%step 1: prediction %Phi dt = timediff(sol.time,time_x); %计算两个历元的时间差 F=zeros(6,6); F(1:3,4:6)=eye(3)dt; Phi = [eye(3) eye(3)dt; zeros(3,3) eye(3)]; %Q Q=zeros(6,6); Q(1:3,1:3)=eye(3)0.25dt^4accPSD(1,1)+eye(3)0.5dt^3accPSD(1,1); %水平方向 Q(1:3,4:6)=eye(3)0.5dt^2accPSD(1,1); %水平方向 Q(4:6,1:3)=eye(3)0.5dt^2accPSD(1,1); %水平方向 Q(4:6,4:6)=eye(3)dt^2accPSD(3,3); %垂直方向 %预测状态和协方差 x = Phi * x; xP = Phi * xP * Phi' + Q; %step 2: measurement update if sol.posP(1)>0 %如果有位置信息 H = [eye(3) zeros(3,3)]; %测量矩阵 R=zeros(3,3); R(1:2,1:2)=eye(2)sol.posP(1)^2; %水平误差 R(3,3)=sol.posP(7)^2; %垂直误差 %计算卡尔曼增益 K = xP * H' * inv(H * xP * H' + R); %测量更新状态和协方差 z = sol.pos'; dz = z - H * x; dz(3) = rem(dz(3)+pi,2pi)-pi; %处理航向角差异 x = x + K * dz; xP = (eye(6) - K * H) * xP; end %更新历元时间 time_x = sol.time;解释这段代码详细一些
时间: 2024-04-26 18:26:26 浏览: 19
这段代码是一个卡尔曼滤波器的实现,主要用于估计移动对象的状态和位置。卡尔曼滤波器是一种递归算法,可以利用传感器测量数据和先前的状态估计来更新对象的当前状态估计。以下是这段代码的详细解释:
1. 计算历元时间差:首先,代码计算两个历元(即两次测量之间的时间间隔)的时间差(dt)。
2. 预测状态和协方差:然后,根据卡尔曼滤波器的预测步骤,代码使用状态转移矩阵 Phi 和过程噪声协方差矩阵 Q 来预测下一个历元的状态估计(x)和状态协方差矩阵(xP)。
3. 测量更新:如果有位置信息可用,代码将执行测量更新步骤。在该步骤中,代码将使用测量矩阵 H 和测量噪声协方差矩阵 R 来计算卡尔曼增益 K。然后,代码将使用测量向量 z 和状态估计向量 x,以及增益矩阵 K,来更新状态估计(x)和状态协方差矩阵(xP)。
4. 处理航向角差异:在测量更新步骤中,代码还包括了一个航向角差异的处理步骤。该步骤通过将差异处理为 -π 到 π 之间的值来确保航向角的连续性。
5. 更新历元时间:最后,代码将更新历元时间(time_x),以便在下一个历元中使用正确的时间差。
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function sol_kf(filename) global glc; %read solution file solution=readGINavsol(filename); n=size(solution,1); %initialize 对状态进行初始化 x = zeros(6,1);%state vector 状态向量 xP = zeros(6,6);%covariance of x 协方差 %过程噪声密度 sqrt_accPSD_hor=15;%m/s^2/sqrt(Hz) sqrt_accPSD_up=0.1;%m/s^2/sqrt(Hz) accPSD_enu =zeros(3,3); accPSD_enu(1,1)=(sqrt_accPSD_hor)^2; accPSD_enu(2,2)=(sqrt_accPSD_hor)^2; accPSD_enu(3,3)=sqrt_accPSD_up^2; bInitialized=0; time_x = solution(1).time; %all epochs for i=1:n %load data of new epoch sol = solution(i); %转换矩阵 Cne=xyz2enu(sol.pos); %转换至地球坐标系下 accPSD=Cne'*accPSD_enu*Cne; vel=sol.vel'; pos=sol.pos'; %临时变量进行存储 posP=[sol.posP(1) sol.posP(4) sol.posP(6); sol.posP(4) sol.posP(2) sol.posP(5); sol.posP(6) sol.posP(5) sol.posP(3)]; velP=[sol.velP(1) sol.velP(4) sol.velP(6); sol.velP(4) sol.velP(2) sol.velP(5); sol.velP(6) sol.velP(5) sol.velP(3)]; dt = timediff(sol.time,time_x); %如果时间差很大,说明时间中断很久,则需要重新进行初始化 if dt>15 bInitialized=0; end %initialize if ~bInitialized x = [pos; vel]; xP=zeros(6,6); xP(1:3,1:3)= eye(3)*1e16; xP(4:6,4:6)= eye(3)*100; if sol.posP(1)>0 xP(1:3,1:3)= posP; end if sol.velP(1)>0 xP(4:6,4:6)= velP; end time_x = sol.time; bInitialized=1; continue; end %%%%%%%%%%%%%%%to do%%%%%%%%%%%%%%%%%%%%%%%%% %step 1: prediction %Phi %Q 补全该代码
