forked from ZhanLi/UWBIns
多种卡尔曼滤波器的参考代码
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Code/Matlab/AOA-IMU/RUN_AEKF.m
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580
Code/Matlab/AOA-IMU/RUN_AEKF.m
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clear
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clc
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close all
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load('data1.mat');
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nn = size(imuPosX,1);
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%% lightHouse坐标系转换
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x = lightHousePosX * 100;
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y = -lightHousePosZ * 100;
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% 定义误差函数，即均方根误差
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errorFunction = @(params) sqrt(mean((x(1:500) * cos(params(1)) - y(1:500) * sin(params(1)) + params(2) - imuPosX(1:500)).^2 + (x(1:500) * sin(params(1)) + y(1:500) * cos(params(1)) + params(3) - imuPosY(1:500)).^2));
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% 使用 fminsearch 优化误差函数，找到使误差最小的旋转角和位移
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initialGuess = [0, 10, 10]; % 初始猜测值，[旋转角, 位移]
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optimizedParams = fminsearch(errorFunction, initialGuess);
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% 输出优化后的旋转角和位移
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rotationAngle = optimizedParams(1);
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xOffset = optimizedParams(2);
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yOffset = optimizedParams(3);
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% 旋转坐标
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xt = x * cos(rotationAngle) - y * sin(rotationAngle) + xOffset;
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yt = x * sin(rotationAngle) + y * cos(rotationAngle) + yOffset;
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%%
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tagN = 4;
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%标签坐标
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XN(:,1)=[-300;-300];
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XN(:,2)=[-300;300];
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XN(:,3)=[300;300];
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XN(:,4)=[300;-300];
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sim2=6;
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Q=diag(repmat(sim2,1,2*tagN));%协方差矩阵
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measure_AOA = zeros(4,nn);
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measure_d = zeros(4,nn);
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measure_AOA(1,:) = aoa1';
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measure_AOA(2,:) = aoa2';
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measure_AOA(3,:) = aoa3';
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measure_AOA(4,:) = aoa4';
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measure_d(1,:) = d1';
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measure_d(2,:) = d2';
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measure_d(3,:) = d3';
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measure_d(4,:) = d4';
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%% uwb解算
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x_uwb(1) = 0;
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y_uwb(1) = 0;
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theta_uwb=zeros(nn,1);
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for i=2:nn
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if measure_d(1,i) == 0
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x_uwb(i) = x_uwb(i-1);
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y_uwb(i) = y_uwb(i-1);
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continue;
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end
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[t1,theta] = WLS(XN,measure_AOA(:,i),measure_d(:,i),Q);
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x_uwb(i) = t1(1);
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y_uwb(i) = t1(2);
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theta_uwb(i) = 90-theta;
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theta_uwb(i) = mod(theta_uwb(i)+180,360)-180;
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derr_WLS(i)=norm(t1-[xt(i);yt(i)]);
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end
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thetat=zeros(nn,1);
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for i=2:nn
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detx=xt(i)-xt(i-1);
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dety=yt(i)-yt(i-1);
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thetat(i)=atan2d(detx,dety);
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end
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% Uwb.x=x_uwb;
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% Uwb.y=y_uwb;
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% Uwb.alpha=theta_uwb;
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% 角速度校准
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detW = mean(wZ(1:200));
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wZ = wZ - detW;
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x_imu(1) = 0;
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y_imu(1) = 0;
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Z=zeros(3,1);
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WW = 0.05;
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theta_imu(1) = 0;
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%
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% Imu.x=x_imu;
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% Imu.y=y_imu;
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% Imu.v=v_imu;
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% Imu.alpha=alpha_imu;
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% Imu.omega=omega_imu;
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%% KF
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R = diag([1 1 1]);
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% qq = 1;
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qq = 0.00001;
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Q1 = diag([qq qq qq qq qq]);
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P0 = diag([0 0 0 0 0]);
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H = [1 0 0 0 0;
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0 1 0 0 0;
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0 0 0 1 0];
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I = eye(5);
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JF = zeros(5,5);
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X_pre = zeros(5,nn);
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X_kf(:,1) = [imuPosX(1);imuPosY(1);vXY(1)*100;0;wZ(1)];
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for i=2:nn
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% 计算IMU和里程计的时间差值
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detImuTime = imuDataRxTime(i) - imuDataRxTime(i-1);
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detOdomTime = odomDataRxTime(i)-odomDataRxTime(i-1);
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% 获得此时Z轴角速度
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w = wZ(i);
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% 获得小车的水平速度
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v = vXY(i)*100;
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% 计算速度增量
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detV=(vXY(i)-vXY(i-1))*100;
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% 计算位置增量
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detD = v*detImuTime;
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% 计算角度增量
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detTheta = w*180/pi*detImuTime;
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% 计算角速度的变化量
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detW = w-wZ(i-1);
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% 积分计算IMU的航位角
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theta_imu(i) = theta_imu(i-1)+detTheta;
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% 航向约束
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theta_imu(i) = mod(theta_imu(i)+180,360)-180;
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% 状态更新方程
