Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 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 | |
| 23 | namespace android { |
| 24 | |
| 25 | // ----------------------------------------------------------------------- |
| 26 | |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 27 | static const float gyroSTDEV = 3.16e-4; // rad/s^3/2 |
| 28 | static const float accSTDEV = 0.05f; // m/s^2 (measured 0.08 / CDD 0.05) |
| 29 | static const float magSTDEV = 0.5f; // uT (measured 0.7 / CDD 0.5) |
| 30 | static const float biasSTDEV = 3.16e-5; // rad/s^1/2 (guessed) |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 31 | |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 32 | static const float FREE_FALL_THRESHOLD = 0.981f; |
| 33 | |
| 34 | // ----------------------------------------------------------------------- |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 35 | |
| 36 | template <typename TYPE, size_t C, size_t R> |
| 37 | static mat<TYPE, R, R> scaleCovariance( |
| 38 | const mat<TYPE, C, R>& A, |
| 39 | const mat<TYPE, C, C>& P) { |
| 40 | // A*P*transpose(A); |
| 41 | mat<TYPE, R, R> APAt; |
| 42 | for (size_t r=0 ; r<R ; r++) { |
| 43 | for (size_t j=r ; j<R ; j++) { |
| 44 | double apat(0); |
| 45 | for (size_t c=0 ; c<C ; c++) { |
| 46 | double v(A[c][r]*P[c][c]*0.5); |
| 47 | for (size_t k=c+1 ; k<C ; k++) |
| 48 | v += A[k][r] * P[c][k]; |
| 49 | apat += 2 * v * A[c][j]; |
| 50 | } |
| 51 | APAt[j][r] = apat; |
| 52 | APAt[r][j] = apat; |
| 53 | } |
| 54 | } |
| 55 | return APAt; |
| 56 | } |
| 57 | |
| 58 | template <typename TYPE, typename OTHER_TYPE> |
| 59 | static mat<TYPE, 3, 3> crossMatrix(const vec<TYPE, 3>& p, OTHER_TYPE diag) { |
| 60 | mat<TYPE, 3, 3> r; |
| 61 | r[0][0] = diag; |
| 62 | r[1][1] = diag; |
| 63 | r[2][2] = diag; |
| 64 | r[0][1] = p.z; |
| 65 | r[1][0] =-p.z; |
| 66 | r[0][2] =-p.y; |
| 67 | r[2][0] = p.y; |
| 68 | r[1][2] = p.x; |
| 69 | r[2][1] =-p.x; |
| 70 | return r; |
| 71 | } |
| 72 | |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 73 | |
| 74 | template<typename TYPE, size_t SIZE> |
| 75 | class Covariance { |
| 76 | mat<TYPE, SIZE, SIZE> mSumXX; |
| 77 | vec<TYPE, SIZE> mSumX; |
| 78 | size_t mN; |
| 79 | public: |
| 80 | Covariance() : mSumXX(0.0f), mSumX(0.0f), mN(0) { } |
| 81 | void update(const vec<TYPE, SIZE>& x) { |
| 82 | mSumXX += x*transpose(x); |
| 83 | mSumX += x; |
| 84 | mN++; |
| 85 | } |
| 86 | mat<TYPE, SIZE, SIZE> operator()() const { |
| 87 | const float N = 1.0f / mN; |
| 88 | return mSumXX*N - (mSumX*transpose(mSumX))*(N*N); |
| 89 | } |
| 90 | void reset() { |
| 91 | mN = 0; |
| 92 | mSumXX = 0; |
| 93 | mSumX = 0; |
| 94 | } |
| 95 | size_t getCount() const { |
| 96 | return mN; |
| 97 | } |
| 98 | }; |
| 99 | |
| 100 | // ----------------------------------------------------------------------- |
| 101 | |
| 102 | Fusion::Fusion() { |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 103 | Phi[0][1] = 0; |
| 104 | Phi[1][1] = 1; |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 105 | |
| 106 | Ba.x = 0; |
| 107 | Ba.y = 0; |
| 108 | Ba.z = 1; |
| 109 | |
| 110 | Bm.x = 0; |
| 111 | Bm.y = 1; |
| 112 | Bm.z = 0; |
| 113 | |
| 114 | init(); |
| 115 | } |
| 116 | |
| 117 | void Fusion::init() { |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 118 | mInitState = 0; |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 119 | mGyroRate = 0; |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 120 | mCount[0] = 0; |
| 121 | mCount[1] = 0; |
| 122 | mCount[2] = 0; |
| 123 | mData = 0; |
| 124 | } |
| 125 | |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 126 | void Fusion::initFusion(const vec4_t& q, float dT) |
| 127 | { |
| 128 | // initial estimate: E{ x(t0) } |
| 129 | x0 = q; |
| 130 | x1 = 0; |
| 131 | |
| 132 | // process noise covariance matrix |
| 133 | // G = | -1 0 | |
| 134 | // | 0 1 | |
| 135 | |
| 136 | const float v = gyroSTDEV; |
| 137 | const float u = biasSTDEV; |
| 138 | const float q00 = v*v*dT + 0.33333f*(dT*dT*dT)*u*u; |
| 139 | const float q10 = 0.5f*(dT*dT) *u*u; |
| 140 | const float q01 = q10; |
| 141 | const float q11 = u*u*dT; |
| 142 | GQGt[0][0] = q00; |
| 143 | GQGt[1][0] = -q10; |
| 144 | GQGt[0][1] = -q01; |
| 145 | GQGt[1][1] = q11; |
| 146 | |
| 147 | |
| 148 | // initial covariance: Var{ x(t0) } |
| 149 | P = 0; |
