Fusion.cpp revision a83f45c6c734084422f56733c25350625594bc00
1/* 2 * Copyright (C) 2011 The Android Open Source Project 3 * 4 * Licensed under the Apache License, Version 2.0 (the "License"); 5 * you may not use this file except in compliance with the License. 6 * You may obtain a copy of the License at 7 * 8 * http://www.apache.org/licenses/LICENSE-2.0 9 * 10 * Unless required by applicable law or agreed to in writing, software 11 * distributed under the License is distributed on an "AS IS" BASIS, 12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 13 * See the License for the specific language governing permissions and 14 * limitations under the License. 15 */ 16 17#include <stdio.h> 18 19#include <utils/Log.h> 20 21#include "Fusion.h" 22 23namespace android { 24 25// ----------------------------------------------------------------------- 26 27/* 28 * gyroVAR gives the measured variance of the gyro's output per 29 * Hz (or variance at 1 Hz). This is an "intrinsic" parameter of the gyro, 30 * which is independent of the sampling frequency. 31 * 32 * The variance of gyro's output at a given sampling period can be 33 * calculated as: 34 * variance(T) = gyroVAR / T 35 * 36 * The variance of the INTEGRATED OUTPUT at a given sampling period can be 37 * calculated as: 38 * variance_integrate_output(T) = gyroVAR * T 39 * 40 */ 41static const float gyroVAR = 1e-7; // (rad/s)^2 / Hz 42static const float biasVAR = 1e-8; // (rad/s)^2 / s (guessed) 43 44/* 45 * Standard deviations of accelerometer and magnetometer 46 */ 47static const float accSTDEV = 0.05f; // m/s^2 (measured 0.08 / CDD 0.05) 48static const float magSTDEV = 0.5f; // uT (measured 0.7 / CDD 0.5) 49 50static const float SYMMETRY_TOLERANCE = 1e-10f; 51 52/* 53 * Accelerometer updates will not be performed near free fall to avoid 54 * ill-conditioning and div by zeros. 55 * Threshhold: 10% of g, in m/s^2 56 */ 57static const float FREE_FALL_THRESHOLD = 0.981f; 58static const float FREE_FALL_THRESHOLD_SQ = 59 FREE_FALL_THRESHOLD*FREE_FALL_THRESHOLD; 60 61/* 62 * The geomagnetic-field should be between 30uT and 60uT. 63 * Fields strengths greater than this likely indicate a local magnetic 64 * disturbance which we do not want to update into the fused frame. 65 */ 66static const float MAX_VALID_MAGNETIC_FIELD = 100; // uT 67static const float MAX_VALID_MAGNETIC_FIELD_SQ = 68 MAX_VALID_MAGNETIC_FIELD*MAX_VALID_MAGNETIC_FIELD; 69 70/* 71 * Values of the field smaller than this should be ignored in fusion to avoid 72 * ill-conditioning. This state can happen with anomalous local magnetic 73 * disturbances canceling the Earth field. 74 */ 75static const float MIN_VALID_MAGNETIC_FIELD = 10; // uT 76static const float MIN_VALID_MAGNETIC_FIELD_SQ = 77 MIN_VALID_MAGNETIC_FIELD*MIN_VALID_MAGNETIC_FIELD; 78 79/* 80 * If the cross product of two vectors has magnitude squared less than this, 81 * we reject it as invalid due to alignment of the vectors. 