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1、卡尔曼滤波简介算法实现代码卡尔曼滤波简介算法实现代码Posted on 2007-01-13 17:00 Jason.Jiang 阅读 (10822) 评论 (6) 编辑 收藏网摘 所属分类 : 信号处理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 等人的研究工作，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
2、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(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：预估计 X(k)= F(k,k-1)X(k -1) 计算预估
3、计协方差矩阵C(k)=F(k,k-1)C(k)F(k,k-1)+T(k,k-1)Q(k)T(k,k-1) Q(k) = U(k)U(k) 计算卡尔曼增益矩阵K(k) = C(k)H(k) H(k) C(k) H(k)+R(k)(-1) R(k) = N(k)N(k) 更新估计X(k)=X(k)+K(k)Y(k)- H(k)X(k) 计算更新后估计协防差矩阵C(k) = I-K(k) H(k) C(k) I-K(k) H(k)+K(k)R(k)K(k) 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：i nclude “stdlib.h“ i ncl
4、ude “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; int i,j,kk,ii,l,jj,js; double *e,*a,*b; e=malloc(m*m*sizeof(double); l=m; if (l 1000 #pragma once #endif / _MSC_VER 1000 i nclude i nclude “cv.h“ class kalman public: void init_kalman(int x,int xv,int y,int yv); CvKalman
5、* 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_8B74_8BF57636F2C0_INCLUDED_) =kalman.cpp= i nclud
6、e “kalman.h“ i nclude /* 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,int xv,int y,int yv) cvkalman = cvCreateKalman( 4, 4, 0 ); state = cvCre
7、ateMat( 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 = 1, T, 0, 0, 0, 1, 0, 0, 0, 0, 1, T, 0, 0, 0, 1 ; const float H = 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ; const float
8、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 = pow(T,3)/3, pow(T,2)/2, 0, 0, pow(T,2)/2, T, 0, 0, 0, 0, pow(T,3)/3, pow(T,2)/2, 0, 0, pow(T,2)/2, T ; const float R = 1, 0, 0, 0, 0,
9、 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 ; cvRandInit( cvZero( measurement ); cvRandSetRange( rng.disttype = CV_RAND_NORMAL; cvRand( memcpy( cvkalman-transition_matrix-data.fl, A, sizeof(A); memcpy( cvkalman-measurement_matrix-data.fl, H, sizeof(H); memcpy( cvkalman-process_noise_cov-data.fl, Q, sizeof(Q);
10、memcpy( cvkalman-error_cov_post-data.fl, P, sizeof(P); memcpy( cvkalman-measurement_noise_cov-data.fl, R, sizeof(R); /cvSetIdentity( cvkalman-process_noise_cov, cvRealScalar(1e-5) ); /cvSetIdentity( cvkalman-error_cov_post, cvRealScalar(1); /cvSetIdentity( cvkalman-measurement_noise_cov, cvRealScala
11、r(1e-1) ); /* choose initial state */ 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; cvRandSetRange( cvRand( CvPoint2D32f kalman:get_predict(fl
12、oat x, float y) /* update state with current position */ state-data.fl0=x; state-data.fl2=y; /* predict point position */ /* xk=Ak+Bk Pk=Ak-1*AT + Q */ cvRandSetRange( cvRand( /* xk=A?xk-1+B?uk+wk */ cvMatMulAdd( cvkalman-transition_matrix, state, process_noise, cvkalman-state_post ); /* zk=H?xk+vk
13、*/ cvMatMulAdd( cvkalman-measurement_matrix, cvkalman-state_post, measurement, measurement ); /* adjust Kalman filter state */ /* Kk=PkT 鈥?HkT+R)-1 xk=xk+Kk鈥?zk-Hk) Pk=(I-Kk)k */ cvKalmanCorrect( cvkalman, measurement ); float measured_value_x = measurement-data.fl0; float measured_value_y = measure
14、ment-data.fl2; const CvMat* prediction = cvKalmanPredict( cvkalman, 0 ); float predict_value_x = prediction-data.fl0; float 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;
