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+/****************************************************************************
+ *
+ * Copyright (c) 2012, 2013 PX4 Development Team. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in
+ * the documentation and/or other materials provided with the
+ * distribution.
+ * 3. Neither the name PX4 nor the names of its contributors may be
+ * used to endorse or promote products derived from this software
+ * without specific prior written permission.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
+ * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
+ * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
+ * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
+ * OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
+ * AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
+ * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
+ * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+ * POSSIBILITY OF SUCH DAMAGE.
+ *
+ ****************************************************************************/
+
+/**
+ * @file KalmanNav.cpp
+ *
+ * Kalman filter navigation code
+ */
+
+#include <poll.h>
+
+#include "KalmanNav.hpp"
+#include <systemlib/err.h>
+#include <geo/geo.h>
+
+// constants
+// Titterton pg. 52
+static const float omega = 7.2921150e-5f; // earth rotation rate, rad/s
+static const float R0 = 6378137.0f; // earth radius, m
+static const float g0 = 9.806f; // standard gravitational accel. m/s^2
+static const int8_t ret_ok = 0; // no error in function
+static const int8_t ret_error = -1; // error occurred
+
+KalmanNav::KalmanNav(SuperBlock *parent, const char *name) :
+ SuperBlock(parent, name),
+ // subscriptions
+ _sensors(&getSubscriptions(), ORB_ID(sensor_combined), 5), // limit to 200 Hz
+ _gps(&getSubscriptions(), ORB_ID(vehicle_gps_position), 100), // limit to 10 Hz
+ _param_update(&getSubscriptions(), ORB_ID(parameter_update), 1000), // limit to 1 Hz
+ // publications
+ _pos(&getPublications(), ORB_ID(vehicle_global_position)),
+ _localPos(&getPublications(), ORB_ID(vehicle_local_position)),
+ _att(&getPublications(), ORB_ID(vehicle_attitude)),
+ // timestamps
+ _pubTimeStamp(hrt_absolute_time()),
+ _predictTimeStamp(hrt_absolute_time()),
+ _attTimeStamp(hrt_absolute_time()),
+ _outTimeStamp(hrt_absolute_time()),
+ // frame count
+ _navFrames(0),
+ // miss counts
+ _miss(0),
+ // accelerations
+ fN(0), fE(0), fD(0),
+ // state
+ phi(0), theta(0), psi(0),
+ vN(0), vE(0), vD(0),
+ lat(0), lon(0), alt(0),
+ lat0(0), lon0(0), alt0(0),
+ // parameters for ground station
+ _vGyro(this, "V_GYRO"),
+ _vAccel(this, "V_ACCEL"),
+ _rMag(this, "R_MAG"),
+ _rGpsVel(this, "R_GPS_VEL"),
+ _rGpsPos(this, "R_GPS_POS"),
+ _rGpsAlt(this, "R_GPS_ALT"),
+ _rPressAlt(this, "R_PRESS_ALT"),
+ _rAccel(this, "R_ACCEL"),
+ _magDip(this, "ENV_MAG_DIP"),
+ _magDec(this, "ENV_MAG_DEC"),
+ _g(this, "ENV_G"),
+ _faultPos(this, "FAULT_POS"),
+ _faultAtt(this, "FAULT_ATT"),
