ms/roll_pitch_yaw/magnetic.txt")(:,1))'))(1:BUFFER_SIZE);
\r
79 My = (((dlmread("sensor_data/100ms/roll_pitch_yaw/magnetic.txt")(:,2))'))(1:BUFFER_SIZE);
\r
80 Mz = (((dlmread("sensor_data/100ms/roll_pitch_yaw/magnetic.txt")(:,3))'))(1:BUFFER_SIZE);
\r
81 MTime = ((dlmread("sensor_data/100ms/roll_pitch_yaw/magnetic.txt")(:,4))');
\r
83 % Gyroscope Bias Variables
\r
84 Bx = 0; By = 0; Bz = 0;
\r
86 % 1st order smoothening filter
\r
88 a = [1.0000000 0.02 ];
\r
90 % initialize filter output variables to zero
\r
91 filt_Ax = zeros(1,BUFFER_SIZE);
\r
92 filt_Ay = zeros(1,BUFFER_SIZE);
\r
93 filt_Az = zeros(1,BUFFER_SIZE);
\r
94 filt_Gx = zeros(1,BUFFER_SIZE);
\r
95 filt_Gy = zeros(1,BUFFER_SIZE);
\r
96 filt_Gz = zeros(1,BUFFER_SIZE);
\r
97 filt_Mx = zeros(1,BUFFER_SIZE);
\r
98 filt_My = zeros(1,BUFFER_SIZE);
\r
99 filt_Mz = zeros(1,BUFFER_SIZE);
\r
101 acc_x = zeros(1,BUFFER_SIZE);
\r
102 acc_y = zeros(1,BUFFER_SIZE);
\r
103 acc_z = zeros(1,BUFFER_SIZE);
\r
104 gyr_x = zeros(1,BUFFER_SIZE);
\r
105 gyr_y = zeros(1,BUFFER_SIZE);
\r
106 gyr_z = zeros(1,BUFFER_SIZE);
\r
107 mag_x = zeros(1,BUFFER_SIZE);
\r
108 mag_y = zeros(1,BUFFER_SIZE);
\r
109 mag_z = zeros(1,BUFFER_SIZE);
\r
111 % User Acceleration mean and Variance
\r
112 A_T = zeros(1,BUFFER_SIZE);
\r
113 G_T = zeros(1,BUFFER_SIZE);
\r
114 M_T = zeros(1,BUFFER_SIZE);
\r
115 var_roll = zeros(1,BUFFER_SIZE);
\r
116 var_pitch = zeros(1,BUFFER_SIZE);
\r
117 var_yaw = zeros(1,BUFFER_SIZE);
\r
118 var_Gx = zeros(1,BUFFER_SIZE);
\r
119 var_Gy = zeros(1,BUFFER_SIZE);
\r
120 var_Gz = zeros(1,BUFFER_SIZE);
\r
122 roll = zeros(1,BUFFER_SIZE);
\r
123 pitch = zeros(1,BUFFER_SIZE);
\r
124 yaw = zeros(1,BUFFER_SIZE);
\r
125 quat_driv = zeros(BUFFER_SIZE,4);
\r
126 quat_aid = zeros(BUFFER_SIZE,4);
\r
127 quat_error = zeros(BUFFER_SIZE,4);
\r
128 euler = zeros(BUFFER_SIZE,3);
\r
129 Ro = zeros(3, 3, BUFFER_SIZE);
\r
131 % system covariance matrix
\r
134 % measurement covariance matrix
\r
141 acc_e = [0.0;0.0;1.0]; % gravity vector in earth frame
\r
142 mag_e = [0.0;1.0;0.0]; % magnetic field vector in earth frame
\r
144 H = [eye(3) zeros(3,3); zeros(3,6)];
\r
145 x = zeros(6,BUFFER_SIZE);
\r
147 P = 1 * eye(6);% state covariance matrix
\r
149 quat_driv(1,:) = [1 0 0 0];
\r
151 % first order filtering
\r
152 for i = 1:BUFFER_SIZE
\r
153 if LOW_PASS_FILTERING_ON == 1
\r
