You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
566 lines
16 KiB
566 lines
16 KiB
/*
|
|
* Copyright (C) 2011 The Android Open Source Project
|
|
*
|
|
* Licensed under the Apache License, Version 2.0 (the "License");
|
|
* you may not use this file except in compliance with the License.
|
|
* You may obtain a copy of the License at
|
|
*
|
|
* http://www.apache.org/licenses/LICENSE-2.0
|
|
*
|
|
* Unless required by applicable law or agreed to in writing, software
|
|
* distributed under the License is distributed on an "AS IS" BASIS,
|
|
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
|
* See the License for the specific language governing permissions and
|
|
* limitations under the License.
|
|
*/
|
|
|
|
#include <stdio.h>
|
|
|
|
#include <utils/Log.h>
|
|
|
|
#include "Fusion.h"
|
|
|
|
namespace android {
|
|
|
|
// -----------------------------------------------------------------------
|
|
|
|
/*==================== BEGIN FUSION SENSOR PARAMETER =========================*/
|
|
|
|
/* Note:
|
|
* If a platform uses software fusion, it is necessary to tune the following
|
|
* parameters to fit the hardware sensors prior to release.
|
|
*
|
|
* The DEFAULT_ parameters will be used in FUSION_9AXIS and FUSION_NOMAG mode.
|
|
* The GEOMAG_ parameters will be used in FUSION_NOGYRO mode.
|
|
*/
|
|
|
|
/*
|
|
* GYRO_VAR gives the measured variance of the gyro's output per
|
|
* Hz (or variance at 1 Hz). This is an "intrinsic" parameter of the gyro,
|
|
* which is independent of the sampling frequency.
|
|
*
|
|
* The variance of gyro's output at a given sampling period can be
|
|
* calculated as:
|
|
* variance(T) = GYRO_VAR / T
|
|
*
|
|
* The variance of the INTEGRATED OUTPUT at a given sampling period can be
|
|
* calculated as:
|
|
* variance_integrate_output(T) = GYRO_VAR * T
|
|
*/
|
|
static const float DEFAULT_GYRO_VAR = 1e-7; // (rad/s)^2 / Hz
|
|
static const float DEFAULT_GYRO_BIAS_VAR = 1e-12; // (rad/s)^2 / s (guessed)
|
|
static const float GEOMAG_GYRO_VAR = 1e-4; // (rad/s)^2 / Hz
|
|
static const float GEOMAG_GYRO_BIAS_VAR = 1e-8; // (rad/s)^2 / s (guessed)
|
|
|
|
/*
|
|
* Standard deviations of accelerometer and magnetometer
|
|
*/
|
|
static const float DEFAULT_ACC_STDEV = 0.015f; // m/s^2 (measured 0.08 / CDD 0.05)
|
|
static const float DEFAULT_MAG_STDEV = 0.1f; // uT (measured 0.7 / CDD 0.5)
|
|
static const float GEOMAG_ACC_STDEV = 0.05f; // m/s^2 (measured 0.08 / CDD 0.05)
|
|
static const float GEOMAG_MAG_STDEV = 0.1f; // uT (measured 0.7 / CDD 0.5)
|
|
|
|
|
|
/* ====================== END FUSION SENSOR PARAMETER ========================*/
|
|
|
|
static const float SYMMETRY_TOLERANCE = 1e-10f;
|
|
|
|
/*
|
|
* Accelerometer updates will not be performed near free fall to avoid
|
|
* ill-conditioning and div by zeros.
|
|
* Threshhold: 10% of g, in m/s^2
|
|
*/
|
|
static const float NOMINAL_GRAVITY = 9.81f;
|
|
static const float FREE_FALL_THRESHOLD = 0.1f * (NOMINAL_GRAVITY);
|
|
|
|
/*
|
|
* The geomagnetic-field should be between 30uT and 60uT.
|
|
* Fields strengths greater than this likely indicate a local magnetic
|
|
* disturbance which we do not want to update into the fused frame.