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F = [1 0 detImuTime*cosd(X_kf(4,i-1)) 0 0;
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0 1 detImuTime*sind(X_kf(4,i-1)) 0 0;
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0 0 0 0 0;
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0 0 0 0 0;
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0 0 0 0 0;];
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% 获得水平和垂直方向的位置增量
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vtx = detD*cosd(theta_imu(i));
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vty = detD*sind(theta_imu(i));
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x_imu(i) = x_imu(i-1)+vtx;
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y_imu(i) = y_imu(i-1)+vty;
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X_next = [vtx;vty;detV;detTheta;detW];
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if (x_uwb(i) == x_uwb(i-1))&&(y_uwb(i) == y_uwb(i-1))
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X_kf(:,i) = X_kf(:,i-1)+X_next;
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errKf(i) = norm(X_kf(1:2,i)-[xt(i);yt(i)]);
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theta_kf(i) = X_kf(4,i);
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continue
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end
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X_pre(:,i) = X_kf(:,i-1)+X_next;
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Z = [x_uwb(i);y_uwb(i);theta_uwb(i)];
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P = F*P0*F'+Q1;
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Kg_kf = P*H'*inv(H*P*H'+R);
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X_kf(:,i) = X_pre(:,i)+Kg_kf*(Z-H*X_pre(:,i));
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P0 = (I-Kg_kf*H)*P;
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errKf(i) = norm(X_kf(1:2,i)-[xt(i);yt(i)]);
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theta_kf(i) = X_kf(4,i);
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end
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%% EKF
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R = diag([1 1 1]);
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% qq = 1;
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qq = 0.00001;
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Q1 = diag([qq qq qq qq qq]);
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P0 = diag([0 0 0 0 0]);
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H = [1 0 0 0 0;
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0 1 0 0 0;
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0 0 0 1 0];
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KK = zeros(5,3);
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X_ekf(:,1) = [imuPosX(1);imuPosY(1);vXY(1)*100;0;wZ(1)];
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I = eye(5);
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JF = zeros(5,5);
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X_pre = zeros(5,nn);
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for i=2:nn
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detImuTime = imuDataRxTime(i) - imuDataRxTime(i-1);
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detOdomTime = odomDataRxTime(i)-odomDataRxTime(i-1);
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w = wZ(i);
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v = vXY(i)*100;
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detV=(vXY(i)-vXY(i-1))*100;
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detD = v*detImuTime;
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detTheta = w*180/pi*detImuTime;
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detW = w-wZ(i-1);
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theta_imu(i) = theta_imu(i-1)+detTheta;
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theta_imu(i) = mod(theta_imu(i)+180,360)-180;
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F = [1 0 detImuTime*cosd(X_ekf(4,i-1)) 0 0;
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0 1 detImuTime*sind(X_ekf(4,i-1)) 0 0;
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0 0 0 0 0;
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0 0 0 0 0;
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0 0 0 0 0;];
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if w<WW
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vtx = detD*cosd(theta_imu(i));
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vty = detD*sind(theta_imu(i));
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else
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vtx = v/w*(sind(theta_imu(i))-sind(theta_imu(i-1)));
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vty = v/w*(-cosd(theta_imu(i))+cosd(theta_imu(i-1)));
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end
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x_imu(i) = x_imu(i-1)+vtx;
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y_imu(i) = y_imu(i-1)+vty;
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errUwb(i) = norm([x_uwb(i);y_uwb(i)]-[xt(i);yt(i)]);
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errImu(i) = norm([x_imu(i);y_imu(i)]-[xt(i);yt(i)]);
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X_next = [vtx;vty;detV;detTheta;detW];
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if (x_uwb(i) == x_uwb(i-1))&&(y_uwb(i) == y_uwb(i-1))
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X_ekf(:,i) = X_ekf(:,i-1)+X_next;
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errEKf(i) = norm(X_ekf(1:2,i)-[xt(i);yt(i)]);
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theta_ekf(i) = X_ekf(4,i);
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continue
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end
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if w<WW
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X_pre(:,i) = X_ekf(:,i-1)+X_next;
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Z = [x_uwb(i);y_uwb(i);theta_uwb(i)];
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P = F*P0*F'+Q1;
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Kg = P*H'*inv(H*P*H'+R);
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X_ekf(:,i) = X_pre(:,i)+Kg*(Z-H*X_pre(:,i));
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P0 = (I-Kg*H)*P;
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else
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JF = [1 0 1/w*(sind(theta_imu(i))-sind(theta_imu(i-1))) v/w*(cosd(theta_imu(i))-cosd(theta_imu(i-1))) detD/w*cosd(theta_imu(i))-v/(w^2)*(sind(theta_imu(i))-sind(theta_imu(i-1)));
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0 1 1/w*(-cosd(theta_imu(i))+cosd(theta_imu(i-1))) v/w*(sind(theta_imu(i))-sind(theta_imu(i-1))) detD/w*sind(theta_imu(i))-v/(w^2)*(-cosd(theta_imu(i))+cosd(theta_imu(i-1)));
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0 0 1 0 0;
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0 0 0 1 detImuTime;
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0 0 0 0 1];
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X_pre(:,i) = X_ekf(:,i-1)+X_next;
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Z = [x_uwb(i);y_uwb(i);theta_uwb(i)];
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P = JF*P0*JF'+Q1;
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Kg = P*H'*inv(H*P*H'+R);
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X_ekf(:,i) = X_pre(:,i)+Kg*(Z-H*X_pre(:,i));
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P0 = (I-Kg*H)*P;
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end
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errEKf(i) = norm(X_ekf(1:2,i)-[xt(i);yt(i)]);
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theta_ekf(i) = X_ekf(4,i);
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end
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%% UKF
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% UKF settings
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ukf_L = 5; %numer of states
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ukf_m = 3; %numer of measurements
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ukf_kappa = 3 - ukf_L;
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ukf_alpha = 0.9;
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ukf_beta = 2;
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ukf_lambda = ukf_alpha^2*(ukf_L + ukf_kappa) - ukf_L;
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ukf_gamma = sqrt(ukf_L + ukf_lambda);
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ukf_W0_c = ukf_lambda / (ukf_L + ukf_lambda) + (1 - ukf_alpha^2 + ukf_beta);