+ _attitudeInitialized(false),
+ _positionInitialized(false),
+ _attitudeInitCounter(0)
+{
+ using namespace math;
+
+ memset(&ref, 0, sizeof(ref));
+
+ F.zero();
+ G.zero();
+ V.zero();
+ HAtt.zero();
+ RAtt.zero();
+ HPos.zero();
+ RPos.zero();
+
+ // initial state covariance matrix
+ P0.identity();
+ P0 *= 0.01f;
+ P = P0;
+
+ // initial state
+ phi = 0.0f;
+ theta = 0.0f;
+ psi = 0.0f;
+ vN = 0.0f;
+ vE = 0.0f;
+ vD = 0.0f;
+ lat = 0.0f;
+ lon = 0.0f;
+ alt = 0.0f;
+
+ // initialize rotation quaternion with a single raw sensor measurement
+ _sensors.update();
+ q = init(
+ _sensors.accelerometer_m_s2[0],
+ _sensors.accelerometer_m_s2[1],
+ _sensors.accelerometer_m_s2[2],
+ _sensors.magnetometer_ga[0],
+ _sensors.magnetometer_ga[1],
+ _sensors.magnetometer_ga[2]);
+
+ // initialize dcm
+ C_nb = q.to_dcm();
+
+ // HPos is constant
+ HPos(0, 3) = 1.0f;
+ HPos(1, 4) = 1.0f;
+ HPos(2, 6) = 1.0e7f * M_RAD_TO_DEG_F;
+ HPos(3, 7) = 1.0e7f * M_RAD_TO_DEG_F;
+ HPos(4, 8) = 1.0f;
+ HPos(5, 8) = 1.0f;
+
+ // initialize all parameters
+ updateParams();
+}
+
+math::Quaternion KalmanNav::init(float ax, float ay, float az, float mx, float my, float mz)
+{
+ float initialRoll, initialPitch;
+ float cosRoll, sinRoll, cosPitch, sinPitch;
+ float magX, magY;
+ float initialHdg, cosHeading, sinHeading;
+
+ initialRoll = atan2(-ay, -az);
+ initialPitch = atan2(ax, -az);
+
+ cosRoll = cosf(initialRoll);
+ sinRoll = sinf(initialRoll);
+ cosPitch = cosf(initialPitch);
+ sinPitch = sinf(initialPitch);
+
+ magX = mx * cosPitch + my * sinRoll * sinPitch + mz * cosRoll * sinPitch;
+
+ magY = my * cosRoll - mz * sinRoll;
+
+ initialHdg = atan2f(-magY, magX);
+
+ cosRoll = cosf(initialRoll * 0.5f);
+ sinRoll = sinf(initialRoll * 0.5f);
+
+ cosPitch = cosf(initialPitch * 0.5f);
+ sinPitch = sinf(initialPitch * 0.5f);
+
+ cosHeading = cosf(initialHdg * 0.5f);
+ sinHeading = sinf(initialHdg * 0.5f);
+
+ float q0 = cosRoll * cosPitch * cosHeading + sinRoll * sinPitch * sinHeading;
+ float q1 = sinRoll * cosPitch * cosHeading - cosRoll * sinPitch * sinHeading;
+ float q2 = cosRoll * sinPitch * cosHeading + sinRoll * cosPitch * sinHeading;
+ float q3 = cosRoll * cosPitch * sinHeading - sinRoll * sinPitch * cosHeading;
+
+ return math::Quaternion(q0, q1, q2, q3);
+
+}
+
+void KalmanNav::update()
+{
+ using namespace math;
+
+ struct pollfd fds[1];
+ fds[0].fd = _sensors.getHandle();
+ fds[0].events = POLLIN;
+
+ // poll for new data
+ int ret = poll(fds, 1, 1000);
+
+ if (ret < 0) {
+ // XXX this is seriously bad - should be an emergency
+ return;
+
+ } else if (ret == 0) { // timeout
+ return;
+ }
+
+ // get new timestamp
+ uint64_t newTimeStamp = hrt_absolute_time();
+
+ // check updated subscriptions
+ if (_param_update.updated()) updateParams();
+
+ bool gpsUpdate = _gps.updated();
+ bool sensorsUpdate = _sensors.updated();
+
+ // get new information from subscriptions
+ // this clears update flag
+ updateSubscriptions();
+
