ukf算法matlab

UKF（无迹卡尔曼滤波）算法是一种用于非线性系统的滤波器。它通过使用一组带有权重的Sigma点来近似系统的概率分布，并通过传递这些Sigma点来计算系统的均值和协方差。UKF算法的Matlab实现包括三个函数：ukf、ut和sigmas。

ukf函数是UKF算法的主函数，接受系统的状态转移函数fstate、状态估计值x、状态估计误差协方差矩阵P、测量函数hmeas、测量值z、系统噪声协方差矩阵Q和测量噪声协方差矩阵R作为输入。该函数通过计算Sigma点、进行状态转移和测量更新来估计系统的状态和协方差。

ut函数是无迹变换函数，用于计算非线性函数的均值和协方差。它接受非线性函数f、Sigma点集X、均值权重向量Wm、方差权重向量Wc和测量数量n作为输入。该函数通过对Sigma点进行非线性传递和计算均值和协方差来近似非线性函数的输出。

sigmas函数用于选择Sigma点集。它接受参考点x、协方差矩阵P和系数c作为输入。该函数通过使用Cholesky分解计算协方差矩阵的平方根，生成一组与参考点相关的Sigma点。

以上是UKF算法的Matlab实现的简要说明。您可以使用这些函数来实现UKF算法并进行非线性系统的状态估计。

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UKF算法matlab

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6维空间下的ukf算法matlab

以下是一个简单的6维空间下的UKF算法的MATLAB代码示例：

function [x,P] = ukf(fstate,x,P,hmeas,z,Q,R)
% UKF - Unscented Kalman Filter for nonlinear dynamic systems
%
% [x, P] = ukf(f,x,P,h,z,Q,R) returns state estimate, x and state covariance, P 
% for nonlinear dynamic system (for simplicity, noises are assumed as additive):
%           x_k+1 = f(x_k) + w_k
%           y_k   = h(x_k) + v_k
% where w ~ N(0,Q) meaning w is gaussian noise with covariance Q
%       v ~ N(0,R) meaning v is gaussian noise with covariance R
%
% INPUTS:   f       - function handle for f(x)
%           x       - "a priori" state estimate
%           P       - "a priori" estimated state covariance
%           h       - function handle for h(x)
%           z       - current measurement
%           Q       - process noise covariance 
%           R       - measurement noise covariance
%
% OUTPUTS:  x       - "a posteriori" state estimate
%           P       - "a posteriori" state covariance
%
% Example:
%{
n = 3;      %number of state
q = 0.1;    %process noise variance
r = 0.1;    %measurement noise variance
Q = q^2*eye(n); %covariance matrix
R = r^2;        %covariance matrix
x = [0 0 0]';   %initial state
P = eye(n);     %initial state covariance
f = @(x) [x(1)+0.1*x(2);x(2)+0.1*x(3);x(3)+0.1*x(1)+(randn(1)*0.1)];
h = @(x) x(1)^2+x(2)^2+x(3)^2+(randn(1)*0.1);        %measurement function
%sample time and total time
dt = 0.1;
t = 0:dt:10;
%initializing vectors
xV = zeros(n,length(t)); xV(:,1) = x;
zV = zeros(1,length(t));
%main loop
for k = 2:length(t)
    %prediction
    [x1, P] = ukf(f,x,P,h,z(k),Q,R);
    %update
    zV(k) = h(x1) + sqrt(R)*randn;
    [x, P] = kf_update(x1,P,zV(k),h,Q,R);
    xV(:,k) = x;
end
%plotting
figure;
subplot(2,2,1);plot(t,xV(1,:),'r',t,sqrt(zV),'b');
xlabel('time');ylabel('x1');legend('estimate','measurement');
subplot(2,2,2);plot(t,xV(2,:),'r');xlabel('time');ylabel('x2');
subplot(2,2,3);plot(t,xV(3,:),'r');xlabel('time');ylabel('x3');
subplot(2,2,4);plot3(xV(1,:),xV(2,:),xV(3,:),'r');xlabel('x1');ylabel('x2');zlabel('x3');
%}
%
% By Yi Cao at Cranfield University, 01/01/2008
%

L=numel(x);                                 %number of states
m=numel(z);                                 %number of measurements
alpha=1e-3;                                 %default, tunable
ki=0;                                       %default, tunable
beta=2;                                     %default, tunable
lambda=alpha^2*(L+ki)-L;                    %scaling factor
c=L+lambda;                                 %scaling factor
Wm=[lambda/c 0.5/c+zeros(1,2*L)];           %weights for means
Wc=Wm;
Wc(1)=Wc(1)+(1-alpha^2+beta);               %weights for covariance
c=sqrt(c);

X=sigmas(x,P,c);                            %sigma points around x
[x1,X1,P1,X2]=ut(f,X,Wm,Wc,L,Q);            %unscented transformation of process
Z=sigmas(x1,P1,c);                          %sigma points around x1
[z1,Z1,P2,Z2]=ut(h,Z,Wm,Wc,m,R);            %unscented transformation of measurments
P12=X2*diag(Wc)*Z2';                        %transformed cross-covariance
K=P12*inv(P2);
x=x1+K*(z-z1);                              %state update
P=P1-K*P2*K';                                %covariance update

function [y,Y,P,Y1]=ut(f,X,Wm,Wc,n,R)
%Unscented Transformation
%Input:
%       f: nonlinear map
%       X: sigma points
%      Wm: weights for mean
%      Wc: weights for covraiance
%       n: numer of outputs of f
%       R: additive covariance
%Output:
%       y: transformed mean
%       Y: transformed smapling points
%       P: transformed covariance
%      Y1: transformed deviations
%
L=size(X,2);
y=zeros(n,1);
Y=zeros(n,L);
for k=1:L                   
    Y(:,k)=f(X(:,k));       
    y=y+Wm(k)*Y(:,k);       
end
Y1=Y-y(:,ones(1,L));
P=Y1*diag(Wc)*Y1'+R;         


function X=sigmas(x,P,c)
%Sigma points around reference point
%A=[ref+chol(P) ref-chol(P)];
%A=[ref+sqrtm(P) ref-sqrtm(P)];
L=numel(x);
X(:,1)=x;
X(:,2:L+1)=x(:,ones(1,L))+c*[zeros(L,1) eye(L) -eye(L)];
X(:,L+2:2*L+1)=x(:,ones(1,L))-c*[zeros(L,1) eye(L) -eye(L)];

请注意，这是一个简单的示例代码，可能需要根据你的具体问题进行适当修改。