82 * This threshold is used to check for the case where the magnetic field sample 83 * is parallel to the gravity field, which can happen in certain places due 84 * to magnetic field disturbances. 85 */ 86static const float MIN_VALID_CROSS_PRODUCT_MAG = 1.0e-3; 87static const float MIN_VALID_CROSS_PRODUCT_MAG_SQ = 88 MIN_VALID_CROSS_PRODUCT_MAG*MIN_VALID_CROSS_PRODUCT_MAG; 89 90// ----------------------------------------------------------------------- 91 92template <typename TYPE, size_t C, size_t R> 93static mat<TYPE, R, R> scaleCovariance( 94 const mat<TYPE, C, R>& A, 95 const mat<TYPE, C, C>& P) { 96 // A*P*transpose(A); 97 mat<TYPE, R, R> APAt; 98 for (size_t r=0 ; r<R ; r++) { 99 for (size_t j=r ; j<R ; j++) { 100 double apat(0); 101 for (size_t c=0 ; c<C ; c++) { 102 double v(A[c][r]*P[c][c]*0.5); 103 for (size_t k=c+1 ; k<C ; k++) 104 v += A[k][r] * P[c][k]; 105 apat += 2 * v * A[c][j]; 106 } 107 APAt[j][r] = apat; 108 APAt[r][j] = apat; 109 } 110 } 111 return APAt; 112} 113 114template <typename TYPE, typename OTHER_TYPE> 115static mat<TYPE, 3, 3> crossMatrix(const vec<TYPE, 3>& p, OTHER_TYPE diag) { 116 mat<TYPE, 3, 3> r; 117 r[0][0] = diag; 118 r[1][1] = diag; 119 r[2][2] = diag; 120 r[0][1] = p.z; 121 r[1][0] =-p.z; 122 r[0][2] =-p.y; 123 r[2][0] = p.y; 124 r[1][2] = p.x; 125 r[2][1] =-p.x; 126 return r; 127} 128 129 130template<typename TYPE, size_t SIZE> 131class Covariance { 132 mat<TYPE, SIZE, SIZE> mSumXX; 133 vec<TYPE, SIZE> mSumX; 134 size_t mN; 135public: 136 Covariance() : mSumXX(0.0f), mSumX(0.0f), mN(0) { } 137 void update(const vec<TYPE, SIZE>& x) { 138 mSumXX += x*transpose(x); 139 mSumX += x; 140 mN++; 141 } 142 mat<TYPE, SIZE, SIZE> operator()() const { 143 const float N = 1.0f / mN; 144 return mSumXX*N - (mSumX*transpose(mSumX))*(N*N); 145 } 146 void reset() { 147 mN = 0; 148 mSumXX = 0; 149 mSumX = 0; 150 } 151 size_t getCount() const { 152 return mN; 153 } 154}; 155 156// ----------------------------------------------------------------------- 157 158Fusion::Fusion() { 159 Phi[0][1] = 0; 160 Phi[1][1] = 1; 161 162 Ba.x = 0; 163 Ba.y = 0; 164 Ba.z = 1; 165 166 Bm.x = 0; 167 Bm.y = 1; 168 Bm.z = 0; 169 170 init(); 171} 172 173void Fusion::init() { 174 mInitState = 0; 175 176 mGyroRate = 0; 177 178 mCount[0] = 0; 179 mCount[1] = 0; 180 mCount[2] = 0; 181 182 mData = 0; 183} 184 185void Fusion::initFusion(const vec4_t& q, float dT) 186{ 187 // initial estimate: E{ x(t0) } 188 x0 = q; 189 x1 = 0; 190 191 // process noise covariance matrix: G.Q.Gt, with 192 // 193 // G = | -1 0 | Q = | q00 q10 | 194 // | 0 1 | | q01 q11 | 195 // 196 // q00 = sv^2.dt + 1/3.su^2.dt^3 197 // q10 = q01 = 1/2.su^2.dt^2 198 // q11 = su^2.dt 199 // 200 201 // variance of integrated output at 1/dT Hz 202 // (random drift) 203 const float q00 = gyroVAR * dT; 204 205 // variance of drift rate ramp 206 const float q11 = biasVAR * dT; 207 208 const float u = q11 / dT; 209 const float q10 = 0.5f*u*dT*dT; 210 const float q01 = q10; 211 212 GQGt[0][0] = q00; // rad^2 213 GQGt[1][0] = -q10; 214 GQGt[0][1] = -q01; 215 