+ // initialize attitude when sensors online
+ if (!_attitudeInitialized && sensorsUpdate) {
+ if (correctAtt() == ret_ok) _attitudeInitCounter++;
+
+ if (_attitudeInitCounter > 100) {
+ warnx("initialized EKF attitude");
+ warnx("phi: %8.4f, theta: %8.4f, psi: %8.4f",
+ double(phi), double(theta), double(psi));
+ _attitudeInitialized = true;
+ }
+ }
+
+ // initialize position when gps received
+ if (!_positionInitialized &&
+ _attitudeInitialized && // wait for attitude first
+ gpsUpdate &&
+ _gps.fix_type > 2
+ //&& _gps.counter_pos_valid > 10
+ ) {
+ vN = _gps.vel_n_m_s;
+ vE = _gps.vel_e_m_s;
+ vD = _gps.vel_d_m_s;
+ setLatDegE7(_gps.lat);
+ setLonDegE7(_gps.lon);
+ setAltE3(_gps.alt);
+ // set reference position for
+ // local position
+ lat0 = lat;
+ lon0 = lon;
+ alt0 = alt;
+ map_projection_init(&ref, lat0, lon0);
+ _positionInitialized = true;
+ warnx("initialized EKF state with GPS");
+ warnx("vN: %8.4f, vE: %8.4f, vD: %8.4f, lat: %8.4f, lon: %8.4f, alt: %8.4f",
+ double(vN), double(vE), double(vD),
+ lat, lon, double(alt));
+ }
+
+ // prediction step
+ // using sensors timestamp so we can account for packet lag
+ float dt = (_sensors.timestamp - _predictTimeStamp) / 1.0e6f;
+ //printf("dt: %15.10f\n", double(dt));
+ _predictTimeStamp = _sensors.timestamp;
+
+ // don't predict if time greater than a second
+ if (dt < 1.0f) {
+ predictState(dt);
+ predictStateCovariance(dt);
+ // count fast frames
+ _navFrames += 1;
+ }
+
+ // count times 100 Hz rate isn't met
+ if (dt > 0.01f) _miss++;
+
+ // gps correction step
+ if (_positionInitialized && gpsUpdate) {
+ correctPos();
+ }
+
+ // attitude correction step
+ if (_attitudeInitialized // initialized
+ && sensorsUpdate // new data
+ && _sensors.timestamp - _attTimeStamp > 1e6 / 50 // 50 Hz
+ ) {
+ _attTimeStamp = _sensors.timestamp;
+ correctAtt();
+ }
+
+ // publication
+ if (newTimeStamp - _pubTimeStamp > 1e6 / 50) { // 50 Hz
+ _pubTimeStamp = newTimeStamp;
+
+ updatePublications();
+ }
+
+ // output
+ if (newTimeStamp - _outTimeStamp > 10e6) { // 0.1 Hz
+ _outTimeStamp = newTimeStamp;
+ //printf("nav: %4d Hz, miss #: %4d\n",
+ // _navFrames / 10, _miss / 10);
+ _navFrames = 0;
+ _miss = 0;
+ }
+}
+
+void KalmanNav::updatePublications()
+{
+ using namespace math;
+
+ // global position publication
+ _pos.timestamp = _pubTimeStamp;
+ _pos.time_gps_usec = _gps.timestamp_position;
+ _pos.lat = lat * M_RAD_TO_DEG;
+ _pos.lon = lon * M_RAD_TO_DEG;
+ _pos.alt = float(alt);
+ _pos.vel_n = vN;
+ _pos.vel_e = vE;
+ _pos.vel_d = vD;
+ _pos.yaw = psi;
+
+ // local position publication
+ float x;
+ float y;
+ bool landed = alt < (alt0 + 0.1); // XXX improve?
+ map_projection_project(&ref, lat, lon, &x, &y);
+ _localPos.timestamp = _pubTimeStamp;
+ _localPos.xy_valid = true;
+ _localPos.z_valid = true;
+ _localPos.v_xy_valid = true;
+ _localPos.v_z_valid = true;
+ _localPos.x = x;
+ _localPos.y = y;
+ _localPos.z = alt0 - alt;
+ _localPos.vx = vN;
+ _localPos.vy = vE;