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ukf_W0_m = ukf_lambda / (ukf_L + ukf_lambda);
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ukf_Wi_m = 1 / (2*(ukf_L + ukf_lambda));
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ukf_Wi_c = ukf_Wi_m;
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q=0.01; %std of process
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r=5; %std of measurement
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p=2;
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Qu=q*eye(ukf_L); % std matrix of process
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Ru=r*eye(ukf_m); % std of measurement
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Pu=p*eye(ukf_L);
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H = [1 0 0 0 0;
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0 1 0 0 0;
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0 0 0 1 0];
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X_ukf(:,1) = [imuPosX(1);imuPosY(1);vXY(1)*100;0;wZ(1)];
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I = eye(5);
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JF = zeros(5,5);
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X_pre = zeros(5,nn);
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for i=2:nn
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detImuTime = imuDataRxTime(i) - imuDataRxTime(i-1);
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detOdomTime = odomDataRxTime(i)-odomDataRxTime(i-1);
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w = wZ(i);
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v = vXY(i)*100;
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detV=(vXY(i)-vXY(i-1))*100;
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detD = v*detImuTime;
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detTheta = w*180/pi*detImuTime;
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detW = w-wZ(i-1);
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theta_imu(i) = theta_imu(i-1)+detTheta;
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theta_imu(i) = mod(theta_imu(i)+180,360)-180;
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% F = [1 0 detImuTime*cosd(X_ekf(4,i-1)) 0 0;
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% 0 1 detImuTime*sind(X_ekf(4,i-1)) 0 0;
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% 0 0 0 0 0;
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% 0 0 0 0 0;
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% 0 0 0 0 0;];
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if w<WW
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vtx = detD*cosd(theta_imu(i));
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vty = detD*sind(theta_imu(i));
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else
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vtx = v/w*(sind(theta_imu(i))-sind(theta_imu(i-1)));
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vty = v/w*(-cosd(theta_imu(i))+cosd(theta_imu(i-1)));
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end
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x_imu(i) = x_imu(i-1)+vtx;
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y_imu(i) = y_imu(i-1)+vty;
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errUwb(i) = norm([x_uwb(i);y_uwb(i)]-[xt(i);yt(i)]);
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errImu(i) = norm([x_imu(i);y_imu(i)]-[xt(i);yt(i)]);
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X_next = [vtx;vty;detV;detTheta;detW];
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if (x_uwb(i) == x_uwb(i-1))&&(y_uwb(i) == y_uwb(i-1))
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X_ukf(:,i) = X_ukf(:,i-1)+X_next;
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errUKf(i) = norm(X_ukf(1:2,i)-[xt(i);yt(i)]);
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theta_ukf(i) = X_ukf(4,i);
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continue
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end
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xestimate = X_ukf(:,i-1);
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Xx = repmat(xestimate, 1, length(xestimate));
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Xsigma = [xestimate, ( Xx + ukf_gamma * Pu ), ( Xx - ukf_gamma * Pu )];
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%第二步：对Sigma点集进行一步预测
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[Xsigmapre]=fun1(Xsigma,detImuTime);
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%第三步：估计预测状态
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Xpred = ukf_W0_m * Xsigmapre(:,1) + ukf_Wi_m * sum(Xsigmapre(:,2:end), 2);
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%第四步：均值和方差
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Xx = repmat(Xpred, 1, length(xestimate)*2);
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[~, R] = qr([sqrt(ukf_Wi_c) * ( Xsigmapre(:,2:end) - Xx ), Qu]', 0);
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Ppred = cholupdate(R, sqrt(ukf_W0_c) * (Xsigmapre(:,1) - Xpred), '-')';
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%第5步：根据预测值，再一次使用UT变换，得到新的sigma点集
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Xx = repmat(Xpred, 1, length(xestimate));
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Xsigmapre = [Xpred, ( Xx + ukf_gamma * Ppred ), ( Xx - ukf_gamma * Ppred )];
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%第6步：观测预测
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Zsigmapre=H*Xsigmapre;
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%第7步：计算观测预测均值和协方差
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Zpred = ukf_W0_m * Zsigmapre(:,1) + ukf_Wi_m * sum(Zsigmapre(:,2:end), 2);
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Yy = repmat(Zpred, 1, length(xestimate)*2);
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[~, Rz] = qr([sqrt(ukf_Wi_c) * (Zsigmapre(:,2:end) - Yy), Ru]', 0);
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Pzz = cholupdate(Rz, sqrt(ukf_W0_c) * (Zsigmapre(:,1) - Zpred), '-')';
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Xd = Xsigmapre - repmat(Xpred, 1, length(xestimate)*2 + 1);
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Zd = Zsigmapre - repmat(Zpred, 1, length(xestimate)*2 + 1);
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Pxz = ( ukf_W0_c* Xd(:,1) * Zd(:,1)' ) + ( ukf_Wi_c * Xd(:,2:end) * Zd(:,2:end)' );
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%第七步：计算kalman增益
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Kukf= (Pxz / Pzz') / Pzz;
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%第八步：状态和方差更新
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Z = [x_uwb(i);y_uwb(i);theta_uwb(i)];
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Xpred=Xpred+Kukf*(Z-Zpred);
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U = Kukf * Pzz;
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Rp = Ppred';
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for ii=1:size(U, 2)
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Rp = cholupdate(Rp, U(:,ii), '-');
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end
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Ppred = Rp';
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X_ukf(:,i)=Xpred;
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errUKf(i) = norm(X_ukf(1:2,i)-[xt(i);yt(i)]);
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theta_ukf(i) = X_ukf(4,i);
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end
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%%
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%%AEKF
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R = diag([1 1 1]);
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% qq = 50;
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% qq = 10;
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qq = 0.01;
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Q = diag([qq qq qq qq qq]);
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P0 = diag([0 0 0 0 0]);
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H = [1 0 0 0 0;
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0 1 0 0 0;
|
||||
0 0 0 1 0];
|
||||
X_aekf = zeros(5,nn);
|
||||
X_aekf(:,1) = [imuPosX(1);imuPosY(1);vXY(1)*100;0;wZ(1)];
|
||||
I = eye(5);
|
||||
JF = zeros(5,5);
|
||||
X_pre = zeros(5,nn);
|
||||
alfa = 0.97;
|
||||
|
||||
windowlength=5;
|
||||
x_aekf_sw=zeros(1,nn);
|
||||
y_aekf_sw=zeros(1,nn);
|
||||
for i=2:nn
|
||||
detImuTime = imuDataRxTime(i) - imuDataRxTime(i-1);
|
||||
detOdomTime = odomDataRxTime(i)-odomDataRxTime(i-1);
|
||||
w = wZ(i);
|
||||
v = vXY(i)*100;
|
||||
detV=(vXY(i)-vXY(i-1))*100;
|
||||
detD = v*detImuTime;
|
||||