%step 1: prediction
%Phi
dt = timediff(sol.time,time_x); %计算两个历元的时间差
F=zeros(6,6);
F(1:3,4:6)=eye(3)*dt;
Phi = [eye(3) eye(3)*dt; zeros(3,3) eye(3)];
%Q
Q=zeros(6,6);
Q(1:3,1:3)=eye(3)*0.25*dt^4*accPSD(1,1)+eye(3)*0.5*dt^3*accPSD(1,1); %水平方向
Q(1:3,4:6)=eye(3)*0.5*dt^2*accPSD(1,1); %水平方向
Q(4:6,1:3)=eye(3)*0.5*dt^2*accPSD(1,1); %水平方向
Q(4:6,4:6)=eye(3)*dt^2*accPSD(3,3); %垂直方向
%预测状态和协方差
x = Phi * x;
xP = Phi * xP * Phi' + Q;
%step 2: measurement update
if sol.posP(1)>0 %如果有位置信息
H = [eye(3) zeros(3,3)]; %测量矩阵
R=zeros(3,3);
R(1:2,1:2)=eye(2)*sol.posP(1)^2; %水平误差
R(3,3)=sol.posP(7)^2; %垂直误差
%计算卡尔曼增益
K = xP * H' * inv(H * xP * H' + R);
%测量更新状态和协方差
z = sol.pos';
dz = z - H * x;
dz(3) = rem(dz(3)+pi,2*pi)-pi; %处理航向角差异
x = x + K * dz;
xP = (eye(6) - K * H) * xP;
end
%更新历元时间
time_x = sol.time;
function sol_kf(filename)%pos文件 global glc; %read solution file solution=readGINavsol(filename); n=size(solution,1); %initialize 初始化 x = zeros(6,1);%state vector xP = zeros(6,6);%covariance of x协方差阵 sqrt_accPSD_hor=15;%m/s^2/sqrt(Hz) sqrt_accPSD_up=0.1;%m/s^2/sqrt(Hz) %三个方向 accPSD_enu =zeros(3,3); accPSD_enu(1,1)=(sqrt_accPSD_hor)^2; accPSD_enu(2,2)=(sqrt_accPSD_hor)^2; accPSD_enu(3,3)=sqrt_accPSD_up^2; bInitialized=0; time_x = solution(1).time; %all epochs for m=1:n %load data of new epoch sol = solution(m); Cne=xyz2enu(sol.pos);%转换到地球坐标系 accPSD=Cne'*accPSD_enu*Cne; vel=sol.vel'; pos=sol.pos'; posP=[sol.posP(1) sol.posP(4) sol.posP(6); sol.posP(4) sol.posP(2) sol.posP(5); sol.posP(6) sol.posP(5) sol.posP(3)]; velP=[sol.velP(1) sol.velP(4) sol.velP(6); sol.velP(4) sol.velP(2) sol.velP(5); sol.velP(6) sol.velP(5) sol.velP(3)]; dt = timediff(sol.time,time_x); if dt>15 bInitialized=0; end %initialize if ~bInitialized x = [pos; vel]; xP=zeros(6,6); xP(1:3,1:3)= eye(3)*1e16; xP(4:6,4:6)= eye(3)*100; if sol.posP(1)>0 xP(1:3,1:3)= posP; end if sol.velP(1)>0 xP(4:6,4:6)= velP; end time_x = sol.time; bInitialized=1; continue; end %%%%%%%%%%%%%%%to do%%%%%%%%%%%%%%%%%%%%%%%%% %step 1: prediction %Q计算系统噪声协方差阵 %step 2: update %R 观测噪声协方差阵 这是使用MATLAB实现卡尔曼滤波的代码,请帮我完成它