+ _localPos.vz = vD;
+ _localPos.yaw = psi;
+ _localPos.xy_global = true;
+ _localPos.z_global = true;
+ _localPos.ref_timestamp = _pubTimeStamp;
+ _localPos.ref_lat = lat * M_RAD_TO_DEG;
+ _localPos.ref_lon = lon * M_RAD_TO_DEG;
+ _localPos.ref_alt = 0;
+ _localPos.landed = landed;
+
+ // attitude publication
+ _att.timestamp = _pubTimeStamp;
+ _att.roll = phi;
+ _att.pitch = theta;
+ _att.yaw = psi;
+ _att.rollspeed = _sensors.gyro_rad_s[0];
+ _att.pitchspeed = _sensors.gyro_rad_s[1];
+ _att.yawspeed = _sensors.gyro_rad_s[2];
+ // TODO, add gyro offsets to filter
+ _att.rate_offsets[0] = 0.0f;
+ _att.rate_offsets[1] = 0.0f;
+ _att.rate_offsets[2] = 0.0f;
+
+ for (int i = 0; i < 3; i++) for (int j = 0; j < 3; j++)
+ _att.R[i][j] = C_nb(i, j);
+
+ for (int i = 0; i < 4; i++) _att.q[i] = q(i);
+
+ _att.R_valid = true;
+ _att.q_valid = true;
+
+ // selectively update publications,
+ // do NOT call superblock do-all method
+ if (_positionInitialized) {
+ _pos.update();
+ _localPos.update();
+ }
+
+ if (_attitudeInitialized)
+ _att.update();
+}
+
+int KalmanNav::predictState(float dt)
+{
+ using namespace math;
+
+ // trig
+ float sinL = sinf(lat);
+ float cosL = cosf(lat);
+ float cosLSing = cosf(lat);
+
+ // prevent singularity
+ if (fabsf(cosLSing) < 0.01f) {
+ if (cosLSing > 0) cosLSing = 0.01;
+ else cosLSing = -0.01;
+ }
+
+ // attitude prediction
+ if (_attitudeInitialized) {
+ Vector<3> w(_sensors.gyro_rad_s);
+
+ // attitude
+ q = q + q.derivative(w) * dt;
+
+ // renormalize quaternion if needed
+ if (fabsf(q.length() - 1.0f) > 1e-4f) {
+ q.normalize();
+ }
+
+ // C_nb update
+ C_nb = q.to_dcm();
+
+ // euler update
+ Vector<3> euler = C_nb.to_euler();
+ phi = euler.data[0];
+ theta = euler.data[1];
+ psi = euler.data[2];
+
+ // specific acceleration in nav frame
+ Vector<3> accelB(_sensors.accelerometer_m_s2);
+ Vector<3> accelN = C_nb * accelB;
+ fN = accelN(0);
+ fE = accelN(1);
+ fD = accelN(2);
+ }
+
+ // position prediction
+ if (_positionInitialized) {
+ // neglects angular deflections in local gravity
+ // see Titerton pg. 70
+ float R = R0 + float(alt);
+ float LDot = vN / R;
+ float lDot = vE / (cosLSing * R);
+ float rotRate = 2 * omega + lDot;
+
+ // XXX position prediction using speed
+ float vNDot = fN - vE * rotRate * sinL +
+ vD * LDot;
+ float vDDot = fD - vE * rotRate * cosL -
+ vN * LDot + _g.get();
+ float vEDot = fE + vN * rotRate * sinL +
+ vDDot * rotRate * cosL;
+
+ // rectangular integration
+ vN += vNDot * dt;
+ vE += vEDot * dt;
+ vD += vDDot * dt;
+ lat += double(LDot * dt);
+ lon += double(lDot * dt);
+ alt += double(-vD * dt);
+ }
+
+ return ret_ok;
+}
+
+int KalmanNav::predictStateCovariance(float dt)
+{
+ using namespace math;
+
+ // trig
+ float sinL = sinf(lat);
+ float cosL = cosf(lat);
+ float cosLSq = cosL * cosL;
+ float tanL = tanf(lat);
+
+ // prepare for matrix
+ float R = R0 + float(alt);
+ float RSq = R * R;
+
+ // F Matrix
+ // Titterton pg. 291
+