detTheta = w*180/pi*detImuTime;
|
||||
detW = w-wZ(i-1);
|
||||
theta_imu(i) = theta_imu(i-1)+detTheta;
|
||||
theta_imu(i) = mod(theta_imu(i)+180,360)-180;
|
||||
F = [1 0 detImuTime*cosd(X_aekf(4,i-1)) 0 0;
|
||||
0 1 detImuTime*sind(X_aekf(4,i-1)) 0 0;
|
||||
0 0 0 0 0;
|
||||
0 0 0 0 0;
|
||||
0 0 0 0 0;];
|
||||
if w<WW
|
||||
vtx = detD*cosd(theta_imu(i));
|
||||
vty = detD*sind(theta_imu(i));
|
||||
else
|
||||
vtx = v/w*(sind(theta_imu(i))-sind(theta_imu(i-1)));
|
||||
vty = v/w*(-cosd(theta_imu(i))+cosd(theta_imu(i-1)));
|
||||
end
|
||||
x_imu(i) = x_imu(i-1)+vtx;
|
||||
y_imu(i) = y_imu(i-1)+vty;
|
||||
X_next = [vtx;vty;detV;detTheta;detW];
|
||||
if (x_uwb(i) == x_uwb(i-1))&&(y_uwb(i) == y_uwb(i-1))
|
||||
X_aekf(:,i) = X_aekf(:,i-1)+X_next;
|
||||
errAEKf(i) = norm(X_aekf(1:2,i)-[xt(i);yt(i)]);
|
||||
theta_aekf(i) = X_aekf(4,i);
|
||||
continue
|
||||
end
|
||||
if w<WW
|
||||
X_pre(:,i) = X_aekf(:,i-1)+X_next;
|
||||
Z = [x_uwb(i);y_uwb(i);theta_uwb(i)];
|
||||
P = F*P0*F'+Q;
|
||||
Kg = P*H'*inv(H*P*H'+R);
|
||||
KK(1,1) = Kg(1,1);
|
||||
KK(2,2) = Kg(2,2);
|
||||
KK(4,3) = Kg(4,3);
|
||||
X_aekf(:,i) = X_pre(:,i)+KK*(Z-H*X_pre(:,i));
|
||||
P0 = (I-Kg*H)*P;
|
||||
else
|
||||
JF = [1 0 1/w*(sind(theta_imu(i))-sind(theta_imu(i-1))) v/w*(cosd(theta_imu(i))-cosd(theta_imu(i-1))) detD/w*cosd(theta_imu(i))-v/(w^2)*(sind(theta_imu(i))-sind(theta_imu(i-1)));
|
||||
0 1 1/w*(-cosd(theta_imu(i))+cosd(theta_imu(i-1))) v/w*(sind(theta_imu(i))-sind(theta_imu(i-1))) detD/w*sind(theta_imu(i))-v/(w^2)*(-cosd(theta_imu(i))+cosd(theta_imu(i-1)));
|
||||
0 0 1 0 0;
|
||||
0 0 0 1 detImuTime;
|
||||
0 0 0 0 1];
|
||||
X_pre(:,i) = X_aekf(:,i-1)+X_next;
|
||||
dk = Z - H*X_pre(:,i);
|
||||
Z = [x_uwb(i);y_uwb(i);theta_uwb(i)];
|
||||
P = JF*P0*JF'+Q;
|
||||
Kg = P*H'*inv(H*P*H'+R);
|
||||
KK(1,1) = Kg(1,1);
|
||||
KK(2,2) = Kg(2,2);
|
||||
KK(4,3) = Kg(4,3);
|
||||
X_aekf(:,i) = X_pre(:,i)+KK*(Z-H*X_pre(:,i));
|
||||
epz = Z-H*X_aekf(:,i);
|
||||
R=alfa*R+(1-alfa)*(epz*epz'+H*P*H');
|
||||
Q=alfa*Q+(1-alfa)*Kg*dk*dk'*Kg';
|
||||
P0 = (I-Kg*H)*P;
|
||||
end
|
||||
errAEKf(i) = norm(X_aekf(1:2,i)-[xt(i);yt(i)]);
|
||||
theta_aekf(i) = X_aekf(4,i);
|
||||
% if errAEKf(i)>15
|
||||
% xxx = 1;
|
||||
% end
|
||||
end
|
||||
errAEKf_sw=zeros(1,nn);
|
||||
weightedvector=[0.3;0.25;0.2;0.15;0.1];
|
||||
for i=1:nn
|
||||
if i>windowlength-1
|
||||
x_win=X_aekf(1,i-windowlength+1:i);
|
||||
y_win=X_aekf(2,i-windowlength+1:i);
|
||||
x_aekf_sw(i)=x_win*weightedvector;
|
||||
y_aekf_sw(i)=y_win*weightedvector;
|
||||
else
|
||||
x_aekf_sw(i)=X_aekf(1,i);
|
||||
y_aekf_sw(i)=X_aekf(2,i);
|
||||
end
|
||||
errAEKf_sw(i) = norm([x_aekf_sw(i);y_aekf_sw(i)]-[xt(i);yt(i)]);
|
||||
end
|
||||
|
||||
figure;
|
||||
plot(errAEKf_sw);
|
||||
|
||||
%%
|
||||
for i=2:length(theta_uwb)-1
|
||||
if theta_uwb(i) == 0
|
||||
theta_uwb(i) = theta_uwb(i-1);
|
||||
end
|
||||
end
|
||||
figure(1)
|
||||
clf(1)
|
||||
plot(x_uwb,y_uwb,'.','color',[205/255, 133/255, 63/255],'LineWidth',0.2);hold on
|
||||
plot(x_imu, y_imu, '-','color',[0, 128/255, 0],'LineWidth',0.5);
|
||||
plot(xt, yt, '-black','LineWidth',0.5);
|
||||
legend('AUAM','IMU','True value');
|
||||
xlabel('X(cm)');
|
||||
ylabel('Y(cm)');
|
||||
grid on
|
||||
|
||||
|
||||
|
||||
% figure(1)
|
||||
% clf(1)
|
||||
% hold on
|
||||
% plot((1:nn)/100,thetat,'-black','LineWidth',1);
|
||||
% plot((1:nn)/100,theta_uwb,'-','color','#CD853F','LineWidth',1);
|
||||
% plot((1:nn)/100,theta_imu, '-','color','#008000','LineWidth',1);
|
||||
% legend('LightHouse','UWB', 'INS');
|
||||
% xlabel('time(s)');
|
||||
% ylabel('\alpha(°)');
|
||||
% grid on
|
||||
|
||||
% figure(2)
|
||||
% clf(2)
|
||||
% hold on
|
||||
% plot(theta_imu,'.');
|
||||
% plot(theta_uwb,'.');
|
||||
% legend('imu','uwb');
|
||||
% xlabel('运行时间（10ms）');
|
||||
% ylabel('偏航角（°）');
|
||||
% title('角速度校准后imu和uwb测量偏航角');
|
||||
% grid on
|
||||
%
|
||||
% figure(3)
|
||||
% clf(3)
|
||||
% hold on
|
||||
% plot(xt, yt, '.-black','LineWidth',1);
|
||||
% plot(X_ekf(1,:), X_ekf(2,:), '.-','color','#7E2F8E','LineWidth',1);
|
||||
% plot(X_aekf(1,:), X_aekf(2,:), '.-','color','#D95319','LineWidth',0.5)
|
||||
% plot(x_aekf_sw, y_aekf_sw, '.-','color','#2E8B57','LineWidth',0.5)
|
||||
% legend('True','EKF', 'AEKF', 'AEKF-SWF');
|
||||
% xlabel('x(cm)');
|
||||
% ylabel('y(cm)');
|
||||
% grid on
|
||||
%
|
||||
% figure(4)
|
||||
% clf(4)
|
||||
% hold on
|
||||
% plot(errKf,'.','color','#0072BD');
|
||||
% plot(errEKf,'.','color','#EDB120');
|
||||
% plot(errUKf,'.','color','#D95319');
|
||||
% plot(errAEKf,'.','color','#7E2F8E');
|
||||
% plot(errAEKf_sw,'.','color','#77AC30');
|
||||
% legend('KF','EKF','UKF','AEKF','AEKF-SWF');
|
||||
% xlabel('运行时间（10ms）');
|
||||
% ylabel('误差（cm）');
|
||||
% title('定位误差随时间变化图');
|
||||
|
||||
% slt = 1;
|
||||
% uwbcount = 9;
|
||||
% imucount = 15;
|
||||
% ekfcount = 12;
|
||||
% aekfcount = 5;
|
||||
% figure(5)
|
||||
% clf(5)
|
||||
% hold on
|
||||
% [fUWB,xUWB] = ksdensity(errUwb(slt:end));
|
||||
% [fIMU,xIMU] = ksdensity(errImu(slt:end));
|
||||
% [fAEKF,xAEKF] = ksdensity(errAEKf(slt:end));
|
||||
% [fUKF,xUKF] = ksdensity(errUKf(slt:end));
|
||||
% [fAEKF_sw,xAEKF_sw] = ksdensity(errAEKf_sw(slt:end));
|
||||
% [fEKF,xEKF] = ksdensity(errEKf(slt:end));
|
||||
% [fKF,xKF] = ksdensity(errKf(slt:end));
|
||||
% plot(xKF(ekfcount:end),fKF(ekfcount:end), 'color','#0072BD','LineWidth',0.5);
|
||||
% plot(xEKF(ekfcount:end),fEKF(ekfcount:end),'color','#EDB120','LineWidth',0.5);
|
||||
% plot(xUKF(ekfcount:end), fUKF(ekfcount:end),'color','#D95319','LineWidth',0.5);
|
||||
% plot(xAEKF(aekfcount:end),fAEKF(aekfcount:end),'color','#7E2F8E','LineWidth',0.5);
|
||||
% plot(xAEKF_sw(aekfcount:end),fAEKF_sw(aekfcount:end), 'color','#77AC30','LineWidth',0.5)
|
||||
% legend('KF','EKF','UKF','AEKF','AEKF-SWF');%'UWB','INS',
|
||||
% xlabel('Error(cm)');
|
||||
% ylabel('Probability(%)');
|
||||
% grid on
|
||||
%
|
||||
%
|
||||
%
|
||||
% slt = 3000;
|
||||
% uwbcount = 9;
|
||||
% imucount = 9;
|
||||
% ekfcount = 13;
|
||||
% aekfcount = 7;
|
||||
% figure(6)
|
||||
% clf(6)
|
||||
% hold on
|
||||
% [fAEKF,xAEKF] = ksdensity(errAEKf(slt:end));
|
||||
% [fUKF,xUKF] = ksdensity(errUKf(slt:end));
|
||||
% [fAEKF_sw,xAEKF_sw] = ksdensity(errAEKf_sw(slt:end));
|
||||
% [fEKF,xEKF] = ksdensity(errEKf(slt:end));
|
||||
% [fKF,xKF] = ksdensity(errKf(slt:end));
|
||||
% plot(xKF(ekfcount:end),fKF(ekfcount:end), 'color','#0072BD','LineWidth',0.5);
|
||||
% plot(xEKF(ekfcount:end),fEKF(ekfcount:end),'color','#EDB120','LineWidth',0.5);
|
||||
% plot(xUKF(ekfcount:end), fUKF(ekfcount:end),'color','#D95319','LineWidth',0.5);
|
||||
% plot(xAEKF(aekfcount:end),fAEKF(aekfcount:end),'color','#7E2F8E','LineWidth',0.5);
|
||||
% plot(xAEKF_sw(aekfcount:end),fAEKF_sw(aekfcount:end), 'color','#77AC30','LineWidth',0.5)
|
||||
% legend('KF','EKF','UKF','AEKF','AEKF-SWF');%'UWB','INS',
|
||||
% xlabel('Error(cm)');
|
||||
% ylabel('PDF');
|
||||
% grid on
|
||||
%
|
||||
% figure(7)
|
||||
% clf(7)
|
||||
% hold on
|
||||
% h1 = cdfplot(errKf(slt:end));
|
||||
% h2 = cdfplot(errEKf(slt:end));
|
||||
% h3 = cdfplot(errUKf(slt:end));
|
||||
% h4 = cdfplot(errAEKf(slt:end));
|
||||
% h5 = cdfplot(errAEKf_sw(slt:end));
|
||||
% set(h1,'color','#0072BD','LineWidth',0.5);
|
||||
% set(h2,'color','#EDB120','LineWidth',0.5);
|
||||
% set(h3,'color','#D95319','LineWidth',0.5);
|
||||
% set(h4,'color','#7E2F8E','LineWidth',0.5);
|
||||
% set(h5,'color','#77AC30','LineWidth',0.5);
|
||||
% legend('KF','EKF','UKF','AEKF','AEKF-SWF');
|
||||
% xlabel('Error(cm)');
|
||||
% ylabel('CDF');
|
||||
% grid on
|
||||
33
Code/Matlab/AOA-IMU/WLS.m
Normal file
33
Code/Matlab/AOA-IMU/WLS.m
Normal file
@ -0,0 +1,33 @@
|
||||
function [x,theta] = WLS(XN,mean_aoa,mean_d,Q)
|
||||
%PLE 此处显示有关此函数的摘要
|
||||
% 此处显示详细说明
|
||||
nn = size(XN,2);
|
||||
A = zeros(2*nn, 6);
|
||||
b = zeros(2*nn, 1);
|
||||
for j=1:nn
|
||||
XN_Tag(1,j)=mean_d(j)*sind(mean_aoa(j));
|
||||
XN_Tag(2,j)=mean_d(j)*cosd(mean_aoa(j));
|
||||
A(2*j-1,:) = [XN_Tag(1,j) 0 XN_Tag(2,j) 0 1 0];
|
||||
A(2*j,:) = [0 XN_Tag(1,j) 0 XN_Tag(2,j) 0 1];
|
||||
b(2*j-1:2*j)=[XN(1,j) XN(2,j)];
|
||||
end
|
||||
f=(A'*A)^(-1)*A'*b;
|
||||
for i=1:2
|
||||
for j=1:nn
|
||||
B(2*j-1,2*j-1) = XN(2,j)-f(6);
|
||||
B(2*j,2*j) = XN(1,j)-f(5);
|
||||
end
|
||||
W = inv(B*Q*B');
|
||||
f=(A'*W*A)\A'*W*b;
|
||||
end
|
||||
x=(f(5:6));
|
||||
theta1(1)=atan2d(-f(2),f(1));
|
||||
theta1(2)=atan2d(f(3),f(4));
|
||||
% theta1(1)=acosd(-f(1));
|
||||
% theta1(2)=asind(-f(2));
|
||||
% theta1(3)=asind(f(3));
|
||||
% theta1(4)=acosd(-f(4));
|
||||
|
||||
theta = mean(theta1);
|
||||
end
|
||||
|
||||
BIN
Code/Matlab/AOA-IMU/data1.mat
Normal file
BIN
Code/Matlab/AOA-IMU/data1.mat
Normal file
Binary file not shown.