155 filt_Ax(i) = Ax(i);
\r
156 filt_Ay(i) = Ay(i);
\r
157 filt_Az(i) = Az(i);
\r
158 filt_Gx(i) = Gx(i);
\r
159 filt_Gy(i) = Gy(i);
\r
160 filt_Gz(i) = Gz(i);
\r
161 filt_Mx(i) = Mx(i);
\r
162 filt_My(i) = My(i);
\r
163 filt_Mz(i) = Mz(i);
\r
165 filt_Ax(i) = -a(2)*filt_Ax(i-1)+b(1)*Ax(i);
\r
166 filt_Ay(i) = -a(2)*filt_Ay(i-1)+b(1)*Ay(i);
\r
167 filt_Az(i) = -a(2)*filt_Az(i-1)+b(1)*Az(i);
\r
168 filt_Gx(i) = -a(2)*filt_Gx(i-1)+b(1)*Gx(i);
\r
169 filt_Gy(i) = -a(2)*filt_Gy(i-1)+b(1)*Gy(i);
\r
170 filt_Gz(i) = -a(2)*filt_Gz(i-1)+b(1)*Gz(i);
\r
171 filt_Mx(i) = -a(2)*filt_Mx(i-1)+b(1)*Mx(i);
\r
172 filt_My(i) = -a(2)*filt_My(i-1)+b(1)*My(i);
\r
173 filt_Mz(i) = -a(2)*filt_Mz(i-1)+b(1)*Mz(i);
\r
176 filt_Ax(i) = Ax(i);
\r
177 filt_Ay(i) = Ay(i);
\r
178 filt_Az(i) = Az(i);
\r
179 filt_Gx(i) = Gx(i);
\r
180 filt_Gy(i) = Gy(i);
\r
181 filt_Gz(i) = Gz(i);
\r
182 filt_Mx(i) = Mx(i);
\r
183 filt_My(i) = My(i);
\r
184 filt_Mz(i) = Mz(i);
\r
187 % normalize accelerometer measurements
\r
188 norm_acc = 1/sqrt(filt_Ax(i)^2 + filt_Ay(i)^2 + filt_Az(i)^2);
\r
189 acc_x(i) = norm_acc * filt_Ax(i);
\r
190 acc_y(i) = norm_acc * filt_Ay(i);
\r
191 acc_z(i) = norm_acc * filt_Az(i);
\r
193 % normalize magnetometer measurements
\r
194 norm_mag = 1/sqrt(filt_Mx(i)^2 + filt_My(i)^2 + filt_Mz(i)^2);
\r
195 mag_x(i) = norm_mag * filt_Mx(i);
\r
196 mag_y(i) = norm_mag * filt_My(i);
\r
197 mag_z(i) = norm_mag * filt_Mz(i);
\r
199 gyr_x(i) = filt_Gx(i) * PI;
\r
200 gyr_y(i) = filt_Gy(i) * PI;
\r
201 gyr_z(i) = filt_Gz(i) * PI;
\r
203 UA(i) = sqrt(acc_x(i)^2 + acc_y(i)^2 + acc_z(i)^2) - GRAVITY;
\r
205 gyr_x(i) = gyr_x(i) - Bx;
\r
206 gyr_y(i) = gyr_y(i) - By;
\r
207 gyr_z(i) = gyr_z(i) - Bz;
\r
209 % Aiding System (Accelerometer + Geomagnetic) quaternion generation
\r
210 % gravity vector in body frame
\r
211 acc_b =[acc_x(i);acc_y(i);acc_z(i)];
\r
212 % magnetic field vector in body frame
\r
213 mag_b =[mag_x(i);mag_y(i);mag_z(i)];
\r
215 % compute measurement quaternion with TRIAD algorithm
\r
216 acc_b_x_mag_b = cross(acc_b,mag_b);
\r
217 acc_e_x_mag_e = cross(acc_e,mag_e);
\r
218 M_b = [acc_b acc_b_x_mag_b cross(acc_b_x_mag_b,acc_b)];
\r
219 M_e = [acc_e acc_e_x_mag_e cross(acc_e_x_mag_e,acc_e)];
\r
220 Rot_m = M_e * M_b';
\r
221 quat_aid(i,:) = RotMat2Quat(Rot_m);
\r
223 euler = Quat2Euler(quat_aid(i,:));
\r
224 roll(i) = euler(1);
\r