|
|
*/
|
|
static const float MAX_VALID_MAGNETIC_FIELD = 100; // uT
|
|
static const float MAX_VALID_MAGNETIC_FIELD_SQ =
|
|
MAX_VALID_MAGNETIC_FIELD*MAX_VALID_MAGNETIC_FIELD;
|
|
|
|
/*
|
|
* Values of the field smaller than this should be ignored in fusion to avoid
|
|
* ill-conditioning. This state can happen with anomalous local magnetic
|
|
* disturbances canceling the Earth field.
|
|
*/
|
|
static const float MIN_VALID_MAGNETIC_FIELD = 10; // uT
|
|
static const float MIN_VALID_MAGNETIC_FIELD_SQ =
|
|
MIN_VALID_MAGNETIC_FIELD*MIN_VALID_MAGNETIC_FIELD;
|
|
|
|
/*
|
|
* If the cross product of two vectors has magnitude squared less than this,
|
|
* we reject it as invalid due to alignment of the vectors.
|
|
* This threshold is used to check for the case where the magnetic field sample
|
|
* is parallel to the gravity field, which can happen in certain places due
|
|
* to magnetic field disturbances.
|
|
*/
|
|
static const float MIN_VALID_CROSS_PRODUCT_MAG = 1.0e-3;
|
|
static const float MIN_VALID_CROSS_PRODUCT_MAG_SQ =
|
|
MIN_VALID_CROSS_PRODUCT_MAG*MIN_VALID_CROSS_PRODUCT_MAG;
|
|
|
|
static const float SQRT_3 = 1.732f;
|
|
static const float WVEC_EPS = 1e-4f/SQRT_3;
|
|
// -----------------------------------------------------------------------
|
|
|
|
template <typename TYPE, size_t C, size_t R>
|
|
static mat<TYPE, R, R> scaleCovariance(
|
|
const mat<TYPE, C, R>& A,
|
|
const mat<TYPE, C, C>& P) {
|
|
// A*P*transpose(A);
|
|
mat<TYPE, R, R> APAt;
|
|
for (size_t r=0 ; r<R ; r++) {
|
|
for (size_t j=r ; j<R ; j++) {
|
|
double apat(0);
|
|
for (size_t c=0 ; c<C ; c++) {
|
|
double v(A[c][r]*P[c][c]*0.5);
|
|
for (size_t k=c+1 ; k<C ; k++)
|
|
v += A[k][r] * P[c][k];
|
|
apat += 2 * v * A[c][j];
|
|
}
|
|
APAt[j][r] = apat;
|
|
APAt[r][j] = apat;
|
|
}
|
|
}
|
|
return APAt;
|
|
}
|
|
|
|
template <typename TYPE, typename OTHER_TYPE>
|
|
static mat<TYPE, 3, 3> crossMatrix(const vec<TYPE, 3>& p, OTHER_TYPE diag) {
|
|
mat<TYPE, 3, 3> r;
|
|
r[0][0] = diag;
|
|
r[1][1] = diag;
|
|
r[2][2] = diag;
|
|
r[0][1] = p.z;
|
|
r[1][0] =-p.z;
|
|
r[0][2] =-p.y;
|
|
r[2][0] = p.y;
|
|
r[1][2] = p.x;
|
|
r[2][1] =-p.x;
|
|
return r;
|
|
}
|
|
|
|
|
|
template<typename TYPE, size_t SIZE>
|
|
class Covariance {
|
|
mat<TYPE, SIZE, SIZE> mSumXX;
|
|
vec<TYPE, SIZE> mSumX;
|
|
size_t mN;
|
|
public:
|
|
Covariance() : mSumXX(0.0f), mSumX(0.0f), mN(0) { }
|
|
void update(const vec<TYPE, SIZE>& x) {
|
|
mSumXX += x*transpose(x);
|
|
mSumX += x;
|
|
mN++;
|
|
}
|
|
mat<TYPE, SIZE, SIZE> operator()() const {
|
|
const float N = 1.0f / mN;
|
|
return mSumXX*N - (mSumX*transpose(mSumX))*(N*N);
|
|
}
|
|
void reset() {
|
|
mN = 0;
|
|
mSumXX = 0;
|
|
mSumX = 0;