28
Code/Matlab/AOA-IMU/fun1.m
Normal file
28
Code/Matlab/AOA-IMU/fun1.m
Normal file
@ -0,0 +1,28 @@
|
||||
function [Y] = fun1(X,dt)
|
||||
%FUN 此处显示有关此函数的摘要
|
||||
% 此处显示详细说明
|
||||
WW = 0.05;
|
||||
nn = size(X,2);
|
||||
Y = zeros(5,nn);
|
||||
|
||||
for i=1:nn
|
||||
v = X(3,i);
|
||||
alfa = X(4,i);
|
||||
w = X(5,i)*180/pi;
|
||||
if w<WW
|
||||
alfa = alfa+w*dt;
|
||||
Y(:,i) = [X(1,i) + v*dt*cosd(alfa);
|
||||
X(2,i) - v*dt*sind(alfa);
|
||||
v;
|
||||
alfa;
|
||||
w*pi/180];
|
||||
else
|
||||
Y(:,i) = [X(1,i) + v/w*(sind(alfa+w*dt)-sind(alfa));
|
||||
X(2,i) - v/w*(cosd(alfa+w*dt)-cosd(alfa));
|
||||
v;
|
||||
alfa+w*dt;
|
||||
w*pi/180];
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
36
Code/Matlab/AOA-IMU/script.m
Normal file
36
Code/Matlab/AOA-IMU/script.m
Normal file
@ -0,0 +1,36 @@
|
||||
|
||||
|
||||
clear
|
||||
clc
|
||||
close all
|
||||
load('data1.mat');
|
||||
nn = size(imuPosX,1);
|
||||
%% lightHouse坐标系转换
|
||||
x = lightHousePosX * 100;
|
||||
y = -lightHousePosZ * 100;
|
||||
|
||||
plot(x,y,'r',imuPosX,imuPosY);
|
||||
|
||||
% 定义误差函数，即均方根误差
|
||||
errorFunction = @(params) sqrt(mean((x(1:500) * cos(params(1)) - y(1:500) * sin(params(1)) + params(2) - imuPosX(1:500)).^2 + (x(1:500) * sin(params(1)) + y(1:500) * cos(params(1)) + params(3) - imuPosY(1:500)).^2));
|
||||
|
||||
% 使用 fminsearch 优化误差函数，找到使误差最小的旋转角和位移
|
||||
initialGuess = [0, 10, 10]; % 初始猜测值，[旋转角, 位移]
|
||||
optimizedParams = fminsearch(errorFunction, initialGuess);
|
||||
|
||||
% 输出优化后的旋转角和位移
|
||||
rotationAngle = optimizedParams(1);
|
||||
xOffset = optimizedParams(2);
|
||||
yOffset = optimizedParams(3);
|
||||
% 旋转坐标
|
||||
xt = x * cos(rotationAngle) - y * sin(rotationAngle) + xOffset;
|
||||
yt = x * sin(rotationAngle) + y * cos(rotationAngle) + yOffset;
|
||||
|
||||
plot(xt,yt,'r',imuPosX,imuPosY);
|
||||
|
||||
ds = zeros(1,length(imuDataRxTime));
|
||||
for i = 1:length(imuDataRxTime)-1
|
||||
ds(i) = 1 / (imuDataRxTime(i+1)-imuDataRxTime(i));
|
||||
end
|
||||
plot(ds)
|
||||
|
||||
199
Code/Matlab/AOA-IMU/script_aekf.m
Normal file
199
Code/Matlab/AOA-IMU/script_aekf.m
Normal file
@ -0,0 +1,199 @@
|
||||
clear
|
||||
clc
|
||||
close all
|
||||
load('data1.mat');
|
||||
nn = size(imuPosX,1);
|
||||
%% lightHouse坐标系转换
|
||||
x = lightHousePosX * 100;
|
||||
y = -lightHousePosZ * 100;
|
||||
|
||||
% 定义误差函数，即均方根误差
|
||||
errorFunction = @(params) sqrt(mean((x(1:500) * cos(params(1)) - y(1:500) * sin(params(1)) + params(2) - imuPosX(1:500)).^2 + (x(1:500) * sin(params(1)) + y(1:500) * cos(params(1)) + params(3) - imuPosY(1:500)).^2));
|
||||
|
||||
% 使用 fminsearch 优化误差函数，找到使误差最小的旋转角和位移
|
||||
initialGuess = [0, 10, 10]; % 初始猜测值，[旋转角, 位移]
|
||||
optimizedParams = fminsearch(errorFunction, initialGuess);
|
||||
|
||||
% 输出优化后的旋转角和位移
|
||||
rotationAngle = optimizedParams(1);
|
||||
xOffset = optimizedParams(2);
|
||||
yOffset = optimizedParams(3);
|
||||
% 旋转坐标
|
||||
xt = x * cos(rotationAngle) - y * sin(rotationAngle) + xOffset;
|
||||
yt = x * sin(rotationAngle) + y * cos(rotationAngle) + yOffset;
|
||||
%%
|
||||
tagN = 4;
|
||||
%标签坐标
|
||||
XN(:,1)=[-300;-300];
|
||||
XN(:,2)=[-300;300];
|
||||
XN(:,3)=[300;300];
|
||||
XN(:,4)=[300;-300];
|
||||
sim2=6;
|
||||
Q=diag(repmat(sim2,1,2*tagN));%协方差矩阵
|
||||
measure_AOA = zeros(4,nn);
|
||||
measure_d = zeros(4,nn);
|
||||
measure_AOA(1,:) = aoa1';
|
||||
measure_AOA(2,:) = aoa2';
|
||||
measure_AOA(3,:) = aoa3';
|
||||
measure_AOA(4,:) = aoa4';
|
||||
measure_d(1,:) = d1';
|
||||
measure_d(2,:) = d2';
|
||||
measure_d(3,:) = d3';
|
||||
measure_d(4,:) = d4';
|
||||
%% uwb解算
|
||||
x_uwb(1) = 0;
|
||||
y_uwb(1) = 0;
|
||||
theta_uwb=zeros(nn,1);
|
||||
for i=2:nn
|
||||
if measure_d(1,i) == 0
|
||||
x_uwb(i) = x_uwb(i-1);
|
||||
y_uwb(i) = y_uwb(i-1);
|
||||
continue;
|
||||
end
|
||||
[t1,theta] = WLS(XN,measure_AOA(:,i),measure_d(:,i),Q);
|
||||
x_uwb(i) = t1(1);
|
||||
y_uwb(i) = t1(2);
|
||||
theta_uwb(i) = 90-theta;
|
||||
theta_uwb(i) = mod(theta_uwb(i)+180,360)-180;
|
||||
derr_WLS(i)=norm(t1-[xt(i);yt(i)]);
|
||||
end
|
||||
thetat=zeros(nn,1);
|
||||
for i=2:nn
|
||||
detx=xt(i)-xt(i-1);
|
||||
dety=yt(i)-yt(i-1);
|