225 pitch(i) = euler(2);
\r
228 if i <= MOVING_AVERAGE_WINDOW_LENGTH
\r
229 var_Gx(i) = NON_ZERO_VAL;
\r
230 var_Gy(i) = NON_ZERO_VAL;
\r
231 var_Gz(i) = NON_ZERO_VAL;
\r
232 var_roll(i) = NON_ZERO_VAL;
\r
233 var_pitch(i) = NON_ZERO_VAL;
\r
234 var_yaw(i) = NON_ZERO_VAL;
\r
236 var_Gx(i) = var(gyr_x((i-MOVING_AVERAGE_WINDOW_LENGTH):i));
\r
237 var_Gy(i) = var(gyr_y((i-MOVING_AVERAGE_WINDOW_LENGTH):i));
\r
238 var_Gz(i) = var(gyr_z((i-MOVING_AVERAGE_WINDOW_LENGTH):i));
\r
239 var_roll(i) = var(roll((i-MOVING_AVERAGE_WINDOW_LENGTH):i));
\r
240 var_pitch(i) = var(pitch((i-MOVING_AVERAGE_WINDOW_LENGTH):i));
\r
241 var_yaw(i) = var(yaw((i-MOVING_AVERAGE_WINDOW_LENGTH):i));
\r
244 A_T(i) = ATime(i) - ATime(i-1);
\r
245 G_T(i) = GTime(i) - GTime(i-1);
\r
246 M_T(i) = MTime(i) - MTime(i-1);
\r
249 dt = G_T(i) * US2S;
\r
251 Qwn = [var_Gx(i) 0 0;0 var_Gy(i) 0;0 0 var_Gz(i);];
\r
252 Qwb = (2 * (ZigmaW^2) / TauW) * eye(3);
\r
254 % Process Noise Covariance
\r
255 Q = [Qwn zeros(3,3);zeros(3,3) Qwb];
\r
257 % Measurement Noise Covariance
\r
258 R = [[var_roll(i) 0 0;0 var_pitch(i) 0;0 0 var_yaw(i)] zeros(3,3); zeros(3,3) zeros(3,3)];
\r
260 % initialization for q
\r
265 q_t = [q(2) q(3) q(4)]';
\r
266 Rtan = (q(1)^2 - q_t'*q_t)*eye(3) + 2*q_t*q_t' - 2*q(1)*[0 -q(4) q(3);q(4) 0 -q(2);-q(3) q(2) 0];
\r
267 F = [[0 gyr_z(i) -gyr_y(i);-gyr_z(i) 0 gyr_x(i);gyr_y(i) -gyr_x(i) 0] Rtan; zeros(3,3) (-(1/TauW) * eye(3))];
\r
271 x(:,i) = F * x(:,i-1);
\r
274 % compute covariance of prediction
\r
275 P = (F * P * F') + Q;
\r
277 % Driving System (Gyroscope) quaternion generation
\r
278 % convert scaled gyro data to rad/s
\r
279 qDot = 0.5 * QuatProd(q, [0 gyr_x(i) gyr_y(i) gyr_z(i)]);
\r
281 % Integrate to yield quaternion
\r
282 q = q + qDot * dt * PI;
\r
284 % normalise quaternion
\r
285 quat_driv(i,:) = q / norm(q);
\r
288 quat_error(i,:) = QuatProd(quat_aid(i,:), quat_driv(i,:));
\r
290 euler_e = Quat2Euler(quat_error(i,:));
\r
291 x1 = euler_e(1)'/PI;
\r
292 x2 = euler_e(2)'/PI;
\r
293 x3 = euler_e(3)'/PI;
\r
295 q = QuatProd(quat_driv(i,:), [1 x1 x2 x3]) * PI;
\r
303 e = [x1 x2 x3 x(4,i) x(5,i) x(6,i)];
\r
307 % compute Kalman gain
\r
308 K(:,j) = P(j ,:)./(P(j,j)+R(j,j));
\r
309 % update state vector
\r
310 x(:,i) = x(:,i) + K(:,j) * e(j);
\r
311 % update covariance matrix
\r
312 P = (eye(6) - (K(:,j) * H(j,:))) * P;
\r
