卡尔曼滤波程序

1、最佳线性滤波理论起源于40年代美国科学家 Wiener和前苏联科学家Ko ji m o r等队的研究工作，后人统称为维纳滤波理论。从理论上说，维纳滤波 的最大缺点是必须用到无限过去的数据，不适用于实时处理。为了克服这一缺点， 60年代Kalman把状态空间模型引入滤波理论，并导出了一套递推估计算法，后 人称之为卡尔曼滤波理论。卡尔曼滤波是以最小均方误差为估计的最佳准则，来寻求一套递推估计的算法，其基本思想是：采用信号与噪声的状态空间模型，利 用前一时刻地估计值和现时刻的观测值来更新对状态变量的估计，求出现时刻的估计值。它适合于实时处理和计算机运算。现设线性时变系统的离散状态防城和观测方程为：X

2、(k) = F(k,k-1) X(k-1)+T(k,k-1) U(k-1)Y(k) = H(k) X(k)+N(k)其中X(k)和Y(k)分别是k时刻的状态矢量和观测矢量F(k,k-1)为状态转移矩阵U(k)为k时刻动态噪声T(k,k-1)为系统控制矩阵H(k)为k时刻观测矩阵N(k)为k时刻观测噪声则卡尔曼滤波的算法流程为：1.预估计 X(k)A= F(k,k-1) - X(k-1)2. 计算预估计协方差矩阵C(k)A=F(k,k-1) xC(k)xF(k,k-1)'+T(k,k-1) x Q(k) xT(k,k-1)'Q(k) = U(k)义 U(k)'3. 计算卡

3、尔曼增益矩阵K(k) = C(k)A x H(k)' x H(k) 乂 C(k)A 乂 H(k)'+R(k)A(-1)R(k) = N(k) x N(k)'4. 更新估计X(k)=X(k)A+K(k) xY(k)-H(k) x X(k)A5. 计算更新后估计协防差矩阵C(k)- = I-K(k) x H(k) x C(k)A 乂 I-K(k) 乂 H(k)'+K(k) 乂 R(k) 乂 K(k)'6. X(k+1) = X(k)-C(k+1) = C(k)-重复以上步骤其c语言实现代码如下:#include "stdlib.h"#in

4、clude "rinv.c" _ int lman(n,m,k,f,q,r,h,y,x,p,g)int n,m,k;double f,q,r,h,y,x,p,g;UU int i,j,kk,ii,l,jj,js;I _ TI T TIdouble *e,*a,*b;e=malloc(m*m* sizeof(double);l=m;if (l<n) l=n;a=malloc(l*l* sizeof(double);b=malloc(l*l* sizeof(double);for (i=0; i<=n-1; i+)for (j=0; j<=n-1; j+)韩

5、ii=i*l+j; aii=0.0;Ifor (kk=0; kk<=n-1; kk+)I aii=aii+pi*n+kk*fj*n+kk;for (i=0; i<=n-1; i+)I for (j=0; j<=n-1; j+) ii=i*n+j; pii=qii;for (kk=0; kk<=n-1; kk+) pii=pii+fi*n+kk*akk*l+j;)for (ii=2; ii<=k; ii+) for (i=0; i<=n-1; i+)for (j=0; j<=m-1; j+) jj=i*l+j; ajj=0.0;for (kk=0; kk

6、<=n-1; kk+)部.r.下T 韩.ajj=ajj+pi*n+kk*hj*n+kk;)for (i=0; i<=m-1; i+)for (j=0; j<=m-1; j+) jj=i*m+j; ejj=rjj;for (kk=0; kk<=n-1; kk+) ejj=ejj+hi*n+kk*akk*l+j;)js=rinv(e,m);if (js=0)free(e); free(a); free(b); return (js); for (i=0; i<=n-1; i+)for (j=0; j<=m-1; j+) jj=i*m+j; gjj=0.0;for

7、 (kk=0; kk<=m-1; kk+) gjj=gjj+ai*l+kk*ej*m+kk;for (i=0; i<=n-1; i+) jj=(ii-1)*n+i; xjj=0.0;for (j=0; j<=n-1; j+)xjj=xjj+fi*n+j*x(ii-2)*n+j;for (i=0; i<=m-1; i+) jj=i*l; bjj=y(ii-1)*m+i;for (j=0; j<=n-1; j+)bjj=bjj-hi*n+j*x(ii-1)*n+j;for (i=0; i<=n-1; i+) jj=(ii-1)*n+i;for (j=0; j&l

8、t;=m-1; j+) xjj=xjj+gi*m+j*bj*l;if (ii<k) for (i=0; i<=n-1; i+)for (j=0; j<=n-1; j+) jj=i*l+j; ajj=0.0;for (kk=0; kk<=m-1; kk+) ajj=ajj-gi*m+kk*hkk*n+j;if (i=j) ajj=1.0+ajj;for (i=0; i<=n-1; i+)for (j=0; j<=n-1; j+) jj=i*l+j; bjj=0.0;for (kk=0; kk<=n-1; kk+)bjj=bjj+ai*l+kk*pkk*n

9、+j;)for (i=0; i<=n-1; i+)for (j=0; j<=n-1; j+) jj=i*l+j; ajj=0.0;for (kk=0; kk<=n-1; kk+)for (i=0; i<=n-1; i+) for (j=0; j<=n-1; j+) 三Q jj=i*n+j; pjj=qjj;for (kk=0; kk<=n-1; kk+) pjj=pjj+fi*n+kkl*aj*l+kkl;free(e); free(a); free(b);return (js);C+实现代码如下:=kalman.h=/ kalman.h: interfac