| 150 | } |
| 151 | |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 152 | bool Fusion::hasEstimate() const { |
| 153 | return (mInitState == (MAG|ACC|GYRO)); |
| 154 | } |
| 155 | |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 156 | bool Fusion::checkInitComplete(int what, const vec3_t& d, float dT) { |
| 157 | if (hasEstimate()) |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 158 | return true; |
| 159 | |
| 160 | if (what == ACC) { |
| 161 | mData[0] += d * (1/length(d)); |
| 162 | mCount[0]++; |
| 163 | mInitState |= ACC; |
| 164 | } else if (what == MAG) { |
| 165 | mData[1] += d * (1/length(d)); |
| 166 | mCount[1]++; |
| 167 | mInitState |= MAG; |
| 168 | } else if (what == GYRO) { |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 169 | mGyroRate = dT; |
| 170 | mData[2] += d*dT; |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 171 | mCount[2]++; |
| 172 | if (mCount[2] == 64) { |
| 173 | // 64 samples is good enough to estimate the gyro drift and |
| 174 | // doesn't take too much time. |
| 175 | mInitState |= GYRO; |
| 176 | } |
| 177 | } |
| 178 | |
| 179 | if (mInitState == (MAG|ACC|GYRO)) { |
| 180 | // Average all the values we collected so far |
| 181 | mData[0] *= 1.0f/mCount[0]; |
| 182 | mData[1] *= 1.0f/mCount[1]; |
| 183 | mData[2] *= 1.0f/mCount[2]; |
| 184 | |
| 185 | // calculate the MRPs from the data collection, this gives us |
| 186 | // a rough estimate of our initial state |
| 187 | mat33_t R; |
| 188 | vec3_t up(mData[0]); |
| 189 | vec3_t east(cross_product(mData[1], up)); |
| 190 | east *= 1/length(east); |
| 191 | vec3_t north(cross_product(up, east)); |
| 192 | R << east << north << up; |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 193 | const vec4_t q = matrixToQuat(R); |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 194 | |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 195 | initFusion(q, mGyroRate); |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 196 | } |
| 197 | |
| 198 | return false; |
| 199 | } |
| 200 | |
| 201 | void Fusion::handleGyro(const vec3_t& w, float dT) { |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 202 | if (!checkInitComplete(GYRO, w, dT)) |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 203 | return; |
| 204 | |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 205 | predict(w, dT); |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 206 | } |
| 207 | |
| 208 | status_t Fusion::handleAcc(const vec3_t& a) { |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 209 | // ignore acceleration data if we're close to free-fall |
| 210 | if (length(a) < FREE_FALL_THRESHOLD) |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 211 | return BAD_VALUE; |
| 212 | |
| 213 | if (!checkInitComplete(ACC, a)) |
| 214 | return BAD_VALUE; |
| 215 | |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 216 | const float l = 1/length(a); |
| 217 | update(a*l, Ba, accSTDEV*l); |
| 218 | return NO_ERROR; |
| 219 | } |
| 220 | |
| 221 | status_t Fusion::handleMag(const vec3_t& m) { |
| 222 | // the geomagnetic-field should be between 30uT and 60uT |
| 223 | // reject obviously wrong magnetic-fields |
| 224 | if (length(m) > 100) |
| 225 | return BAD_VALUE; |
| 226 | |
| 227 | if (!checkInitComplete(MAG, m)) |
| 228 | return BAD_VALUE; |
| 229 | |
| 230 | const vec3_t up( getRotationMatrix() * Ba ); |
| 231 | const vec3_t east( cross_product(m, up) ); |
| 232 | vec3_t north( cross_product(up, east) ); |
| 233 | |
| 234 | const float l = 1 / length(north); |
| 235 | north *= l; |
| 236 | |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 237 | update(north, Bm, magSTDEV*l); |
| 238 | return NO_ERROR; |
| 239 | } |
| 240 | |
| 241 | bool Fusion::checkState(const vec3_t& v) { |
| 242 | if (isnanf(length(v))) { |
| 243 | LOGW("9-axis fusion diverged. reseting state."); |
| 244 | P = 0; |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 245 | x1 = 0; |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 246 | mInitState = 0; |
| 247 | mCount[0] = 0; |
| 248 | mCount[1] = 0; |
| 249 | mCount[2] = 0; |
| 250 | mData = 0; |
| 251 | return false; |
| 252 | } |
| 253 | return true; |
| 254 | } |
| 255 | |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 256 | vec4_t Fusion::getAttitude() const { |
| 257 | return x0; |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 258 | } |