||||
thetat(i)=atan2d(detx,dety);
|
||||
end
|
||||
% Uwb.x=x_uwb;
|
||||
% Uwb.y=y_uwb;
|
||||
% Uwb.alpha=theta_uwb;
|
||||
|
||||
|
||||
% 角速度校准
|
||||
detW = mean(wZ(1:200));
|
||||
wZ = wZ - detW;
|
||||
|
||||
x_imu(1) = 0;
|
||||
y_imu(1) = 0;
|
||||
Z=zeros(3,1);
|
||||
WW = 0.05;
|
||||
theta_imu(1) = 0;
|
||||
|
||||
|
||||
%% EKF
|
||||
KK = zeros(5,3);
|
||||
|
||||
%%
|
||||
%%AEKF
|
||||
R = diag([1 1 1]);
|
||||
% qq = 50;
|
||||
% qq = 10;
|
||||
qq = 0.01;
|
||||
Q = diag([qq qq qq qq qq]);
|
||||
P0 = diag([0 0 0 0 0]);
|
||||
H = [1 0 0 0 0;
|
||||
0 1 0 0 0;
|
||||
0 0 0 1 0];
|
||||
X_aekf = zeros(5,nn);
|
||||
X_aekf(:,1) = [imuPosX(1);imuPosY(1);vXY(1)*100;0;wZ(1)];
|
||||
I = eye(5);
|
||||
JF = zeros(5,5);
|
||||
X_pre = zeros(5,nn);
|
||||
alfa = 0.97;
|
||||
|
||||
windowlength=5;
|
||||
x_aekf_sw=zeros(1,nn);
|
||||
y_aekf_sw=zeros(1,nn);
|
||||
for i=2:nn
|
||||
detImuTime = imuDataRxTime(i) - imuDataRxTime(i-1);
|
||||
detOdomTime = odomDataRxTime(i)-odomDataRxTime(i-1);
|
||||
w = wZ(i);
|
||||
v = vXY(i)*100;
|
||||
detV=(vXY(i)-vXY(i-1))*100;
|
||||
detD = v*detImuTime;
|
||||
detTheta = w*180/pi*detImuTime;
|
||||
detW = w-wZ(i-1);
|
||||
theta_imu(i) = theta_imu(i-1)+detTheta;
|
||||
theta_imu(i) = mod(theta_imu(i)+180,360)-180;
|
||||
F = [1 0 detImuTime*cosd(X_aekf(4,i-1)) 0 0;
|
||||
0 1 detImuTime*sind(X_aekf(4,i-1)) 0 0;
|
||||
0 0 0 0 0;
|
||||
0 0 0 0 0;
|
||||
0 0 0 0 0;];
|
||||
|
||||
if w<WW
|
||||
vtx = detD*cosd(theta_imu(i));
|
||||
vty = detD*sind(theta_imu(i));
|
||||
else
|
||||
vtx = v/w*(sind(theta_imu(i))-sind(theta_imu(i-1)));
|
||||
vty = v/w*(-cosd(theta_imu(i))+cosd(theta_imu(i-1)));
|
||||
end
|
||||
|
||||
x_imu(i) = x_imu(i-1)+vtx;
|
||||
y_imu(i) = y_imu(i-1)+vty;
|
||||
X_next = [vtx;vty;detV;detTheta;detW];
|
||||
|
||||
if (x_uwb(i) == x_uwb(i-1))&&(y_uwb(i) == y_uwb(i-1))
|
||||
X_aekf(:,i) = X_aekf(:,i-1)+X_next;
|
||||
errAEKf(i) = norm(X_aekf(1:2,i)-[xt(i);yt(i)]);
|
||||
theta_aekf(i) = X_aekf(4,i);
|
||||
continue
|
||||
end
|
||||
if w<WW
|
||||
X_pre(:,i) = X_aekf(:,i-1)+X_next;
|
||||
Z = [x_uwb(i);y_uwb(i);theta_uwb(i)];
|
||||
P = F*P0*F'+Q;
|
||||
Kg = P*H'*inv(H*P*H'+R);
|
||||
KK(1,1) = Kg(1,1);
|
||||
KK(2,2) = Kg(2,2);
|
||||
KK(4,3) = Kg(4,3);
|
||||
X_aekf(:,i) = X_pre(:,i)+KK*(Z-H*X_pre(:,i));
|
||||
P0 = (I-Kg*H)*P;
|
||||
else
|
||||
JF = [1 0 1/w*(sind(theta_imu(i))-sind(theta_imu(i-1))) v/w*(cosd(theta_imu(i))-cosd(theta_imu(i-1))) detD/w*cosd(theta_imu(i))-v/(w^2)*(sind(theta_imu(i))-sind(theta_imu(i-1)));
|
||||
0 1 1/w*(-cosd(theta_imu(i))+cosd(theta_imu(i-1))) v/w*(sind(theta_imu(i))-sind(theta_imu(i-1))) detD/w*sind(theta_imu(i))-v/(w^2)*(-cosd(theta_imu(i))+cosd(theta_imu(i-1)));
|
||||
0 0 1 0 0;
|
||||
0 0 0 1 detImuTime;
|
||||
0 0 0 0 1];
|
||||
X_pre(:,i) = X_aekf(:,i-1)+X_next;
|
||||
dk = Z - H*X_pre(:,i);
|
||||
Z = [x_uwb(i);y_uwb(i);theta_uwb(i)];
|
||||
P = JF*P0*JF'+Q;
|
||||
Kg = P*H'*inv(H*P*H'+R);
|
||||
KK(1,1) = Kg(1,1);
|
||||
KK(2,2) = Kg(2,2);
|
||||
KK(4,3) = Kg(4,3);
|
||||
X_aekf(:,i) = X_pre(:,i)+KK*(Z-H*X_pre(:,i));
|
||||
epz = Z-H*X_aekf(:,i);
|
||||
R=alfa*R+(1-alfa)*(epz*epz'+H*P*H');
|
||||
Q=alfa*Q+(1-alfa)*Kg*dk*dk'*Kg';
|
||||
P0 = (I-Kg*H)*P;
|
||||
end
|
||||
errAEKf(i) = norm(X_aekf(1:2,i)-[xt(i);yt(i)]);
|
||||
theta_aekf(i) = X_aekf(4,i);
|
||||
% if errAEKf(i)>15
|
||||
% xxx = 1;
|
||||
% end
|
||||
end
|
||||
errAEKf_sw=zeros(1,nn);
|
||||
weightedvector=[0.3;0.25;0.2;0.15;0.1];
|
||||
for i=1:nn
|
||||
if i>windowlength-1
|
||||
x_win=X_aekf(1,i-windowlength+1:i);
|
||||
y_win=X_aekf(2,i-windowlength+1:i);
|
||||
x_aekf_sw(i)=x_win*weightedvector;
|
||||
y_aekf_sw(i)=y_win*weightedvector;
|
||||
else
|
||||
x_aekf_sw(i)=X_aekf(1,i);
|
||||
y_aekf_sw(i)=X_aekf(2,i);
|
||||
end
|
||||
errAEKf_sw(i) = norm([x_aekf_sw(i);y_aekf_sw(i)]-[xt(i);yt(i)]);
|
||||
end
|
||||
|
||||
figure;
|
||||
plot(errAEKf_sw);
|
||||
figure;
|
||||
plot(x_imu,y_imu,xt,yt);
|
||||
mean(errAEKf_sw)
|
||||
|
||||
|
||||
|
||||
342
Code/Matlab/AOA-IMU/script_ekf.m
Normal file
342
Code/Matlab/AOA-IMU/script_ekf.m
Normal file
@ -0,0 +1,342 @@
|
||||
clear
|
||||
clc
|
||||
close all