GQGt[1][1] = q11; // (rad/s)^2 216 217 // initial covariance: Var{ x(t0) } 218 // TODO: initialize P correctly 219 P = 0; 220} 221 222bool Fusion::hasEstimate() const { 223 return (mInitState == (MAG|ACC|GYRO)); 224} 225 226bool Fusion::checkInitComplete(int what, const vec3_t& d, float dT) { 227 if (hasEstimate()) 228 return true; 229 230 if (what == ACC) { 231 mData[0] += d * (1/length(d)); 232 mCount[0]++; 233 mInitState |= ACC; 234 } else if (what == MAG) { 235 mData[1] += d * (1/length(d)); 236 mCount[1]++; 237 mInitState |= MAG; 238 } else if (what == GYRO) { 239 mGyroRate = dT; 240 mData[2] += d*dT; 241 mCount[2]++; 242 if (mCount[2] == 64) { 243 // 64 samples is good enough to estimate the gyro drift and 244 // doesn't take too much time. 245 mInitState |= GYRO; 246 } 247 } 248 249 if (mInitState == (MAG|ACC|GYRO)) { 250 // Average all the values we collected so far 251 mData[0] *= 1.0f/mCount[0]; 252 mData[1] *= 1.0f/mCount[1]; 253 mData[2] *= 1.0f/mCount[2]; 254 255 // calculate the MRPs from the data collection, this gives us 256 // a rough estimate of our initial state 257 mat33_t R; 258 vec3_t up(mData[0]); 259 vec3_t east(cross_product(mData[1], up)); 260 east *= 1/length(east); 261 vec3_t north(cross_product(up, east)); 262 R << east << north << up; 263 const vec4_t q = matrixToQuat(R); 264 265 initFusion(q, mGyroRate); 266 } 267 268 return false; 269} 270 271void Fusion::handleGyro(const vec3_t& w, float dT) { 272 if (!checkInitComplete(GYRO, w, dT)) 273 return; 274 275 predict(w, dT); 276} 277 278status_t Fusion::handleAcc(const vec3_t& a) { 279 // ignore acceleration data if we're close to free-fall 280 if (length_squared(a) < FREE_FALL_THRESHOLD_SQ) { 281 return BAD_VALUE; 282 } 283 284 if (!checkInitComplete(ACC, a)) 285 return BAD_VALUE; 286 287 const float l = 1/length(a); 288 update(a*l, Ba, accSTDEV*l); 289 return NO_ERROR; 290} 291 292status_t Fusion::handleMag(const vec3_t& m) { 293 // the geomagnetic-field should be between 30uT and 60uT 294 // reject if too large to avoid spurious magnetic sources 295 const float magFieldSq = length_squared(m); 296 if (magFieldSq > MAX_VALID_MAGNETIC_FIELD_SQ) { 297 return BAD_VALUE; 298 } else if (magFieldSq < MIN_VALID_MAGNETIC_FIELD_SQ) { 299 // Also reject if too small since we will get ill-defined (zero mag) 300 // cross-products below 301 return BAD_VALUE; 302 } 303 304 if (!checkInitComplete(MAG, m)) 305 return BAD_VALUE; 306 307 // Orthogonalize the magnetic field to the gravity field, mapping it into 308 // tangent to Earth. 309 const vec3_t up( getRotationMatrix() * Ba ); 310 const vec3_t east( cross_product(m, up) ); 311 312 // If the m and up vectors align, the cross product magnitude will 313 // approach 0. 314 // Reject this case as well to avoid div by zero problems and 315 // ill-conditioning below. 316 if (length_squared(east) < MIN_VALID_CROSS_PRODUCT_MAG_SQ) { 317 return BAD_VALUE; 318 } 319 320 // If we have created an orthogonal magnetic field successfully, 321 // then pass it in as the update. 