找到一个更易于理解的卡尔曼滤波代码:
https://github.com/TKJElectronics/KalmanFilter
/* Copyright (C) 2012 Kristian Lauszus, TKJ Electronics. All rights reserved.
This software may be distributed and modified under the terms of the GNU
General Public License version 2 (GPL2) as published by the Free Software
Foundation and appearing in the file GPL2.TXT included in the packaging of
this file. Please note that GPL2 Section 2[b] requires that all works based
on this software must also be made publicly available under the terms of
the GPL2 ("Copyleft").
Contact information
-------------------
Kristian Lauszus, TKJ Electronics
Web : http://www.tkjelectronics.com
e-mail : kristianl@tkjelectronics.com
*/
#ifndef _Kalman_h_
#define _Kalman_h_
class Kalman {
public:
Kalman();
// The angle should be in degrees and the rate should be in degrees per second and the delta time in seconds
float getAngle(float newAngle, float newRate, float dt);
void setAngle(float angle); // Used to set angle, this should be set as the starting angle
float getRate(); // Return the unbiased rate
/* These are used to tune the Kalman filter */
void setQangle(float Q_angle);
void setQbias(float Q_bias);
void setRmeasure(float R_measure);
float getQangle();
float getQbias();
float getRmeasure();
private:
/* Kalman filter variables */
float Q_angle; // Process noise variance for the accelerometer
float Q_bias; // Process noise variance for the gyro bias
float R_measure; // Measurement noise variance - this is actually the variance of the measurement noise
float angle; // The angle calculated by the Kalman filter - part of the 2x1 state vector
float bias; // The gyro bias calculated by the Kalman filter - part of the 2x1 state vector
float rate; // Unbiased rate calculated from the rate and the calculated bias - you have to call getAngle to update the rate
float P[2][2]; // Error covariance matrix - This is a 2x2 matrix
};
#endif
/* Copyright (C) 2012 Kristian Lauszus, TKJ Electronics. All rights reserved.
This software may be distributed and modified under the terms of the GNU
General Public License version 2 (GPL2) as published by the Free Software
Foundation and appearing in the file GPL2.TXT included in the packaging of
this file. Please note that GPL2 Section 2[b] requires that all works based
on this software must also be made publicly available under the terms of
the GPL2 ("Copyleft").
Contact information
-------------------
Kristian Lauszus, TKJ Electronics
Web : http://www.tkjelectronics.com
e-mail : kristianl@tkjelectronics.com
*/
#include "Kalman.h"
Kalman::Kalman() {
/* We will set the variables like so, these can also be tuned by the user */
Q_angle = 0.001f;
Q_bias = 0.003f;
R_measure = 0.03f;
angle = 0.0f; // Reset the angle
bias = 0.0f; // Reset bias
P[0][0] = 0.0f; // Since we assume that the bias is 0 and we know the starting angle (use setAngle), the error covariance matrix is set like so - see: http://en.wikipedia.org/wiki/Kalman_filter#Example_application.2C_technical
P[0][1] = 0.0f;
P[1][0] = 0.0f;
P[1][1] = 0.0f;
};
// The angle should be in degrees and the rate should be in degrees per second and the delta time in seconds
float Kalman::getAngle(float newAngle, float newRate, float dt) {
// KasBot V2 - Kalman filter module - http://www.x-firm.com/?page_id=145
// Modified by Kristian Lauszus
// See my blog post for more information: http://blog.tkjelectronics.dk/2012/09/a-practical-approach-to-kalman-filter-and-how-to-implement-it
// Discrete Kalman filter time update equations - Time Update ("Predict")
// Update xhat - Project the state ahead
/* Step 1 */
rate = newRate - bias;
angle += dt * rate;
// Update estimation error covariance - Project the error covariance ahead
/* Step 2 */
P[0][0] += dt * (dt*P[1][1] - P[0][1] - P[1][0] + Q_angle);
P[0][1] -= dt * P[1][1];
P[1][0] -= dt * P[1][1];
P[1][1] += Q_bias * dt;
// Discrete Kalman filter measurement update equations - Measurement Update ("Correct")
// Calculate Kalman gain - Compute the Kalman gain
/* Step 4 */
float S = P[0][0] + R_measure; // Estimate error
/* Step 5 */
float K[2]; // Kalman gain - This is a 2x1 vector
K[0] = P[0][0] / S;
K[1] = P[1][0] / S;
// Calculate angle and bias - Update estimate with measurement zk (newAngle)
/* Step 3 */
float y = newAngle - angle; // Angle difference
/* Step 6 */
angle += K[0] * y;
bias += K[1] * y;
// Calculate estimation error covariance - Update the error covariance
/* Step 7 */
float P00_temp = P[0][0];
float P01_temp = P[0][1];
P[0][0] -= K[0] * P00_temp;
P[0][1] -= K[0] * P01_temp;
P[1][0] -= K[1] * P00_temp;
P[1][1] -= K[1] * P01_temp;
return angle;
};
void Kalman::setAngle(float angle) { this->angle = angle; }; // Used to set angle, this should be set as the starting angle
float Kalman::getRate() { return this->rate; }; // Return the unbiased rate
/* These are used to tune the Kalman filter */
void Kalman::setQangle(float Q_angle) { this->Q_angle = Q_angle; };
void Kalman::setQbias(float Q_bias) { this->Q_bias = Q_bias; };
void Kalman::setRmeasure(float R_measure) { this->R_measure = R_measure; };
float Kalman::getQangle() { return this->Q_angle; };
float Kalman::getQbias() { return this->Q_bias; };
float Kalman::getRmeasure() { return this->R_measure; };