|
|
}
|
|
size_t getCount() const {
|
|
return mN;
|
|
}
|
|
};
|
|
|
|
// -----------------------------------------------------------------------
|
|
|
|
Fusion::Fusion() {
|
|
Phi[0][1] = 0;
|
|
Phi[1][1] = 1;
|
|
|
|
Ba.x = 0;
|
|
Ba.y = 0;
|
|
Ba.z = 1;
|
|
|
|
Bm.x = 0;
|
|
Bm.y = 1;
|
|
Bm.z = 0;
|
|
|
|
x0 = 0;
|
|
x1 = 0;
|
|
|
|
init();
|
|
}
|
|
|
|
void Fusion::init(int mode) {
|
|
mInitState = 0;
|
|
|
|
mGyroRate = 0;
|
|
|
|
mCount[0] = 0;
|
|
mCount[1] = 0;
|
|
mCount[2] = 0;
|
|
|
|
mData = 0;
|
|
mMode = mode;
|
|
|
|
if (mMode != FUSION_NOGYRO) { //normal or game rotation
|
|
mParam.gyroVar = DEFAULT_GYRO_VAR;
|
|
mParam.gyroBiasVar = DEFAULT_GYRO_BIAS_VAR;
|
|
mParam.accStdev = DEFAULT_ACC_STDEV;
|
|
mParam.magStdev = DEFAULT_MAG_STDEV;
|
|
} else {
|
|
mParam.gyroVar = GEOMAG_GYRO_VAR;
|
|
mParam.gyroBiasVar = GEOMAG_GYRO_BIAS_VAR;
|
|
mParam.accStdev = GEOMAG_ACC_STDEV;
|
|
mParam.magStdev = GEOMAG_MAG_STDEV;
|
|
}
|
|
}
|
|
|
|
void Fusion::initFusion(const vec4_t& q, float dT)
|
|
{
|
|
// initial estimate: E{ x(t0) }
|
|
x0 = q;
|
|
x1 = 0;
|
|
|
|
// process noise covariance matrix: G.Q.Gt, with
|
|
//
|
|
// G = | -1 0 | Q = | q00 q10 |
|
|
// | 0 1 | | q01 q11 |
|
|
//
|
|
// q00 = sv^2.dt + 1/3.su^2.dt^3
|
|
// q10 = q01 = 1/2.su^2.dt^2
|
|
// q11 = su^2.dt
|
|
//
|
|
|
|
const float dT2 = dT*dT;
|
|
const float dT3 = dT2*dT;
|
|
|
|
// variance of integrated output at 1/dT Hz (random drift)
|
|
const float q00 = mParam.gyroVar * dT + 0.33333f * mParam.gyroBiasVar * dT3;
|
|
|
|
// variance of drift rate ramp
|
|
const float q11 = mParam.gyroBiasVar * dT;
|
|
const float q10 = 0.5f * mParam.gyroBiasVar * dT2;
|
|
const float q01 = q10;
|
|
|
|
GQGt[0][0] = q00; // rad^2
|
|
GQGt[1][0] = -q10;
|
|
GQGt[0][1] = -q01;
|
|
GQGt[1][1] = q11; // (rad/s)^2
|
|
|
|
// initial covariance: Var{ x(t0) }
|
|
// TODO: initialize P correctly
|
|
P = 0;
|
|
}
|
|
|
|
bool Fusion::hasEstimate() const {
|
|
return ((mInitState & MAG) || (mMode == FUSION_NOMAG)) &&
|
|
((mInitState & GYRO) || (mMode == FUSION_NOGYRO)) &&
|
|
(mInitState & ACC);
|
|
}
|
|
|
|
bool Fusion::checkInitComplete(int what, const vec3_t& d, float dT) {
|
|
if (hasEstimate())
|
|
return true;
|
|
|
|
if (what == ACC) {
|
|
mData[0] += d * (1/length(d));
|
|
mCount[0]++;
|
|
mInitState |= ACC;
|
|
if (mMode == FUSION_NOGYRO ) {
|
|
mGyroRate = dT;
|
|
}
|
|
} else if (what == MAG) {
|
|
mData[1] += d * (1/length(d));
|
|
mCount[1]++;
|
|
mInitState |= MAG;
|
|
} else if (what == GYRO) {
|
|
mGyroRate = dT;
|
|
mData[2] += d*dT;
|
|
mCount[2]++;
|
|
mInitState |= GYRO;
|
|
}
|
|
|
|
if (hasEstimate()) {
|
|
// Average all the values we collected so far
|
|