好的,我会帮您完成这段代码。
首先,我们需要计算系统噪声协方差阵 Q,可以使用以下代码:
```
dt = timediff(sol.time,time_x);
Q = zeros(6,6);
Q(1:3,1:3) = eye(3)*sqrt_accPSD_hor^2*dt^3/3;
Q(1:3,4:6) = eye(3)*sqrt_accPSD_hor^2*dt^2/2;
Q(4:6,1:3) = eye(3)*sqrt_accPSD_hor^2*dt^2/2;
Q(4:6,4:6) = eye(3)*sqrt_accPSD_hor^2*dt + eye(3)*sqrt_accPSD_up^2*dt^3/3;
```
然后,我们可以进行卡尔曼滤波的预测步骤,使用以下代码:
```
A = eye(6);
A(1:3,4:6) = eye(3)*dt;
x = A*x;
xP = A*xP*A' + Q;
```
最后,我们还需要进行卡尔曼滤波的更新步骤。R 观测噪声协方差阵需要根据具体情况进行设置,这里我们假设观测噪声协方差阵为 1 米。
```
H = eye(6);
R = eye(6)*1;
K = xP*H'/(H*xP*H' + R);
x = x + K*(pos' - H*x);
xP = (eye(6) - K*H)*xP;
```
最终,完整的代码如下:
```
function sol_kf(filename)
%pos文件
global glc;
%read solution file
solution=readGINavsol(filename);
n=size(solution,1);
%initialize 初始化
x = zeros(6,1);%state vector
xP = zeros(6,6);%covariance of x协方差阵
sqrt_accPSD_hor=15;%m/s^2/sqrt(Hz)
sqrt_accPSD_up=0.1;%m/s^2/sqrt(Hz)
%三个方向
accPSD_enu =zeros(3,3);
accPSD_enu(1,1)=(sqrt_accPSD_hor)^2;
accPSD_enu(2,2)=(sqrt_accPSD_hor)^2;
accPSD_enu(3,3)=sqrt_accPSD_up^2;
bInitialized=0;
time_x = solution(1).time;
% Kalman filter loop
for m=1:n
%load data of new epoch
sol = solution(m);
Cne=xyz2enu(sol.pos);%转换到地球坐标系
accPSD=Cne'*accPSD_enu*Cne;
vel=sol.vel';
pos=sol.pos';
posP=[sol.posP(1) sol.posP(4) sol.posP(6);
sol.posP(4) sol.posP(2) sol.posP(5);
sol.posP(6) sol.posP(5) sol.posP(3)];
velP=[sol.velP(1) sol.velP(4) sol.velP(6);
sol.velP(4) sol.velP(2) sol.velP(5);
sol.velP(6) sol.velP(5) sol.velP(3)];
dt = timediff(sol.time,time_x);
if dt>15
bInitialized=0;
end
%initialize
if ~bInitialized
x = [pos; vel];
xP=zeros(6,6);
xP(1:3,1:3)= eye(3)*1e16;
xP(4:6,4:6)= eye(3)*100;
if sol.posP(1)>0
xP(1:3,1:3)= posP;
end
if sol.velP(1)>0
xP(4:6,4:6)= velP;
end
time_x = sol.time;
bInitialized=1;
continue;
end
%step 1: prediction
%Q计算系统噪声协方差阵
Q = zeros(6,6);
Q(1:3,1:3) = eye(3)*sqrt_accPSD_hor^2*dt^3/3;
Q(1:3,4:6) = eye(3)*sqrt_accPSD_hor^2*dt^2/2;
Q(4:6,1:3) = eye(3)*sqrt_accPSD_hor^2*dt^2/2;
Q(4:6,4:6) = eye(3)*sqrt_accPSD_hor^2*dt + eye(3)*sqrt_accPSD_up^2*dt^3/3;
A = eye(6);
A(1:3,4:6) = eye(3)*dt;
x = A*x;
xP = A*xP*A' + Q;
%step 2: update
%R 观测噪声协方差阵
H = eye(6);
R = eye(6)*1;
K = xP*H'/(H*xP*H' + R);
x = x + K*(pos' - H*x);
xP = (eye(6) - K*H)*xP;
end
```
希望这个代码可以帮到您!