|
||||
load('data1.mat');
|
||||
nn = size(imuPosX,1);
|
||||
%% lightHouse坐标系转换
|
||||
x = lightHousePosX * 100;
|
||||
y = -lightHousePosZ * 100;
|
||||
|
||||
% 定义误差函数，即均方根误差
|
||||
errorFunction = @(params) sqrt(mean((x(1:500) * cos(params(1)) - y(1:500) * sin(params(1)) + params(2) - imuPosX(1:500)).^2 + (x(1:500) * sin(params(1)) + y(1:500) * cos(params(1)) + params(3) - imuPosY(1:500)).^2));
|
||||
|
||||
% 使用 fminsearch 优化误差函数，找到使误差最小的旋转角和位移
|
||||
initialGuess = [0, 10, 10]; % 初始猜测值，[旋转角, 位移]
|
||||
optimizedParams = fminsearch(errorFunction, initialGuess);
|
||||
|
||||
% 输出优化后的旋转角和位移
|
||||
rotationAngle = optimizedParams(1);
|
||||
xOffset = optimizedParams(2);
|
||||
yOffset = optimizedParams(3);
|
||||
% 旋转坐标
|
||||
xt = x * cos(rotationAngle) - y * sin(rotationAngle) + xOffset;
|
||||
yt = x * sin(rotationAngle) + y * cos(rotationAngle) + yOffset;
|
||||
%%
|
||||
tagN = 4;
|
||||
%标签坐标
|
||||
XN(:,1)=[-300;-300];
|
||||
XN(:,2)=[-300;300];
|
||||
XN(:,3)=[300;300];
|
||||
XN(:,4)=[300;-300];
|
||||
sim2=6;
|
||||
Q=diag(repmat(sim2,1,2*tagN));%协方差矩阵
|
||||
measure_AOA = zeros(4,nn);
|
||||
measure_d = zeros(4,nn);
|
||||
measure_AOA(1,:) = aoa1';
|
||||
measure_AOA(2,:) = aoa2';
|
||||
measure_AOA(3,:) = aoa3';
|
||||
measure_AOA(4,:) = aoa4';
|
||||
measure_d(1,:) = d1';
|
||||
measure_d(2,:) = d2';
|
||||
measure_d(3,:) = d3';
|
||||
measure_d(4,:) = d4';
|
||||
%% uwb解算
|
||||
x_uwb(1) = 0;
|
||||
y_uwb(1) = 0;
|
||||
theta_uwb=zeros(nn,1);
|
||||
for i=2:nn
|
||||
if measure_d(1,i) == 0
|
||||
x_uwb(i) = x_uwb(i-1);
|
||||
y_uwb(i) = y_uwb(i-1);
|
||||
continue;
|
||||
end
|
||||
[t1,theta] = WLS(XN,measure_AOA(:,i),measure_d(:,i),Q);
|
||||
x_uwb(i) = t1(1);
|
||||
y_uwb(i) = t1(2);
|
||||
theta_uwb(i) = 90-theta;
|
||||
theta_uwb(i) = mod(theta_uwb(i)+180,360)-180;
|
||||
derr_WLS(i)=norm(t1-[xt(i);yt(i)]);
|
||||
end
|
||||
thetat=zeros(nn,1);
|
||||
for i=2:nn
|
||||
detx=xt(i)-xt(i-1);
|
||||
dety=yt(i)-yt(i-1);
|
||||
thetat(i)=atan2d(detx,dety);
|
||||
end
|
||||
% Uwb.x=x_uwb;
|
||||
% Uwb.y=y_uwb;
|
||||
% Uwb.alpha=theta_uwb;
|
||||
|
||||
|
||||
% 角速度校准
|
||||
detW = mean(wZ(1:200));
|
||||
wZ = wZ - detW;
|
||||
|
||||
x_imu(1) = 0;
|
||||
y_imu(1) = 0;
|
||||
Z=zeros(3,1);
|
||||
WW = 0.05;
|
||||
theta_imu(1) = 0;
|
||||
|
||||
|
||||
%
|
||||
% Imu.x=x_imu;
|
||||
% Imu.y=y_imu;
|
||||
% Imu.v=v_imu;
|
||||
% Imu.alpha=alpha_imu;
|
||||
% Imu.omega=omega_imu;
|
||||
|
||||
%% KF
|
||||
R = diag([1 1 1]);
|
||||
% qq = 1;
|
||||
qq = 0.00001;
|
||||
Q1 = diag([qq qq qq qq qq]);
|
||||
P0 = diag([0 0 0 0 0]);
|
||||
H = [1 0 0 0 0;
|
||||
0 1 0 0 0;
|
||||
0 0 0 1 0];
|
||||
I = eye(5);
|
||||
JF = zeros(5,5);
|
||||
X_pre = zeros(5,nn);
|
||||
X_kf(:,1) = [imuPosX(1);imuPosY(1);vXY(1)*100;0;wZ(1)];
|
||||
for i=2:nn
|
||||
% 计算IMU和里程计的时间差值
|
||||
detImuTime = imuDataRxTime(i) - imuDataRxTime(i-1);
|
||||
detOdomTime = odomDataRxTime(i)-odomDataRxTime(i-1);
|
||||
% 获得此时Z轴角速度
|
||||
w = wZ(i);
|
||||
% 获得小车的水平速度
|
||||
v = vXY(i)*100;
|
||||
% 计算速度增量
|
||||
detV=(vXY(i)-vXY(i-1))*100;
|
||||
% 计算位置增量
|
||||
detD = v*detImuTime;
|
||||
% 计算角度增量
|
||||
detTheta = w*180/pi*detImuTime;
|
||||
% 计算角速度的变化量
|
||||
detW = w-wZ(i-1);
|
||||
% 积分计算IMU的航位角
|
||||
theta_imu(i) = theta_imu(i-1)+detTheta;
|
||||
% 航向约束
|
||||
theta_imu(i) = mod(theta_imu(i)+180,360)-180;
|
||||
|
||||
% 状态更新方程
|
||||
F = [1 0 detImuTime*cosd(X_kf(4,i-1)) 0 0;
|
||||
0 1 detImuTime*sind(X_kf(4,i-1)) 0 0;
|
||||
0 0 0 0 0;
|
||||
0 0 0 0 0;
|
||||
0 0 0 0 0;];
|
||||
% 获得水平和垂直方向的位置增量
|
||||
vtx = detD*cosd(theta_imu(i));
|
||||
vty = detD*sind(theta_imu(i));
|
||||
|
||||
x_imu(i) = x_imu(i-1)+vtx;
|
||||
y_imu(i) = y_imu(i-1)+vty;
|
||||
|
||||
X_next = [vtx;vty;detV;detTheta;detW];
|
||||
if (x_uwb(i) == x_uwb(i-1))&&(y_uwb(i) == y_uwb(i-1))
|
||||
X_kf(:,i) = X_kf(:,i-1)+X_next;
|
||||
errKf(i) = norm(X_kf(1:2,i)-[xt(i);yt(i)]);
|
||||
theta_kf(i) = X_kf(4,i);
|
||||
continue
|
||||
end
|
||||
X_pre(:,i) = X_kf(:,i-1)+X_next;
|
||||
Z = [x_uwb(i);y_uwb(i);theta_uwb(i)];
|
||||
P = F*P0*F'+Q1;
|
||||
Kg_kf = P*H'*inv(H*P*H'+R);
|
||||
X_kf(:,i) = X_pre(:,i)+Kg_kf*(Z-H*X_pre(:,i));
