Fusion.cpp revision eaf2d0bfe37415ba1e42a97608823e8dbef53220 
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 FREE_FALL_THRESHOLD = 0.981f;
51
52// -----------------------------------------------------------------------
53
54template <typename TYPE, size_t C, size_t R>
55static mat<TYPE, R, R> scaleCovariance(
56        const mat<TYPE, C, R>& A,
57        const mat<TYPE, C, C>& P) {
58    // A*P*transpose(A);
59    mat<TYPE, R, R> APAt;
60    for (size_t r=0 ; r<R ; r++) {
61        for (size_t j=r ; j<R ; j++) {
62            double apat(0);
63            for (size_t c=0 ; c<C ; c++) {
64                double v(A[c][r]*P[c][c]*0.5);
65                for (size_t k=c+1 ; k<C ; k++)
66                    v += A[k][r] * P[c][k];
67                apat += 2 * v * A[c][j];
68            }
69            APAt[j][r] = apat;
70            APAt[r][j] = apat;
71        }
72    }
73    return APAt;
74}
75
76template <typename TYPE, typename OTHER_TYPE>
77static mat<TYPE, 3, 3> crossMatrix(const vec<TYPE, 3>& p, OTHER_TYPE diag) {
78    mat<TYPE, 3, 3> r;
79    r[0][0] = diag;
80    r[1][1] = diag;
81    r[2][2] = diag;
82    r[0][1] = p.z;
83    r[1][0] =-p.z;
84    r[0][2] =-p.y;
85    r[2][0] = p.y;
86    r[1][2] = p.x;
87    r[2][1] =-p.x;
88    return r;
89}
90
91
92template<typename TYPE, size_t SIZE>
93class Covariance {
94    mat<TYPE, SIZE, SIZE> mSumXX;
95    vec<TYPE, SIZE> mSumX;
96    size_t mN;
97public:
98    Covariance() : mSumXX(0.0f), mSumX(0.0f), mN(0) { }
99    void update(const vec<TYPE, SIZE>& x) {
100        mSumXX += x*transpose(x);
101        mSumX  += x;
102        mN++;
103    }
104    mat<TYPE, SIZE, SIZE> operator()() const {
105        const float N = 1.0f / mN;
106        return mSumXX*N - (mSumX*transpose(mSumX))*(N*N);
107    }
108    void reset() {
109        mN = 0;
110        mSumXX = 0;
111        mSumX = 0;
112    }
113    size_t getCount() const {
114        return mN;
115    }
116};
117
118// -----------------------------------------------------------------------
119
120Fusion::Fusion() {
121    Phi[0][1] = 0;
122    Phi[1][1] = 1;
123
124    Ba.x = 0;
125    Ba.y = 0;
126    Ba.z = 1;
127
128    Bm.x = 0;
129    Bm.y = 1;
130    Bm.z = 0;
131
132    init();
133}
134
135void Fusion::init() {
136    mInitState = 0;
137    mGyroRate = 0;
138    mCount[0] = 0;
139    mCount[1] = 0;
140    mCount[2] = 0;
141    mData = 0;
142}
143
144void Fusion::initFusion(const vec4_t& q, float dT)
145{
146    // initial estimate: E{ x(t0) }
147    x0 = q;
148    x1 = 0;
149
150    // process noise covariance matrix: G.Q.Gt, with
151    //
152    //  G = | -1 0 |        Q = | q00 q10 |
153    //      |  0 1 |            | q01 q11 |
154    //
155    // q00 = sv^2.dt + 1/3.su^2.dt^3
156    // q10 = q01 = 1/2.su^2.dt^2
157    // q11 = su^2.dt
158    //
159
160    // variance of integrated output at 1/dT Hz
161    // (random drift)
162    const float q00 = gyroVAR * dT;
163
164    // variance of drift rate ramp
165    const float q11 = biasVAR * dT;
166
167    const float u   = q11 / dT;
168    const float q10 = 0.5f*u*dT*dT;
169    const float q01 = q10;
170
171    GQGt[0][0] =  q00;      // rad^2
172    GQGt[1][0] = -q10;
173    GQGt[0][1] = -q01;
174    GQGt[1][1] =  q11;      // (rad/s)^2
175
176    // initial covariance: Var{ x(t0) }
177    // TODO: initialize P correctly
178    P = 0;
179}
180
181bool Fusion::hasEstimate() const {
182    return (mInitState == (MAG|ACC|GYRO));
183}
184
185bool Fusion::checkInitComplete(int what, const vec3_t& d, float dT) {
186    if (hasEstimate())
187        return true;
188
189    if (what == ACC) {
190        mData[0] += d * (1/length(d));
191        mCount[0]++;
192        mInitState |= ACC;
193    } else if (what == MAG) {
194        mData[1] += d * (1/length(d));
195        mCount[1]++;
196        mInitState |= MAG;
197    } else if (what == GYRO) {
198        mGyroRate = dT;
199        mData[2] += d*dT;
200        mCount[2]++;
201        if (mCount[2] == 64) {
202            // 64 samples is good enough to estimate the gyro drift and
203            // doesn't take too much time.