322 vec3_t north( cross_product(up, east) ); 323 324 const float l = 1 / length(north); 325 north *= l; 326 327 update(north, Bm, magSTDEV*l); 328 return NO_ERROR; 329} 330 331void Fusion::checkState() { 332 // P needs to stay positive semidefinite or the fusion diverges. When we 333 // detect divergence, we reset the fusion. 334 // TODO(braun): Instead, find the reason for the divergence and fix it. 335 336 if (!isPositiveSemidefinite(P[0][0], SYMMETRY_TOLERANCE) || 337 !isPositiveSemidefinite(P[1][1], SYMMETRY_TOLERANCE)) { 338 LOGW("Sensor fusion diverged; resetting state."); 339 P = 0; 340 } 341} 342 343vec4_t Fusion::getAttitude() const { 344 return x0; 345} 346 347vec3_t Fusion::getBias() const { 348 return x1; 349} 350 351mat33_t Fusion::getRotationMatrix() const { 352 return quatToMatrix(x0); 353} 354 355mat34_t Fusion::getF(const vec4_t& q) { 356 mat34_t F; 357 F[0].x = q.w; F[1].x =-q.z; F[2].x = q.y; 358 F[0].y = q.z; F[1].y = q.w; F[2].y =-q.x; 359 F[0].z =-q.y; F[1].z = q.x; F[2].z = q.w; 360 F[0].w =-q.x; F[1].w =-q.y; F[2].w =-q.z; 361 return F; 362} 363 364void Fusion::predict(const vec3_t& w, float dT) { 365 const vec4_t q = x0; 366 const vec3_t b = x1; 367 const vec3_t we = w - b; 368 const vec4_t dq = getF(q)*((0.5f*dT)*we); 369 x0 = normalize_quat(q + dq); 370 371 // P(k+1) = F*P(k)*Ft + G*Q*Gt 372 373 // Phi = | Phi00 Phi10 | 374 // | 0 1 | 375 const mat33_t I33(1); 376 const mat33_t I33dT(dT); 377 const mat33_t wx(crossMatrix(we, 0)); 378 const mat33_t wx2(wx*wx); 379 const float lwedT = length(we)*dT; 380 const float ilwe = 1/length(we); 381 const float k0 = (1-cosf(lwedT))*(ilwe*ilwe); 382 const float k1 = sinf(lwedT); 383 384 Phi[0][0] = I33 - wx*(k1*ilwe) + wx2*k0; 385 Phi[1][0] = wx*k0 - I33dT - wx2*(ilwe*ilwe*ilwe)*(lwedT-k1); 386 387 P = Phi*P*transpose(Phi) + GQGt; 388 389 checkState(); 390} 391 392void Fusion::update(const vec3_t& z, const vec3_t& Bi, float sigma) { 393 vec4_t q(x0); 394 // measured vector in body space: h(p) = A(p)*Bi 395 const mat33_t A(quatToMatrix(q)); 396 const vec3_t Bb(A*Bi); 397 398 // Sensitivity matrix H = dh(p)/dp 399 // H = [ L 0 ] 400 const mat33_t L(crossMatrix(Bb, 0)); 401 402 // gain... 403 // K = P*Ht / [H*P*Ht + R] 404 vec<mat33_t, 2> K; 405 const mat33_t R(sigma*sigma); 406 const mat33_t S(scaleCovariance(L, P[0][0]) + R); 407 const mat33_t Si(invert(S)); 408 const mat33_t LtSi(transpose(L)*Si); 409 K[0] = P[0][0] * LtSi; 410 K[1] = transpose(P[1][0])*LtSi; 411 412 // update... 413 // P -= K*H*P; 414 const mat33_t K0L(K[0] * L); 415 const mat33_t K1L(K[1] * L); 416 P[0][0] -= K0L*P[0][0]; 417 P[1][1] -= K1L*P[1][0]; 418 P[1][0] -= K0L*P[1][0]; 419 P[0][1] = transpose(P[1][0]); 420 421 const vec3_t e(z - Bb); 422 const vec3_t dq(K[0]*e); 423 const vec3_t db(K[1]*e); 424 425 q += getF(q)*(0.5f*dq); 426 x0 = normalize_quat(q); 427 x1 += db; 428 429 checkState(); 430} 431 432// ----------------------------------------------------------------------- 433 434}; // namespace android 435 436