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Код: Выделить всё • Развернуть

# Kalman filter example demo in Python

# A Python implementation of the example given in pages 11-15 of "An
# Introduction to the Kalman Filter" by Greg Welch and Gary Bishop,
# University of North Carolina at Chapel Hill, Department of Computer
# Science, TR 95-041,
# http://www.cs.unc.edu/~welch/kalman/kalmanIntro.html

# by Andrew D. Straw

import numpy
import pylab

# intial parameters
n_iter = 50
sz = (n_iter,) # size of array
x = -0.37727 # truth value (typo in example at top of p. 13 calls this z)
z = numpy.random.normal(x,0.1,size=sz) # observations (normal about x, sigma=0.1)

Q = 1e-5 # process variance

# allocate space for arrays
xhat=numpy.zeros(sz)      # a posteri estimate of x
P=numpy.zeros(sz)         # a posteri error estimate
xhatminus=numpy.zeros(sz) # a priori estimate of x
Pminus=numpy.zeros(sz)    # a priori error estimate
K=numpy.zeros(sz)         # gain or blending factor

R = 0.1**2 # estimate of measurement variance, change to see effect

# intial guesses
xhat[0] = 0.0
P[0] = 1.0

for k in range(1,n_iter):
    # time update
    xhatminus[k] = xhat[k-1]
    Pminus[k] = P[k-1]+Q

    # measurement update
    K[k] = Pminus[k]/( Pminus[k]+R )
    xhat[k] = xhatminus[k]+K[k]*(z[k]-xhatminus[k])
    P[k] = (1-K[k])*Pminus[k]

pylab.figure()
pylab.plot(z,'k+',label='noisy measurements')
pylab.plot(xhat,'b-',label='a posteri estimate')
pylab.axhline(x,color='g',label='truth value')
pylab.legend()
pylab.xlabel('Iteration')
pylab.ylabel('Voltage')

pylab.figure()
valid_iter = range(1,n_iter) # Pminus not valid at step 0
pylab.plot(valid_iter,Pminus[valid_iter],label='a priori error estimate')
pylab.xlabel('Iteration')
pylab.ylabel('$(Voltage)^2$')
pylab.setp(pylab.gca(),'ylim',[0,.01])
pylab.show()

Код: Выделить всё • Развернуть

/** A simple kalman filter example by Adrian Boeing 
 www.adrianboeing.com 
 */ 

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

double frand() {
    return 2*((rand()/(double)RAND_MAX) - 0.5);
}

int main() {

    //initial values for the kalman filter
    float x_est_last = 0;
    float P_last = 0;
    //the noise in the system
    float Q = 0.022;
    float R = 0.617;
    
    float K;
    float P;
    float P_temp;
    float x_temp_est;
    float x_est;
    float z_measured; //the 'noisy' value we measured
    float z_real = 0.5; //the ideal value we wish to measure
    
    srand(0);
    
    //initialize with a measurement
    x_est_last = z_real + frand()*0.09;
    
    float sum_error_kalman = 0;
    float sum_error_measure = 0;
    
    for (int i=0;i<30;i++) {
        //do a prediction
        x_temp_est = x_est_last;
        P_temp = P_last + Q;
        //calculate the Kalman gain
        K = P_temp * (1.0/(P_temp + R));
        //measure
        z_measured = z_real + frand()*0.09; //the real measurement plus noise
        //correct
        x_est = x_temp_est + K * (z_measured - x_temp_est); 
        P = (1- K) * P_temp;
        //we have our new system
        
        printf("Ideal    position: %6.3f \n",z_real);
        printf("Mesaured position: %6.3f [diff:%.3f]\n",z_measured,fabs(z_real-z_measured));
        printf("Kalman   position: %6.3f [diff:%.3f]\n",x_est,fabs(z_real - x_est));
        
        sum_error_kalman += fabs(z_real - x_est);
        sum_error_measure += fabs(z_real-z_measured);
        
        //update our last's
        P_last = P;
        x_est_last = x_est;
    }
    
    printf("Total error if using raw measured:  %f\n",sum_error_measure);
    printf("Total error if using kalman filter: %f\n",sum_error_kalman);
    printf("Reduction in error: %d%% \n",100-(int)((sum_error_kalman/sum_error_measure)*100));
    
    return 0;
}

Мне понятна в принципе работа ФК

все это калман нам отфильтровывает и выдает уже нормальное значение