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/*
filters.cpp: Filter class implementations
*/
//#include <cmath>
#include <stdlib.h> // XXX eventually use fabs() instead of abs() ?
#include "filters.h"
void KalmanFilter::getPredictionCovariance(float covariance[3][3], float previousState[3], float deltat)
{
// required matrices for the operations
float sigma[3][3];
float identity[3][3];
identityMatrix3x3(identity);
float skewMatrix[3][3];
skew(skewMatrix, previousState);
float tmp[3][3];
// Compute the prediction covariance matrix
scaleMatrix3x3(sigma, pow(sigmaGyro, 2), identity);
matrixProduct3x3(tmp, skewMatrix, sigma);
matrixProduct3x3(covariance, tmp, skewMatrix);
scaleMatrix3x3(covariance, -pow(deltat, 2), covariance);
}
void KalmanFilter::getMeasurementCovariance(float covariance[3][3])
{
// required matrices for the operations
float sigma[3][3];
float identity[3][3];
identityMatrix3x3(identity);
float norm;
// Compute measurement covariance
scaleMatrix3x3(sigma, pow(sigmaAccel, 2), identity);
vectorLength(& norm, previousAccelSensor);
scaleAndAccumulateMatrix3x3(sigma, (1.0/3.0)*pow(ca, 2)*norm, identity);
copyMatrix3x3(covariance, sigma);
}
void KalmanFilter::predictState(float predictedState[3], float gyro[3], float deltat)
{
// helper matrices
float identity[3][3];
identityMatrix3x3(identity);
float skewFromGyro[3][3];
skew(skewFromGyro, gyro);
// Predict state
scaleAndAccumulateMatrix3x3(identity, -deltat, skewFromGyro);
matrixDotVector3x3(predictedState, identity, currentState);
normalizeVector(predictedState);
}
void KalmanFilter::predictErrorCovariance(float covariance[3][3], float gyro[3], float deltat)
{
// required matrices
float Q[3][3];
float identity[3][3];
identityMatrix3x3(identity);
float skewFromGyro[3][3];
skew(skewFromGyro, gyro);
float tmp[3][3];
float tmpTransposed[3][3];
float tmp2[3][3];
// predict error covariance
getPredictionCovariance(Q, currentState, deltat);
scaleAndAccumulateMatrix3x3(identity, -deltat, skewFromGyro);
copyMatrix3x3(tmp, identity);
transposeMatrix3x3(tmpTransposed, tmp);
matrixProduct3x3(tmp2, tmp, currErrorCovariance);
matrixProduct3x3(covariance, tmp2, tmpTransposed);
scaleAndAccumulateMatrix3x3(covariance, 1.0, Q);
}
void KalmanFilter::updateGain(float gain[3][3], float errorCovariance[3][3])
{
// required matrices
float R[3][3];
float HTransposed[3][3];
transposeMatrix3x3(HTransposed, H);
float tmp[3][3];
float tmp2[3][3];
float tmp2Inverse[3][3];
// update kalman gain
// P.dot(H.T).dot(inv(H.dot(P).dot(H.T) + R))
getMeasurementCovariance(R);
matrixProduct3x3(tmp, errorCovariance, HTransposed);
matrixProduct3x3(tmp2, H, tmp);
scaleAndAccumulateMatrix3x3(tmp2, 1.0, R);
invert3x3(tmp2Inverse, tmp2);
matrixProduct3x3(gain, tmp, tmp2Inverse);
}
void KalmanFilter::updateState(float updatedState[3], float predictedState[3], float gain[3][3], float accel[3])
{
// required matrices
float tmp[3];
float tmp2[3];
float measurement[3];
scaleVector(tmp, ca, previousAccelSensor);
subtractVectors(measurement, accel, tmp);
// update state with measurement
// predicted_state + K.dot(measurement - H.dot(predicted_state))
matrixDotVector3x3(tmp, H, predictedState);
subtractVectors(tmp, measurement, tmp);
matrixDotVector3x3(tmp2, gain, tmp);
sumVectors(updatedState, predictedState, tmp2);
normalizeVector(updatedState);
}
void KalmanFilter::updateErrorCovariance(float covariance[3][3], float errorCovariance[3][3], float gain[3][3])
{
// required matrices
float identity[3][3];
identityMatrix3x3(identity);
float tmp[3][3];
float tmp2[3][3];
// update error covariance with measurement
matrixProduct3x3(tmp, gain, H);
matrixProduct3x3(tmp2, tmp, errorCovariance);
scaleAndAccumulateMatrix3x3(identity, -1.0, tmp2);
copyMatrix3x3(covariance, tmp2);
}
KalmanFilter::KalmanFilter(float ca, float sigmaGyro, float sigmaAccel)
{
this->ca = ca;
this->sigmaGyro = sigmaGyro;
this->sigmaAccel = sigmaAccel;
}
float KalmanFilter::estimate(float gyro[3], float accel[3], float deltat)
{
float predictedState[3];
float updatedState[3];
float errorCovariance[3][3];
float updatedErrorCovariance[3][3];
float gain[3][3];
float accelSensor[3];
float tmp[3];
float accelEarth;
scaleVector(accel, 9.81, accel); // Scale accel readings since they are measured in gs
// perform estimation
// predictions
predictState(predictedState, gyro, deltat);
predictErrorCovariance(errorCovariance, gyro, deltat);
// updates
updateGain(gain, errorCovariance);
updateState(updatedState, predictedState, gain, accel);
updateErrorCovariance(updatedErrorCovariance, errorCovariance, gain);
// Store required values for next iteration
copyVector(currentState, updatedState);
copyMatrix3x3(currErrorCovariance, updatedErrorCovariance);
// return vertical acceleration estimate
scaleVector(tmp, 9.81, updatedState);
subtractVectors(accelSensor, accel, tmp);
copyVector(previousAccelSensor, accelSensor);
dotProductVectors(& accelEarth, accelSensor, updatedState);
return accelEarth;
}
float ComplementaryFilter::ApplyZUPT(float accel, float vel)
{
// first update ZUPT array with latest estimation
ZUPT[ZUPTIdx] = accel;
// and move index to next slot
uint8_t nextIndex = (ZUPTIdx + 1) % ZUPT_SIZE;
ZUPTIdx = nextIndex;
// Apply Zero-velocity update
for (uint8_t k = 0; k < ZUPT_SIZE; ++k) {
if (abs(ZUPT[k]) > accelThreshold) return vel;
}
return 0.0;
}
ComplementaryFilter::ComplementaryFilter(float sigmaAccel, float sigmaBaro, float accelThreshold)
{
// Compute the filter gain
gain[0] = sqrt(2 * sigmaAccel / sigmaBaro);
gain[1] = sigmaAccel / sigmaBaro;
// If acceleration is below the threshold the ZUPT counter
// will be increased
this->accelThreshold = accelThreshold;
// initialize zero-velocity update
ZUPTIdx = 0;
for (uint8_t k = 0; k < ZUPT_SIZE; ++k) {
ZUPT[k] = 0;
}
}
void ComplementaryFilter::estimate(float * velocity, float * altitude, float baroAltitude,
float pastAltitude, float pastVelocity, float accel, float deltat)
{
// Apply complementary filter
*altitude = pastAltitude + deltat*(pastVelocity + (gain[0] + gain[1]*deltat/2)*(baroAltitude-pastAltitude))+
accel*pow(deltat, 2)/2;
*velocity = pastVelocity + deltat*(gain[1]*(baroAltitude-pastAltitude) + accel);
// Compute zero-velocity update
*velocity = ApplyZUPT(accel, *velocity);
}
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