| 259 | |
| 260 | vec3_t Fusion::getBias() const { |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 261 | return x1; |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 262 | } |
| 263 | |
| 264 | mat33_t Fusion::getRotationMatrix() const { |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 265 | return quatToMatrix(x0); |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 266 | } |
| 267 | |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 268 | mat34_t Fusion::getF(const vec4_t& q) { |
| 269 | mat34_t F; |
| 270 | F[0].x = q.w; F[1].x =-q.z; F[2].x = q.y; |
| 271 | F[0].y = q.z; F[1].y = q.w; F[2].y =-q.x; |
| 272 | F[0].z =-q.y; F[1].z = q.x; F[2].z = q.w; |
| 273 | F[0].w =-q.x; F[1].w =-q.y; F[2].w =-q.z; |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 274 | return F; |
| 275 | } |
| 276 | |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 277 | void Fusion::predict(const vec3_t& w, float dT) { |
| 278 | const vec4_t q = x0; |
| 279 | const vec3_t b = x1; |
| 280 | const vec3_t we = w - b; |
| 281 | const vec4_t dq = getF(q)*((0.5f*dT)*we); |
| 282 | x0 = normalize_quat(q + dq); |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 283 | |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 284 | // P(k+1) = F*P(k)*Ft + G*Q*Gt |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 285 | |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 286 | // Phi = | Phi00 Phi10 | |
| 287 | // | 0 1 | |
| 288 | const mat33_t I33(1); |
| 289 | const mat33_t I33dT(dT); |
| 290 | const mat33_t wx(crossMatrix(we, 0)); |
| 291 | const mat33_t wx2(wx*wx); |
| 292 | const float lwedT = length(we)*dT; |
| 293 | const float ilwe = 1/length(we); |
| 294 | const float k0 = (1-cosf(lwedT))*(ilwe*ilwe); |
| 295 | const float k1 = sinf(lwedT); |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 296 | |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 297 | Phi[0][0] = I33 - wx*(k1*ilwe) + wx2*k0; |
| 298 | Phi[1][0] = wx*k0 - I33dT - wx2*(ilwe*ilwe*ilwe)*(lwedT-k1); |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 299 | |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 300 | P = Phi*P*transpose(Phi) + GQGt; |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 301 | } |
| 302 | |
| 303 | void Fusion::update(const vec3_t& z, const vec3_t& Bi, float sigma) { |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 304 | vec4_t q(x0); |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 305 | // measured vector in body space: h(p) = A(p)*Bi |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 306 | const mat33_t A(quatToMatrix(q)); |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 307 | const vec3_t Bb(A*Bi); |
| 308 | |
| 309 | // Sensitivity matrix H = dh(p)/dp |
| 310 | // H = [ L 0 ] |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 311 | const mat33_t L(crossMatrix(Bb, 0)); |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 312 | |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 313 | // gain... |
| 314 | // K = P*Ht / [H*P*Ht + R] |
| 315 | vec<mat33_t, 2> K; |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 316 | const mat33_t R(sigma*sigma); |
| 317 | const mat33_t S(scaleCovariance(L, P[0][0]) + R); |
| 318 | const mat33_t Si(invert(S)); |
| 319 | const mat33_t LtSi(transpose(L)*Si); |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 320 | K[0] = P[0][0] * LtSi; |
| 321 | K[1] = transpose(P[1][0])*LtSi; |
| 322 | |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 323 | // update... |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 324 | // P -= K*H*P; |
| 325 | const mat33_t K0L(K[0] * L); |
| 326 | const mat33_t K1L(K[1] * L); |
| 327 | P[0][0] -= K0L*P[0][0]; |
| 328 | P[1][1] -= K1L*P[1][0]; |
| 329 | P[1][0] -= K0L*P[1][0]; |
Mathias Agopian | 3301542 | 2011-05-27 18:18:13 -0700 | [diff] [blame^] | 330 | P[0][1] = transpose(P[1][0]); |
| 331 | |
| 332 | const vec3_t e(z - Bb); |
| 333 | const vec3_t dq(K[0]*e); |
| 334 | const vec3_t db(K[1]*e); |
| 335 | |
| 336 | q += getF(q)*(0.5f*dq); |
| 337 | x0 = normalize_quat(q); |
| 338 | x1 += db; |
Mathias Agopian | 984826c | 2011-05-17 22:54:42 -0700 | [diff] [blame] | 339 | } |
| 340 | |
| 341 | // ----------------------------------------------------------------------- |
| 342 | |
| 343 | }; // namespace android |
| 344 | |