10、e for the kalman class./#if !defined(AFX_KALMAN_H_ED3D740F_01D2_4616_8B74_8BF57636F2C0_IN CLUDED_)#define AFX_KALMAN_H_ED3D740F_01D2_4616_8B74_8BF57636F2C0_INCLU DED_#if _MSC_VER > 1000#pragma once#endif / _MSC_VER > 1000#include <math.h>#include "cv.h" class kalman(public :voi

11、d init_kalman( int x, int xv, int y, int yv);CvKalman* cvkalman;CvMat* state;CvMat* process_noise;CvMat* measurement;const CvMat* prediction;CvPoint2D32f get_predict(float x, float y);kalman( int x=0, int xv=0, int y=0, int yv=0);/virtual kalman();#endif / !defined(AFX_KALMAN_H_ED3D740F_01D2_4616_8B

12、74_8BF57636F2c 0_INCLUDED_)=kalman.cpp=#include "kalman.h"#include <stdio.h>/* tester de printer toutes les valeurs des vecteurs*/* tester de changer les matrices du noises */ /* replace state by cvkalman->state_post ? */CvRandState rng;const double T = 0.1; kalman:kalman( int x,

13、int xv, int y, int yv) (cvkalman = cvCreateKalman( 4, 4, 0 );state = cvCreateMat( 4, 1, CV_32FC1 );process_noise = cvCreateMat( 4, 1, CV_32FC1 );measurement = cvCreateMat( 4, 1, CV_32FC1 ); int code = -1;/* create matrix data */ const float A口 = 1, T, 0, 0, 0, 1, 0, 0, 0, 0, 1, T, 0, 0, 0, 1)；const

14、float H = 1, 0, 0, 0,0, 0, 0, 0,0, 0, 1, 0, 0, 0, 0, 0)；const float P = pow(320,2), pow(320,2)/T, 0, 0, pow(320,2)/T, pow(320,2)/pow(T,2), 0, 0, 0, 0, pow(240,2), pow(240,2)/T, 0, 0, pow(240,2)/T, pow(240,2)/pow(T,2) );const float Q口 = pow(T,3)/3, pow(T,2)/2, 0, 0, pow(T,2)/2, T, 0, 0,0, 0, pow(T,3)

15、/3, pow(T,2)/2,0, 0, pow(T,2)/2, T );const float R = 1, 0, 0, 0,0, 0, 0, 0,0, 0, 1, 0,0, 0, 0, 0 );cvRandInit( &rng, 0, 1, -1, CV_RAND_UNI );cvZero( measurement );cvRandSetRange( &rng, 0, 0.1, 0 ); rng.disttype = CV_RAND_NORMAL;cvRand( &rng, state );memcpy( cvkalman->transition_matrix

16、->data.fl, A,sizeof (A);memcpy( cvkalman->measurement_matrix->data.fl, H,sizeof (H);memcpy( cvkalman->process_noise_cov->data.fl, Q,sizeof (Q);memcpy( cvkalman->error_cov_post->data.fl, P,sizeof (P);memcpy( cvkalman->measurement_noise_cov->data.fl, R,sizeof (R);/cvSetIdent

17、ity( cvkalman->process_noise_cov, cvRealScalar(1e-5);/cvSetIdentity( cvkalman->error_cov_post, cvRealScalar(1);/cvSetIdentity( cvkalman->measurement_noise_cov, cvRealScalar(1e-1);/* choose initial state */state->data.fl0=x;state->data.fl1=xv;state->data.fl2=y;state->data.fl3=yv;

18、cvkalman->state_post->data.fl0=x;cvkalman->state_post->data.fl1=xv;cvkalman->state_post->data.fl2=y;cvkalman->state_post->data.fl3=yv;cvRandSetRange( &rng, 0, sqrt(cvkalman->process_noise_cov->data.fl0), 0 );cvRand( &rng, process_noise );CvPoint2D32f kalman:get_

19、predict(float x, float y)/* update state with current position */state->data.fl0=x;state->data.fl2=y;/* predict point position */* x'k=A 敏 k+B 敏kP'k=A 敏 k-1*AT + Q */cvRandSetRange( &rng, 0, sqrt(cvkalman->measurement_noise_cov->data.fl0), 0 );cvRand( &rng, measurement );

20、/* xk=A?xk-1+B?uk+wk */cvMatMulAdd( cvkalman->transition_matrix, state, process_noise, cvkalman->state_post );/* zk=H?xk+vk */cvMatMulAdd( cvkalman->measurement_matrix, cvkalman->state_post, meas urement, measurement );/* adjust Kalman filter state */* Kk=P'k 敏 T 敏？H 敏'k 敏 T+R)-1

21、xk=x'k+Kk 敏？zk-H 敏 'k)Pk=(I-Kk敦阳'k */cvKalmanCorrect( cvkalman, measurement );float measured_value_x = measurement->data.fl0;float measured_value_y = measurement->data.fl2;const CvMat* prediction = cvKalmanPredict( cvkalman, 0 );float predict_value_x = prediction->data.fl0;float

22、 predict_value_y = prediction->data.fl2;return (cvPoint2D32f(predict_value_x,predict_value_y);void kalman:init_kalman( int x, int xv, int y, int yv)state->data.fl0=x;state->data.fl1=xv;state->data.fl2=y;state->data.fl3=yv;cvkalman->state_post->data.fl0=x;cvkalman->state_post->data.fl1=xv;cvkalman->state_post->data.fl2=y;cvkalman->state_post->data.fl3=yv;其中专业理论知识内容包括：保安理论知识、消防业务知识1 职业道德、法律常识、保安礼仪、救护知识。作技能训练内容包括：岗位操作指引、勤务技能、消防技能、军事技能。二,培训的及要求培训目的安全生产目标责任书为了进一步落实安全生产责任制，做到“责、权、禾/相结合，根据我公司2