+ F(0, 1) = -(omega * sinL + vE * tanL / R);
+ F(0, 2) = vN / R;
+ F(0, 4) = 1.0f / R;
+ F(0, 6) = -omega * sinL;
+ F(0, 8) = -vE / RSq;
+
+ F(1, 0) = omega * sinL + vE * tanL / R;
+ F(1, 2) = omega * cosL + vE / R;
+ F(1, 3) = -1.0f / R;
+ F(1, 8) = vN / RSq;
+
+ F(2, 0) = -vN / R;
+ F(2, 1) = -omega * cosL - vE / R;
+ F(2, 4) = -tanL / R;
+ F(2, 6) = -omega * cosL - vE / (R * cosLSq);
+ F(2, 8) = vE * tanL / RSq;
+
+ F(3, 1) = -fD;
+ F(3, 2) = fE;
+ F(3, 3) = vD / R;
+ F(3, 4) = -2 * (omega * sinL + vE * tanL / R);
+ F(3, 5) = vN / R;
+ F(3, 6) = -vE * (2 * omega * cosL + vE / (R * cosLSq));
+ F(3, 8) = (vE * vE * tanL - vN * vD) / RSq;
+
+ F(4, 0) = fD;
+ F(4, 2) = -fN;
+ F(4, 3) = 2 * omega * sinL + vE * tanL / R;
+ F(4, 4) = (vN * tanL + vD) / R;
+ F(4, 5) = 2 * omega * cosL + vE / R;
+ F(4, 6) = 2 * omega * (vN * cosL - vD * sinL) +
+ vN * vE / (R * cosLSq);
+ F(4, 8) = -vE * (vN * tanL + vD) / RSq;
+
+ F(5, 0) = -fE;
+ F(5, 1) = fN;
+ F(5, 3) = -2 * vN / R;
+ F(5, 4) = -2 * (omega * cosL + vE / R);
+ F(5, 6) = 2 * omega * vE * sinL;
+ F(5, 8) = (vN * vN + vE * vE) / RSq;
+
+ F(6, 3) = 1 / R;
+ F(6, 8) = -vN / RSq;
+
+ F(7, 4) = 1 / (R * cosL);
+ F(7, 6) = vE * tanL / (R * cosL);
+ F(7, 8) = -vE / (cosL * RSq);
+
+ F(8, 5) = -1;
+
+ // G Matrix
+ // Titterton pg. 291
+ G(0, 0) = -C_nb(0, 0);
+ G(0, 1) = -C_nb(0, 1);
+ G(0, 2) = -C_nb(0, 2);
+ G(1, 0) = -C_nb(1, 0);
+ G(1, 1) = -C_nb(1, 1);
+ G(1, 2) = -C_nb(1, 2);
+ G(2, 0) = -C_nb(2, 0);
+ G(2, 1) = -C_nb(2, 1);
+ G(2, 2) = -C_nb(2, 2);
+
+ G(3, 3) = C_nb(0, 0);
+ G(3, 4) = C_nb(0, 1);
+ G(3, 5) = C_nb(0, 2);
+ G(4, 3) = C_nb(1, 0);
+ G(4, 4) = C_nb(1, 1);
+ G(4, 5) = C_nb(1, 2);
+ G(5, 3) = C_nb(2, 0);
+ G(5, 4) = C_nb(2, 1);
+ G(5, 5) = C_nb(2, 2);
+
+ // continuous prediction equations
+ // for discrete time EKF
+ // http://en.wikipedia.org/wiki/Extended_Kalman_filter
+ P = P + (F * P + P * F.transposed() + G * V * G.transposed()) * dt;
+
+ return ret_ok;
+}
+
+int KalmanNav::correctAtt()
+{
+ using namespace math;
+
+ // trig
+ float cosPhi = cosf(phi);
+ float cosTheta = cosf(theta);
+ // float cosPsi = cosf(psi);
+ float sinPhi = sinf(phi);
+ float sinTheta = sinf(theta);
+ // float sinPsi = sinf(psi);
+
+ // mag predicted measurement
+ // choosing some typical magnetic field properties,
+ // TODO dip/dec depend on lat/ lon/ time
+ //float dip = _magDip.get() / M_RAD_TO_DEG_F; // dip, inclination with level
+ float dec = _magDec.get() / M_RAD_TO_DEG_F; // declination, clockwise rotation from north
+
+ // compensate roll and pitch, but not yaw
+ // XXX take the vectors out of the C_nb matrix to avoid singularities
+ math::Matrix<3,3> C_rp;
+ C_rp.from_euler(phi, theta, 0.0f);//C_nb.transposed();
+
+ // mag measurement
+ Vector<3> magBody(_sensors.magnetometer_ga);
+
+ // transform to earth frame
+ Vector<3> magNav = C_rp * magBody;
+
+ // calculate error between estimate and measurement
+ // apply declination correction for true heading as well.