317 roll = roll * RAD2DEG;
\r
318 pitch = pitch * RAD2DEG;
\r
319 yaw = yaw * RAD2DEG;
\r
321 euler = Quat2Euler(quat_driv);
\r
322 phi = euler(:,1)' * RAD2DEG;
\r
323 theta = euler(:,2)' * RAD2DEG;
\r
324 psi = -euler(:,3)' * RAD2DEG;
\r
326 euler = Quat2Euler(quat_error);
\r
327 roll_e = euler(:,1)' * RAD2DEG;
\r
328 pitch_e = euler(:,2)' * RAD2DEG;
\r
329 yaw_e = euler(:,3)' * RAD2DEG;
\r
334 % Rotation Plot Results
\r
336 scrsz = get(0,'ScreenSize');
\r
337 set(hfig,'position',scrsz);
\r
340 p1 = plot(1:length(UA),UA(1,1:length(UA)),'r');
\r
344 p2 = plot(1:length(UA),UA(1,1:length(UA)),'b');
\r
348 p3 = plot(1:length(UA),UA(1,1:length(UA)),'g');
\r
350 legend([p1 p2 p3],'Aiding System', 'Driving System', 'Quaternion based error');
\r
353 p1 = plot(1:length(UA),UA(1,1:length(UA)),'r');
\r
357 p2 = plot(1:length(UA),UA(1,1:length(UA)),'b');
\r
361 p3 = plot(1:length(UA),UA(1,1:length(UA)),'g');
\r
363 legend([p1 p2 p3],'Aiding System', 'Driving System', 'Quaternion based error');
\r
366 p1 = plot(1:length(UA),UA(1,1:length(UA)),'r');
\r
370 p2 = plot(1:length(UA),UA(1,1:length(UA)),'b');
\r
374 p3 = plot(1:length(UA),UA(1,1:length(UA)),'g');
\r
376 legend([p1 p2 p3],'Aiding System', 'Driving System', 'Quaternion based error');
\r
378 % Accelerometer/Gyroscope/Magnetometer scaled Plot results
\r
380 scrsz = get(0,'ScreenSize');
\r
381 set(hfig,'position',scrsz);
\r
383 p1 = plot(1:BUFFER_SIZE,acc_x(1,1:BUFFER_SIZE),'r');
\r
386 p2 = plot(1:BUFFER_SIZE,gyr_x(1,1:BUFFER_SIZE),'b');
\r
389 p3 = plot(1:BUFFER_SIZE,mag_x(1,1:BUFFER_SIZE),'k');
\r
390 title(['Accelerometer/Gyroscope/Magnetometer X-Axis Plot']);
\r
391 legend([p1 p2 p3],'Acc_X', 'Gyr_X', 'Mag_X');
\r
393 p1 = plot(1:BUFFER_SIZE,acc_y(1,1:BUFFER_SIZE),'r');
\r
396 p2 = plot(1:BUFFER_SIZE,gyr_y(1,1:BUFFER_SIZE),'b');
\r
399 p3 = plot(1:BUFFER_SIZE,mag_y(1,1:BUFFER_SIZE),'k');
\r
400 title(['Accelerometer/Gyroscope/Magnetometer Y-Axis Plot']);
\r
401 legend([p1 p2 p3],'Acc_Y', 'Gyr_Y', 'Mag_Y');
\r
403 p1 = plot(1:BUFFER_SIZE,acc_z(1,1:BUFFER_SIZE),'r');
\r
406 p2 = plot(1:BUFFER_SIZE,gyr_z(1,1:BUFFER_SIZE),'b');
\r
409 p3 = plot(1:BUFFER_SIZE,mag_z(1,1:BUFFER_SIZE),'k');
\r
410 title(['Accelerometer/Gyroscope/Magnetometer Z-Axis Plot']);
\r
411 legend([p1 p2 p3],'Acc_Z', 'Gyr_Z', 'Mag_Z');
\r
413 % Accelerometer Raw (vs) filtered output
\r