mData[0] *= 1.0f/mCount[0];
|
|
if (mMode != FUSION_NOMAG) {
|
|
mData[1] *= 1.0f/mCount[1];
|
|
}
|
|
mData[2] *= 1.0f/mCount[2];
|
|
|
|
// calculate the MRPs from the data collection, this gives us
|
|
// a rough estimate of our initial state
|
|
mat33_t R;
|
|
vec3_t up(mData[0]);
|
|
vec3_t east;
|
|
|
|
if (mMode != FUSION_NOMAG) {
|
|
east = normalize(cross_product(mData[1], up));
|
|
} else {
|
|
east = getOrthogonal(up);
|
|
}
|
|
|
|
vec3_t north(cross_product(up, east));
|
|
R << east << north << up;
|
|
const vec4_t q = matrixToQuat(R);
|
|
|
|
initFusion(q, mGyroRate);
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
void Fusion::handleGyro(const vec3_t& w, float dT) {
|
|
if (!checkInitComplete(GYRO, w, dT))
|
|
return;
|
|
|
|
predict(w, dT);
|
|
}
|
|
|
|
status_t Fusion::handleAcc(const vec3_t& a, float dT) {
|
|
if (!checkInitComplete(ACC, a, dT))
|
|
return BAD_VALUE;
|
|
|
|
// ignore acceleration data if we're close to free-fall
|
|
const float l = length(a);
|
|
if (l < FREE_FALL_THRESHOLD) {
|
|
return BAD_VALUE;
|
|
}
|
|
|
|
const float l_inv = 1.0f/l;
|
|
|
|
if ( mMode == FUSION_NOGYRO ) {
|
|
//geo mag
|
|
vec3_t w_dummy;
|
|
w_dummy = x1; //bias
|
|
predict(w_dummy, dT);
|
|
}
|
|
|
|
if ( mMode == FUSION_NOMAG) {
|
|
vec3_t m;
|
|
m = getRotationMatrix()*Bm;
|
|
update(m, Bm, mParam.magStdev);
|
|
}
|
|
|
|
vec3_t unityA = a * l_inv;
|
|
const float d = sqrtf(fabsf(l- NOMINAL_GRAVITY));
|
|
const float p = l_inv * mParam.accStdev*expf(d);
|
|
|
|
update(unityA, Ba, p);
|
|
return NO_ERROR;
|
|
}
|
|
|
|
status_t Fusion::handleMag(const vec3_t& m) {
|
|
if (!checkInitComplete(MAG, m))
|
|
return BAD_VALUE;
|
|
|
|
// the geomagnetic-field should be between 30uT and 60uT
|
|
// reject if too large to avoid spurious magnetic sources
|
|
const float magFieldSq = length_squared(m);
|
|
if (magFieldSq > MAX_VALID_MAGNETIC_FIELD_SQ) {
|
|
return BAD_VALUE;
|
|
} else if (magFieldSq < MIN_VALID_MAGNETIC_FIELD_SQ) {
|
|
// Also reject if too small since we will get ill-defined (zero mag)
|
|
// cross-products below
|
|
return BAD_VALUE;
|
|
}
|
|
|
|
// Orthogonalize the magnetic field to the gravity field, mapping it into
|
|
// tangent to Earth.
|
|
const vec3_t up( getRotationMatrix() * Ba );
|
|
const vec3_t east( cross_product(m, up) );
|
|
|
|
// If the m and up vectors align, the cross product magnitude will
|
|
// approach 0.
|
|
// Reject this case as well to avoid div by zero problems and
|
|
// ill-conditioning below.
|
|
if (length_squared(east) < MIN_VALID_CROSS_PRODUCT_MAG_SQ) {
|
|
return BAD_VALUE;
|
|
}
|
|
|
|
// If we have created an orthogonal magnetic field successfully,
|
|
// then pass it in as the update.