204            mInitState |= GYRO;
205        }
206    }
207
208    if (mInitState == (MAG|ACC|GYRO)) {
209        // Average all the values we collected so far
210        mData[0] *= 1.0f/mCount[0];
211        mData[1] *= 1.0f/mCount[1];
212        mData[2] *= 1.0f/mCount[2];
213
214        // calculate the MRPs from the data collection, this gives us
215        // a rough estimate of our initial state
216        mat33_t R;
217        vec3_t up(mData[0]);
218        vec3_t east(cross_product(mData[1], up));
219        east *= 1/length(east);
220        vec3_t north(cross_product(up, east));
221        R << east << north << up;
222        const vec4_t q = matrixToQuat(R);
223
224        initFusion(q, mGyroRate);
225    }
226
227    return false;
228}
229
230void Fusion::handleGyro(const vec3_t& w, float dT) {
231    if (!checkInitComplete(GYRO, w, dT))
232        return;
233
234    predict(w, dT);
235}
236
237status_t Fusion::handleAcc(const vec3_t& a) {
238    // ignore acceleration data if we're close to free-fall
239    if (length(a) < FREE_FALL_THRESHOLD)
240        return BAD_VALUE;
241
242    if (!checkInitComplete(ACC, a))
243        return BAD_VALUE;
244
245    const float l = 1/length(a);
246    update(a*l, Ba, accSTDEV*l);
247    return NO_ERROR;
248}
249
250status_t Fusion::handleMag(const vec3_t& m) {
251    // the geomagnetic-field should be between 30uT and 60uT
252    // reject obviously wrong magnetic-fields
253    if (length(m) > 100)
254        return BAD_VALUE;
255
256    if (!checkInitComplete(MAG, m))
257        return BAD_VALUE;
258
259    const vec3_t up( getRotationMatrix() * Ba );
260    const vec3_t east( cross_product(m, up) );
261    vec3_t north( cross_product(up, east) );
262
263    const float l = 1 / length(north);
264    north *= l;
265
266    update(north, Bm, magSTDEV*l);
267    return NO_ERROR;
268}
269
270bool Fusion::checkState(const vec3_t& v) {
271    if (isnanf(length(v))) {
272        LOGW("9-axis fusion diverged. reseting state.");
273        P = 0;
274        x1 = 0;
275        mInitState = 0;
276        mCount[0] = 0;
277        mCount[1] = 0;
278        mCount[2] = 0;
279        mData = 0;
280        return false;
281    }
282    return true;
283}
284
285vec4_t Fusion::getAttitude() const {
286    return x0;
287}
288
289vec3_t Fusion::getBias() const {
290    return x1;
291}
292
293mat33_t Fusion::getRotationMatrix() const {
294    return quatToMatrix(x0);
295}
296
297mat34_t Fusion::getF(const vec4_t& q) {
298    mat34_t F;
299    F[0].x = q.w;   F[1].x =-q.z;   F[2].x = q.y;
300    F[0].y = q.z;   F[1].y = q.w;   F[2].y =-q.x;
301    F[0].z =-q.y;   F[1].z = q.x;   F[2].z = q.w;
302    F[0].w =-q.x;   F[1].w =-q.y;   F[2].w =-q.z;
303    return F;
304}
305
306void Fusion::predict(const vec3_t& w, float dT) {
307    const vec4_t q  = x0;
308    const vec3_t b  = x1;
309    const vec3_t we = w - b;
310    const vec4_t dq = getF(q)*((0.5f*dT)*we);
311    x0 = normalize_quat(q + dq);
312
313    // P(k+1) = F*P(k)*Ft + G*Q*Gt
314
315    //  Phi = | Phi00 Phi10 |
316    //        |   0     1   |
317    const mat33_t I33(1);
318    const mat33_t I33dT(dT);
319    const mat33_t wx(crossMatrix(we, 0));
320    const mat33_t wx2(wx*wx);
321    const float lwedT = length(we)*dT;
322    const float ilwe = 1/length(we);
323    const float k0 = (1-cosf(lwedT))*(ilwe*ilwe);
324    const float k1 = sinf(lwedT);
325
326    Phi[0][0] = I33 - wx*(k1*ilwe) + wx2*k0;
327    Phi[1][0] = wx*k0 - I33dT - wx2*(ilwe*ilwe*ilwe)*(lwedT-k1);
328
329    P = Phi*P*transpose(Phi) + GQGt;
330}
331
332void Fusion::update(const vec3_t& z, const vec3_t& Bi, float sigma) {
333    vec4_t q(x0);
334    // measured vector in body space: h(p) = A(p)*Bi
335    const mat33_t A(quatToMatrix(q));
336    const vec3_t Bb(A*Bi);
337
338    // Sensitivity matrix H = dh(p)/dp
339    // H = [ L 0 ]
340    const mat33_t L(crossMatrix(Bb, 0));
341
342    // gain...
343    // K = P*Ht / [H*P*Ht + R]
344    vec<mat33_t, 2> K;
345    const mat33_t R(sigma*sigma);
346    const mat33_t S(scaleCovariance(L, P[0][0]) + R);
347    const mat33_t Si(invert(S));
348    const mat33_t LtSi(transpose(L)*Si);
349    K[0] = P[0][0] * LtSi;
350    K[1] = transpose(P[1][0])*LtSi;
351
352    // update...
353    // P -= K*H*P;
354    const mat33_t K0L(K[0] * L);
355    const mat33_t K1L(K[1] * L);
356    P[0][0] -= K0L*P[0][0];
357    P[1][1] -= K1L*P[1][0];
358    P[1][0] -= K0L*P[1][0];
359    P[0][1] = transpose(P[1][0]);
360
361    const vec3_t e(z - Bb);
362    const vec3_t dq(K[0]*e);
363    const vec3_t db(K[1]*e);
364
365    q += getF(q)*(0.5f*dq);
366    x0 = normalize_quat(q);
367    x1 += db;
368}
369
370// -----------------------------------------------------------------------
371
372}; // namespace android
373
374