415 scrsz = get(0,'ScreenSize');
\r
416 set(hfig,'position',scrsz);
\r
418 p1 = plot(1:BUFFER_SIZE,Ax(1,1:BUFFER_SIZE),'r');
\r
421 p2 = plot(1:BUFFER_SIZE,filt_Ax(1,1:BUFFER_SIZE),'b');
\r
422 title(['Accelerometer X-Axis Plot']);
\r
423 legend([p1 p2],'input signal','low-pass filtered signal');
\r
425 p1 = plot(1:BUFFER_SIZE,Ay(1,1:BUFFER_SIZE),'r');
\r
428 p2 = plot(1:BUFFER_SIZE,filt_Ay(1,1:BUFFER_SIZE),'b');
\r
429 title(['Accelerometer Y-Axis Plot']);
\r
430 legend([p1 p2],'input signal','low-pass filtered signal');
\r
432 p1 = plot(1:BUFFER_SIZE,Az(1,1:BUFFER_SIZE),'r');
\r
435 p2 = plot(1:BUFFER_SIZE,filt_Az(1,1:BUFFER_SIZE),'b');
\r
436 title(['Accelerometer Z-Axis Plot']);
\r
437 legend([p1 p2],'input signal','low-pass filtered signal');
\r
439 % Gyroscope Raw (vs) filtered output
\r
441 scrsz = get(0,'ScreenSize');
\r
442 set(hfig,'position',scrsz);
\r
444 p1 = plot(1:BUFFER_SIZE,Gx(1,1:BUFFER_SIZE),'r');
\r
447 p2 = plot(1:BUFFER_SIZE,filt_Gx(1,1:BUFFER_SIZE),'b');
\r
448 title(['Gyroscope X-Axis Plot']);
\r
449 legend([p1 p2],'input signal','low-pass filtered signal');
\r
451 p1 = plot(1:BUFFER_SIZE,Gy(1,1:BUFFER_SIZE),'r');
\r
454 p2 = plot(1:BUFFER_SIZE,filt_Gy(1,1:BUFFER_SIZE),'b');
\r
455 title(['Gyroscope Y-Axis Plot']);
\r
456 legend([p1 p2],'input signal','low-pass filtered signal');
\r
458 p1 = plot(1:BUFFER_SIZE,Gz(1,1:BUFFER_SIZE),'r');
\r
461 p2 = plot(1:BUFFER_SIZE,filt_Gz(1,1:BUFFER_SIZE),'b');
\r
462 title(['Gyroscope Z-Axis Plot']);
\r
463 legend([p1 p2],'input signal','low-pass filtered signal');
\r
465 % Magnetometer Raw (vs) filtered output
\r
467 scrsz = get(0,'ScreenSize');
\r
468 set(hfig,'position',scrsz);
\r
470 p1 = plot(1:BUFFER_SIZE,Mx(1,1:BUFFER_SIZE),'r');
\r
473 p2 = plot(1:BUFFER_SIZE,filt_Mx(1,1:BUFFER_SIZE),'b');
\r
474 title(['Magnetometer X-Axis Plot']);
\r
475 legend([p1 p2],'input signal','low-pass filtered signal');
\r
477 p1 = plot(1:BUFFER_SIZE,My(1,1:BUFFER_SIZE),'r');
\r
480 p2 = plot(1:BUFFER_SIZE,filt_My(1,1:BUFFER_SIZE),'b');
\r
481 title(['Magnetometer Y-Axis Plot']);
\r
482 legend([p1 p2],'input signal','low-pass filtered signal');
\r
484 p1 = plot(1:BUFFER_SIZE,Mz(1,1:BUFFER_SIZE),'r');
\r
487 p2 = plot(1:BUFFER_SIZE,filt_Mz(1,1:BUFFER_SIZE),'b');
\r
488 title(['Magnetometer Z-Axis Plot']);
\r
489 legend([p1 p2],'input signal','low-pass filtered signal');
\r