+ float yMag = -atan2f(magNav(1),magNav(0)) - psi - dec;
+ if (yMag > M_PI_F) yMag -= 2*M_PI_F;
+ if (yMag < -M_PI_F) yMag += 2*M_PI_F;
+
+ // accel measurement
+ Vector<3> zAccel(_sensors.accelerometer_m_s2);
+ float accelMag = zAccel.length();
+ zAccel.normalize();
+
+ // ignore accel correction when accel mag not close to g
+ Matrix<4,4> RAttAdjust = RAtt;
+
+ bool ignoreAccel = fabsf(accelMag - _g.get()) > 1.1f;
+
+ if (ignoreAccel) {
+ RAttAdjust(1, 1) = 1.0e10;
+ RAttAdjust(2, 2) = 1.0e10;
+ RAttAdjust(3, 3) = 1.0e10;
+
+ } else {
+ //printf("correcting attitude with accel\n");
+ }
+
+ // accel predicted measurement
+ Vector<3> zAccelHat = (C_nb.transposed() * Vector<3>(0, 0, -_g.get())).normalized();
+
+ // calculate residual
+ Vector<4> y(yMag, zAccel(0) - zAccelHat(0), zAccel(1) - zAccelHat(1), zAccel(2) - zAccelHat(2));
+
+ // HMag
+ HAtt(0, 2) = 1;
+
+ // HAccel
+ HAtt(1, 1) = cosTheta;
+ HAtt(2, 0) = -cosPhi * cosTheta;
+ HAtt(2, 1) = sinPhi * sinTheta;
+ HAtt(3, 0) = sinPhi * cosTheta;
+ HAtt(3, 1) = cosPhi * sinTheta;
+
+ // compute correction
+ // http://en.wikipedia.org/wiki/Extended_Kalman_filter
+ Matrix<4, 4> S = HAtt * P * HAtt.transposed() + RAttAdjust; // residual covariance
+ Matrix<9, 4> K = P * HAtt.transposed() * S.inversed();
+ Vector<9> xCorrect = K * y;
+
+ // check correciton is sane
+ for (size_t i = 0; i < xCorrect.get_size(); i++) {
+ float val = xCorrect(i);
+
+ if (isnan(val) || isinf(val)) {
+ // abort correction and return
+ warnx("numerical failure in att correction");
+ // reset P matrix to P0
+ P = P0;
+ return ret_error;
+ }
+ }
+
+ // correct state
+ if (!ignoreAccel) {
+ phi += xCorrect(PHI);
+ theta += xCorrect(THETA);
+ }
+
+ psi += xCorrect(PSI);
+
+ // attitude also affects nav velocities
+ if (_positionInitialized) {
+ vN += xCorrect(VN);
+ vE += xCorrect(VE);
+ vD += xCorrect(VD);
+ }
+
+ // update state covariance
+ // http://en.wikipedia.org/wiki/Extended_Kalman_filter
+ P = P - K * HAtt * P;
+
+ // fault detection
+ float beta = y * (S.inversed() * y);
+
+ if (beta > _faultAtt.get()) {
+ warnx("fault in attitude: beta = %8.4f", (double)beta);
+ warnx("y:"); y.print();
+ }
+
+ // update quaternions from euler
+ // angle correction
+ q.from_euler(phi, theta, psi);
+
+ return ret_ok;
+}
+
+int KalmanNav::correctPos()
+{
+ using namespace math;
+
+ // residual
+ Vector<6> y;
+ y(0) = _gps.vel_n_m_s - vN;
+ y(1) = _gps.vel_e_m_s - vE;
+ y(2) = double(_gps.lat) - double(lat) * 1.0e7 * M_RAD_TO_DEG;
+ y(3) = double(_gps.lon) - double(lon) * 1.0e7 * M_RAD_TO_DEG;
+ y(4) = _gps.alt / 1.0e3f - alt;
+ y(5) = _sensors.baro_alt_meter - alt;
+
+ // compute correction
+ // http://en.wikipedia.org/wiki/Extended_Kalman_filter
+ Matrix<6,6> S = HPos * P * HPos.transposed() + RPos; // residual covariance
+ Matrix<9,6> K = P * HPos.transposed() * S.inversed();
+ Vector<9> xCorrect = K * y;
+
+ // check correction is sane
+ for (size_t i = 0; i < xCorrect.get_size(); i++) {
+ float val = xCorrect(i);
+
+ if (!isfinite(val)) {
+ // abort correction and return
+ warnx("numerical failure in gps correction");