|
|
vec3_t north( cross_product(up, east) );
|
|
|
|
const float l_inv = 1 / length(north);
|
|
north *= l_inv;
|
|
|
|
update(north, Bm, mParam.magStdev*l_inv);
|
|
return NO_ERROR;
|
|
}
|
|
|
|
void Fusion::checkState() {
|
|
// P needs to stay positive semidefinite or the fusion diverges. When we
|
|
// detect divergence, we reset the fusion.
|
|
// TODO(braun): Instead, find the reason for the divergence and fix it.
|
|
|
|
if (!isPositiveSemidefinite(P[0][0], SYMMETRY_TOLERANCE) ||
|
|
!isPositiveSemidefinite(P[1][1], SYMMETRY_TOLERANCE)) {
|
|
ALOGW("Sensor fusion diverged; resetting state.");
|
|
P = 0;
|
|
}
|
|
}
|
|
|
|
vec4_t Fusion::getAttitude() const {
|
|
return x0;
|
|
}
|
|
|
|
vec3_t Fusion::getBias() const {
|
|
return x1;
|
|
}
|
|
|
|
mat33_t Fusion::getRotationMatrix() const {
|
|
return quatToMatrix(x0);
|
|
}
|
|
|
|
mat34_t Fusion::getF(const vec4_t& q) {
|
|
mat34_t F;
|
|
|
|
// This is used to compute the derivative of q
|
|
// F = | [q.xyz]x |
|
|
// | -q.xyz |
|
|
|
|
F[0].x = q.w; F[1].x =-q.z; F[2].x = q.y;
|
|
F[0].y = q.z; F[1].y = q.w; F[2].y =-q.x;
|
|
F[0].z =-q.y; F[1].z = q.x; F[2].z = q.w;
|
|
F[0].w =-q.x; F[1].w =-q.y; F[2].w =-q.z;
|
|
return F;
|
|
}
|
|
|
|
void Fusion::predict(const vec3_t& w, float dT) {
|
|
const vec4_t q = x0;
|
|
const vec3_t b = x1;
|
|
vec3_t we = w - b;
|
|
|
|
if (length(we) < WVEC_EPS) {
|
|
we = (we[0]>0.f)?WVEC_EPS:-WVEC_EPS;
|
|
}
|
|
// q(k+1) = O(we)*q(k)
|
|
// --------------------
|
|
//
|
|
// O(w) = | cos(0.5*||w||*dT)*I33 - [psi]x psi |
|
|
// | -psi' cos(0.5*||w||*dT) |
|
|
//
|
|
// psi = sin(0.5*||w||*dT)*w / ||w||
|
|
//
|
|
//
|
|
// P(k+1) = Phi(k)*P(k)*Phi(k)' + G*Q(k)*G'
|
|
// ----------------------------------------
|
|
//
|
|
// G = | -I33 0 |
|
|
// | 0 I33 |
|
|
//
|
|
// Phi = | Phi00 Phi10 |
|
|
// | 0 1 |
|
|
//
|
|
// Phi00 = I33
|
|
// - [w]x * sin(||w||*dt)/||w||
|
|
// + [w]x^2 * (1-cos(||w||*dT))/||w||^2
|
|
//
|
|
// Phi10 = [w]x * (1 - cos(||w||*dt))/||w||^2
|
|
// - [w]x^2 * (||w||*dT - sin(||w||*dt))/||w||^3
|
|
// - I33*dT
|
|
|
|
const mat33_t I33(1);
|
|
const mat33_t I33dT(dT);
|
|
const mat33_t wx(crossMatrix(we, 0));
|
|
const mat33_t wx2(wx*wx);
|
|
const float lwedT = length(we)*dT;
|
|
const float hlwedT = 0.5f*lwedT;
|
|
const float ilwe = 1.f/length(we);
|
|
const float k0 = (1-cosf(lwedT))*(ilwe*ilwe);
|
|
const float k1 = sinf(lwedT);
