爾曼濾波器英文資料與C語言源程序

ID:847251 · 發表于 2020-11-22 14:32

詳細介紹卡爾曼濾波器。
附有程序源碼

源程序如下:

/***************************************************************************/
/* kalman.c */
/* 1-D Kalman filter Algorithm, using an inclinometer and gyro */
/* Author: Rich Chi Ooi */
/* Version: 1.0 */
/* Date:30.05.2003 */
/* Adapted from Trammel Hudson(hudson@rotomotion.com) */
/* ------------------------------- */
/* Compilation procedure: */
/* Linux */
/* gcc68 -c XXXXXX.c (to create object file) */
/* gcc68 -o XXXXXX.hex XXXXXX.o ppwa.o */
/*Upload data : */
/* ul filename.txt */
/***************************************************************************/
/* In this version: */
/***************************************************************************/
/* This is a free software; you can redistribute it and/or modify */
/* it under the terms of the GNU General Public License as published */
/* by the Free Software Foundation; either version 2 of the License, */
/* or (at your option) any later version. */
/* */
/* this code is distributed in the hope that it will be useful, */
/* but WITHOUT ANY WARRANTY; without even the implied warranty of */
/* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the */
/* GNU General Public License for more details. */
/* */
/* You should have received a copy of the GNU General Public License */
/* along with Autopilot; if not, write to the Free Software */
/* Foundation, Inc., 59 Temple Place, Suite 330, Boston, */
/* MA 02111-1307 USA */
/***************************************************************************/
#include <math.h>
#include "eyebot.h"
/*
* The state is updated with gyro rate measurement every 20ms
* change this value if you update at a different rate.
*/
static const float dt = 0.02;
/*
* The covariance matrix.This is updated at every time step to
* determine how well the sensors are tracking the actual state.
*/
static float P[2][2] = {{ 1, 0 },
{ 0, 1 }};
/*
* Our two states, the angle and the gyro bias.As a byproduct of computing
* the angle, we also have an unbiased angular rate available.These are
* read-only to the user of the module.
*/
float angle;
float q_bias;
float rate;
/*
* The R represents the measurement covariance noise.R=E[vvT]
* In this case,it is a 1x1 matrix that says that we expect
* 0.1 rad jitter from the inclinometer.
* for a 1x1 matrix in this case v = 0.1
*/
static const float R_angle = 0.001 ;
/*
* Q is a 2x2 matrix that represents the process covariance noise.
* In this case, it indicates how much we trust the inclinometer
* relative to the gyros.
*/
static const float Q_angle = 0.001;
static const float Q_gyro = 0.0015;
/*
* state_update is called every dt with a biased gyro measurement
* by the user of the module. It updates the current angle and
* rate estimate.
*
* The pitch gyro measurement should be scaled into real units, but
* does not need any bias removal. The filter will track the bias.
*
* A = [ 0 -1 ]
* [ 0 0 ]
*/
void stateUpdate(const float q_m){
float q;
float Pdot[4];
/* Unbias our gyro */
q = q_m - q_bias;
/*
* Compute the derivative of the covariance matrix
* (equation 22-1)
* Pdot = A*P + P*A' + Q
*
*/
Pdot[0] = Q_angle - P[0][1] - P[1][0]; /* 0,0 */
Pdot[1] = - P[1][1]; /* 0,1 */
Pdot[2] = - P[1][1]; /* 1,0 */
Pdot[3] = Q_gyro; /* 1,1 */
/* Store our unbias gyro estimate */
rate = q;
/*
* Update our angle estimate
* angle += angle_dot * dt
* += (gyro - gyro_bias) * dt
* += q * dt
*/
angle += q * dt;
/* Update the covariance matrix */
P[0][0] += Pdot[0] * dt;
P[0][1] += Pdot[1] * dt;
P[1][0] += Pdot[2] * dt;
P[1][1] += Pdot[3] * dt;
}
/*
* kalman_update is called by a user of the module when a new
* inclinoometer measurement is available.
*
* This does not need to be called every time step, but can be if
* the accelerometer data are available at the same rate as the
* rate gyro measurement.
*
* H = [ 1 0 ]
*
* because the angle measurement directly corresponds to the angle
* estimate and the angle measurement has no relation to the gyro
* bias.
*/
void kalmanUpdate(const float incAngle)
{
/* Compute our measured angle and the error in our estimate */
float angle_m = incAngle;
float angle_err = angle_m - angle;
/*
* h_0 shows how the state measurement directly relates to
* the state estimate.
*
* H = [h_0 h_1]
*
* The h_1 shows that the state measurement does not relate
* to the gyro bias estimate. We don't actually use this, so
* we comment it out.
*/
float h_0 = 1;
/* const float h_1 = 0; */
/*
* Precompute PH' as the term is used twice
* Note that H[0,1] = h_1 is zero, so that term is not not computed
*/
const float PHt_0 = h_0*P[0][0]; /* + h_1*P[0][1] = 0*/
const float PHt_1 = h_0*P[1][0]; /* + h_1*P[1][1] = 0*/
/*
* Compute the error estimate:
* (equation 21-1)
*
* E = H P H' + R
*/
float E = R_angle +(h_0 * PHt_0);
/*
* Compute the Kalman filter gains:
* (equation 21-2)
*
* K = P H' inv(E)
*/
float K_0 = PHt_0 / E;
float K_1 = PHt_1 / E;
/*
* Update covariance matrix:
* (equation 21-3)
*
* P = P - K H P
* Let
* Y = H P
*/
float Y_0 = PHt_0; /*h_0 * P[0][0]*/
float Y_1 = h_0 * P[0][1];
P[0][0] -= K_0 * Y_0;
P[0][1] -= K_0 * Y_1;
P[1][0] -= K_1 * Y_0;
P[1][1] -= K_1 * Y_1;
/*
* Update our state estimate:
*
* Xnew = X + K * error
*
* err is a measurement of the difference in the measured state
* and the estimate state. In our case, it is just the difference
* between the inclinometer measured angle and the estimated angle.
*/
angle += K_0 * angle_err;
q_bias += K_1 * angle_err;
}

復制代碼

所有資料51hei提供下載:

卡爾曼.zip (580.13 KB, 下載次數: 14)

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爾曼濾波器英文資料與C語言源程序

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