+ // fallback to GPS
+ vN = _gps.vel_n_m_s;
+ vE = _gps.vel_e_m_s;
+ vD = _gps.vel_d_m_s;
+ setLatDegE7(_gps.lat);
+ setLonDegE7(_gps.lon);
+ setAltE3(_gps.alt);
+ // reset P matrix to P0
+ P = P0;
+ return ret_error;
+ }
+ }
+
+ // correct state
+ vN += xCorrect(VN);
+ vE += xCorrect(VE);
+ vD += xCorrect(VD);
+ lat += double(xCorrect(LAT));
+ lon += double(xCorrect(LON));
+ alt += xCorrect(ALT);
+
+ // update state covariance
+ // http://en.wikipedia.org/wiki/Extended_Kalman_filter
+ P = P - K * HPos * P;
+
+ // fault detetcion
+ float beta = y * (S.inversed() * y);
+
+ static int counter = 0;
+ if (beta > _faultPos.get() && (counter % 10 == 0)) {
+ warnx("fault in gps: beta = %8.4f", (double)beta);
+ warnx("Y/N: vN: %8.4f, vE: %8.4f, lat: %8.4f, lon: %8.4f, alt: %8.4f, baro: %8.4f",
+ double(y(0) / sqrtf(RPos(0, 0))),
+ double(y(1) / sqrtf(RPos(1, 1))),
+ double(y(2) / sqrtf(RPos(2, 2))),
+ double(y(3) / sqrtf(RPos(3, 3))),
+ double(y(4) / sqrtf(RPos(4, 4))),
+ double(y(5) / sqrtf(RPos(5, 5))));
+ }
+ counter++;
+
+ return ret_ok;
+}
+
+void KalmanNav::updateParams()
+{
+ using namespace math;
+ using namespace control;
+ SuperBlock::updateParams();
+
+ // gyro noise
+ V(0, 0) = _vGyro.get(); // gyro x, rad/s
+ V(1, 1) = _vGyro.get(); // gyro y
+ V(2, 2) = _vGyro.get(); // gyro z
+
+ // accel noise
+ V(3, 3) = _vAccel.get(); // accel x, m/s^2
+ V(4, 4) = _vAccel.get(); // accel y
+ V(5, 5) = _vAccel.get(); // accel z
+
+ // magnetometer noise
+ float noiseMin = 1e-6f;
+ float noiseMagSq = _rMag.get() * _rMag.get();
+
+ if (noiseMagSq < noiseMin) noiseMagSq = noiseMin;
+
+ RAtt(0, 0) = noiseMagSq; // normalized direction
+
+ // accelerometer noise
+ float noiseAccelSq = _rAccel.get() * _rAccel.get();
+
+ // bound noise to prevent singularities
+ if (noiseAccelSq < noiseMin) noiseAccelSq = noiseMin;
+
+ RAtt(1, 1) = noiseAccelSq; // normalized direction
+ RAtt(2, 2) = noiseAccelSq;
+ RAtt(3, 3) = noiseAccelSq;
+
+ // gps noise
+ float R = R0 + float(alt);
+ float cosLSing = cosf(lat);
+
+ // prevent singularity
+ if (fabsf(cosLSing) < 0.01f) {
+ if (cosLSing > 0) cosLSing = 0.01;
+ else cosLSing = -0.01;
+ }
+
+ float noiseVel = _rGpsVel.get();
+ float noiseLatDegE7 = 1.0e7f * M_RAD_TO_DEG_F * _rGpsPos.get() / R;
+ float noiseLonDegE7 = noiseLatDegE7 / cosLSing;
+ float noiseGpsAlt = _rGpsAlt.get();
+ float noisePressAlt = _rPressAlt.get();
+
+ // bound noise to prevent singularities
+ if (noiseVel < noiseMin) noiseVel = noiseMin;
+
+ if (noiseLatDegE7 < noiseMin) noiseLatDegE7 = noiseMin;
+
+ if (noiseLonDegE7 < noiseMin) noiseLonDegE7 = noiseMin;
+
+ if (noiseGpsAlt < noiseMin) noiseGpsAlt = noiseMin;
+
+ if (noisePressAlt < noiseMin) noisePressAlt = noiseMin;
+
+ RPos(0, 0) = noiseVel * noiseVel; // vn
+ RPos(1, 1) = noiseVel * noiseVel; // ve
+ RPos(2, 2) = noiseLatDegE7 * noiseLatDegE7; // lat
+ RPos(3, 3) = noiseLonDegE7 * noiseLonDegE7; // lon
+ RPos(4, 4) = noiseGpsAlt * noiseGpsAlt; // h
+ RPos(5, 5) = noisePressAlt * noisePressAlt; // h
+ // XXX, note that RPos depends on lat, so updateParams should
+ // be called if lat changes significantly
+}