当前位置:网站首页>[filter tracking] comparison between EKF and UKF based on MATLAB extended Kalman filter [including Matlab source code 1933]
[filter tracking] comparison between EKF and UKF based on MATLAB extended Kalman filter [including Matlab source code 1933]
2022-07-07 11:46:00 【Poseidon light】
One 、 How to get the code
How to get the code 1:
The complete code has been uploaded to my resources :【 Filter tracking 】 be based on matlab Extended Kalman filter EKF And unscented Kalman filter UKF Compare 【 contain Matlab Source code 1933 period 】
How to get the code 2:
By subscribing to Ziji Shenguang blog Paid column , With proof of payment , Private Blogger , This code is available .
remarks : Subscribe to Ziji Shenguang blog Paid column , Free access to 1 Copy code ( The period of validity From the Subscription Date , Valid for three days );
Two 、EKF Introduction to the algorithm
stay SLAM Problem solving method ,EKF Algorithm is a commonly used classical algorithm . The self localization process of robot is a nonlinear process ,EKF To solve the problem Kalman Filters cannot be applied to nonlinear systems , The main process of the filtering algorithm is prediction and update . In the process of prediction and update ,EKF The algorithm linearizes the original system equation and observation equation and obtains a high estimation result . If the nonlinearity in the system is weak ,EKF It can also give good estimation results .
When predicting , The system model used is as follows :
In style ,z(k+1) It means No k+1 The observation obtained in step ,W (k+1) Express Kalman gain , It also includes the weight of forward estimation in practice .
Realization EKF-SLAM The following aspects are required : System dynamic equation and corresponding parameters , Type of sensor used and observation equation , According to these, we can get EKF The corresponding form of . In two-dimensional plane EKF-SLAM Need to know that robots are X、Y The value of the direction , We also need to know the orientation of the robot's head in the two-dimensional plane and X The angle in the positive direction of the axis .
3、 ... and 、 Partial source code
%% Main function function :EKF And UKF error analysis , Performance comparison
% Figure 1 : True state and EKF Filter state comparison
% Figure 2 : True state and UKF Filter state comparison
% Figure 3 :EKF Floating range of filtering error
% Figure 4 :UKF Floating range of filtering error
N=150; % Simulation time
L=1;
Q=6; % Noise variance
R=1;
W=sqrtm(Q)*randn(L,N);
V=sqrt(R)*randn(1,N);
X=zeros(L,N);
X(:,1)=[0.1]';
Z=zeros(1,N);
Z(1)=X(:,1)^2/20+V(1);
Xukf=zeros(L,N);
Xukf(:,1)=X(:,1)+sqrtm(Q)*randn(L,1);
Pukf=eye(L);
Xekf=zeros(L,N);
Xekf(:,1)=X(:,1)+sqrtm(Q)*randn(L,1);
Pekf=eye(L);
% Algorithm simulation verification
for k=2:N
X(:,k)=0.5*X(:,k-1)+2.5*X(:,k-1)/(1+X(:,k-1)^2)+8*cos(1.2*k)+W(k);
Z(k)=X(:,k)^2/20+V(k);
[Xekf(:,k),Pekf]=EKF(Xekf(:,k-1),Pekf,Z(k),Q,R,k);
[Xukf(:,k),Pukf]=UKF(Xukf(:,k-1),Pukf,Z(k),Q,R,k);
end
Four 、 Running results
5、 ... and 、matlab Edition and references
1 matlab edition
2014a
2 reference
[1] Shen Zaiyang . Master MATLAB signal processing [M]. tsinghua university press ,2015.
[2] Gao Baojian , Peng Jinye , Wang Lin , Pan Jianshou . Signals and systems —— Use MATLAB Analysis and Implementation [M]. tsinghua university press ,2020.
[3] Wang Wenguang , Wei Shaoming , Ren Xin . Signal processing and system analysis MATLAB Realization [M]. Electronic industry press ,2018.
[4] Lin Zhidong . Based on extended Kalman Filter Algorithm SLAM Problem analysis [J]. City Building . 2020,17(11)
3 remarks
This part of the introduction is taken from the Internet , For reference only , If infringement , Contact deletion
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