|
|
const float k2 = cosf(hlwedT);
|
|
const vec3_t psi(sinf(hlwedT)*ilwe*we);
|
|
const mat33_t O33(crossMatrix(-psi, k2));
|
|
mat44_t O;
|
|
O[0].xyz = O33[0]; O[0].w = -psi.x;
|
|
O[1].xyz = O33[1]; O[1].w = -psi.y;
|
|
O[2].xyz = O33[2]; O[2].w = -psi.z;
|
|
O[3].xyz = psi; O[3].w = k2;
|
|
|
|
Phi[0][0] = I33 - wx*(k1*ilwe) + wx2*k0;
|
|
Phi[1][0] = wx*k0 - I33dT - wx2*(ilwe*ilwe*ilwe)*(lwedT-k1);
|
|
|
|
x0 = O*q;
|
|
|
|
if (x0.w < 0)
|
|
x0 = -x0;
|
|
|
|
P = Phi*P*transpose(Phi) + GQGt;
|
|
|
|
checkState();
|
|
}
|
|
|
|
void Fusion::update(const vec3_t& z, const vec3_t& Bi, float sigma) {
|
|
vec4_t q(x0);
|
|
// measured vector in body space: h(p) = A(p)*Bi
|
|
const mat33_t A(quatToMatrix(q));
|
|
const vec3_t Bb(A*Bi);
|
|
|
|
// Sensitivity matrix H = dh(p)/dp
|
|
// H = [ L 0 ]
|
|
const mat33_t L(crossMatrix(Bb, 0));
|
|
|
|
// gain...
|
|
// K = P*Ht / [H*P*Ht + R]
|
|
vec<mat33_t, 2> K;
|
|
const mat33_t R(sigma*sigma);
|
|
const mat33_t S(scaleCovariance(L, P[0][0]) + R);
|
|
const mat33_t Si(invert(S));
|
|
const mat33_t LtSi(transpose(L)*Si);
|
|
K[0] = P[0][0] * LtSi;
|
|
K[1] = transpose(P[1][0])*LtSi;
|
|
|
|
// update...
|
|
// P = (I-K*H) * P
|
|
// P -= K*H*P
|
|
// | K0 | * | L 0 | * P = | K0*L 0 | * | P00 P10 | = | K0*L*P00 K0*L*P10 |
|
|
// | K1 | | K1*L 0 | | P01 P11 | | K1*L*P00 K1*L*P10 |
|
|
// Note: the Joseph form is numerically more stable and given by:
|
|
// P = (I-KH) * P * (I-KH)' + K*R*R'
|
|
const mat33_t K0L(K[0] * L);
|
|
const mat33_t K1L(K[1] * L);
|
|
P[0][0] -= K0L*P[0][0];
|
|
P[1][1] -= K1L*P[1][0];
|
|
P[1][0] -= K0L*P[1][0];
|
|
P[0][1] = transpose(P[1][0]);
|
|
|
|
const vec3_t e(z - Bb);
|
|
const vec3_t dq(K[0]*e);
|
|
|
|
q += getF(q)*(0.5f*dq);
|
|
x0 = normalize_quat(q);
|
|
|
|
if (mMode != FUSION_NOMAG) {
|
|
const vec3_t db(K[1]*e);
|
|
x1 += db;
|
|
}
|
|
|
|
checkState();
|
|
}
|
|
|
|
vec3_t Fusion::getOrthogonal(const vec3_t &v) {
|
|
vec3_t w;
|
|
if (fabsf(v[0])<= fabsf(v[1]) && fabsf(v[0]) <= fabsf(v[2])) {
|
|
w[0]=0.f;
|
|
w[1] = v[2];
|
|
w[2] = -v[1];
|
|
} else if (fabsf(v[1]) <= fabsf(v[2])) {
|
|
w[0] = v[2];
|
|
w[1] = 0.f;
|
|
w[2] = -v[0];
|
|
}else {
|
|
w[0] = v[1];
|
|
w[1] = -v[0];
|
|
w[2] = 0.f;
|
|
}
|
|
return normalize(w);
|
|
}
|
|
|
|
|
|
// -----------------------------------------------------------------------
|
|
|
|
}; // namespace android
|
|
|