|
||||
P0 = (I-Kg_kf*H)*P;
|
||||
|
||||
errKf(i) = norm(X_kf(1:2,i)-[xt(i);yt(i)]);
|
||||
theta_kf(i) = X_kf(4,i);
|
||||
end
|
||||
|
||||
|
||||
|
||||
|
||||
%% EKF
|
||||
R = diag([1 1 1]);
|
||||
% qq = 1;
|
||||
qq = 0.00001;
|
||||
Q1 = diag([qq qq qq qq qq]);
|
||||
P0 = diag([0 0 0 0 0]);
|
||||
H = [1 0 0 0 0;
|
||||
0 1 0 0 0;
|
||||
0 0 0 1 0];
|
||||
KK = zeros(5,3);
|
||||
X_ekf(:,1) = [imuPosX(1);imuPosY(1);vXY(1)*100;0;wZ(1)];
|
||||
I = eye(5);
|
||||
JF = zeros(5,5);
|
||||
X_pre = zeros(5,nn);
|
||||
|
||||
for i=2:nn
|
||||
detImuTime = imuDataRxTime(i) - imuDataRxTime(i-1);
|
||||
detOdomTime = odomDataRxTime(i)-odomDataRxTime(i-1);
|
||||
w = wZ(i);
|
||||
v = vXY(i)*100;
|
||||
detV=(vXY(i)-vXY(i-1))*100;
|
||||
detD = v*detImuTime;
|
||||
detTheta = w*180/pi*detImuTime;
|
||||
detW = w-wZ(i-1);
|
||||
theta_imu(i) = theta_imu(i-1)+detTheta;
|
||||
theta_imu(i) = mod(theta_imu(i)+180,360)-180;
|
||||
F = [1 0 detImuTime*cosd(X_ekf(4,i-1)) 0 0;
|
||||
0 1 detImuTime*sind(X_ekf(4,i-1)) 0 0;
|
||||
0 0 0 0 0;
|
||||
0 0 0 0 0;
|
||||
0 0 0 0 0;];
|
||||
if w<WW
|
||||
vtx = detD*cosd(theta_imu(i));
|
||||
vty = detD*sind(theta_imu(i));
|
||||
else
|
||||
vtx = v/w*(sind(theta_imu(i))-sind(theta_imu(i-1)));
|
||||
vty = v/w*(-cosd(theta_imu(i))+cosd(theta_imu(i-1)));
|
||||
end
|
||||
x_imu(i) = x_imu(i-1)+vtx;
|
||||
y_imu(i) = y_imu(i-1)+vty;
|
||||
errUwb(i) = norm([x_uwb(i);y_uwb(i)]-[xt(i);yt(i)]);
|
||||
errImu(i) = norm([x_imu(i);y_imu(i)]-[xt(i);yt(i)]);
|
||||
X_next = [vtx;vty;detV;detTheta;detW];
|
||||
if (x_uwb(i) == x_uwb(i-1))&&(y_uwb(i) == y_uwb(i-1))
|
||||
X_ekf(:,i) = X_ekf(:,i-1)+X_next;
|
||||
errEKf(i) = norm(X_ekf(1:2,i)-[xt(i);yt(i)]);
|
||||
theta_ekf(i) = X_ekf(4,i);
|
||||
continue
|
||||
end
|
||||
if w<WW
|
||||
X_pre(:,i) = X_ekf(:,i-1)+X_next;
|
||||
Z = [x_uwb(i);y_uwb(i);theta_uwb(i)];
|
||||
P = F*P0*F'+Q1;
|
||||
Kg = P*H'*inv(H*P*H'+R);
|
||||
X_ekf(:,i) = X_pre(:,i)+Kg*(Z-H*X_pre(:,i));
|
||||
P0 = (I-Kg*H)*P;
|
||||
else
|
||||
JF = [1 0 1/w*(sind(theta_imu(i))-sind(theta_imu(i-1))) v/w*(cosd(theta_imu(i))-cosd(theta_imu(i-1))) detD/w*cosd(theta_imu(i))-v/(w^2)*(sind(theta_imu(i))-sind(theta_imu(i-1)));
|
||||
0 1 1/w*(-cosd(theta_imu(i))+cosd(theta_imu(i-1))) v/w*(sind(theta_imu(i))-sind(theta_imu(i-1))) detD/w*sind(theta_imu(i))-v/(w^2)*(-cosd(theta_imu(i))+cosd(theta_imu(i-1)));
|
||||
0 0 1 0 0;
|
||||
0 0 0 1 detImuTime;
|
||||
0 0 0 0 1];
|
||||
|
||||
X_pre(:,i) = X_ekf(:,i-1)+X_next;
|
||||
Z = [x_uwb(i);y_uwb(i);theta_uwb(i)];
|
||||
P = JF*P0*JF'+Q1;
|
||||
Kg = P*H'*inv(H*P*H'+R);
|
||||
X_ekf(:,i) = X_pre(:,i)+Kg*(Z-H*X_pre(:,i));
|
||||
P0 = (I-Kg*H)*P;
|
||||
end
|
||||
errEKf(i) = norm(X_ekf(1:2,i)-[xt(i);yt(i)]);
|
||||
theta_ekf(i) = X_ekf(4,i);
|
||||
end
|
||||
%% UKF
|
||||
% UKF settings
|
||||
ukf_L = 5; %numer of states
|
||||
ukf_m = 3; %numer of measurements
|
||||
ukf_kappa = 3 - ukf_L;
|
||||
ukf_alpha = 0.9;
|
||||
ukf_beta = 2;
|
||||
|
||||
ukf_lambda = ukf_alpha^2*(ukf_L + ukf_kappa) - ukf_L;
|
||||
ukf_gamma = sqrt(ukf_L + ukf_lambda);
|
||||
ukf_W0_c = ukf_lambda / (ukf_L + ukf_lambda) + (1 - ukf_alpha^2 + ukf_beta);
|
||||
ukf_W0_m = ukf_lambda / (ukf_L + ukf_lambda);
|
||||
ukf_Wi_m = 1 / (2*(ukf_L + ukf_lambda));
|
||||
ukf_Wi_c = ukf_Wi_m;
|
||||
|
||||
q=0.01; %std of process
|
||||
r=5; %std of measurement
|
||||
p=2;
|
||||
Qu=q*eye(ukf_L); % std matrix of process
|
||||
Ru=r*eye(ukf_m); % std of measurement
|
||||
Pu=p*eye(ukf_L);
|
||||
H = [1 0 0 0 0;
|
||||
0 1 0 0 0;
|
||||
0 0 0 1 0];
|
||||
X_ukf(:,1) = [imuPosX(1);imuPosY(1);vXY(1)*100;0;wZ(1)];
|
||||
I = eye(5);
|
||||
JF = zeros(5,5);
|
||||
X_pre = zeros(5,nn);
|
||||
for i=2:nn
|
||||
detImuTime = imuDataRxTime(i) - imuDataRxTime(i-1);
|
||||
detOdomTime = odomDataRxTime(i)-odomDataRxTime(i-1);
|
||||
w = wZ(i);
|
||||
v = vXY(i)*100;
|
||||
detV=(vXY(i)-vXY(i-1))*100;
|
||||
detD = v*detImuTime;
|
||||
detTheta = w*180/pi*detImuTime;
|
||||
detW = w-wZ(i-1);
|
||||
theta_imu(i) = theta_imu(i-1)+detTheta;
|
||||
theta_imu(i) = mod(theta_imu(i)+180,360)-180;
|
||||
% F = [1 0 detImuTime*cosd(X_ekf(4,i-1)) 0 0;
|
||||
% 0 1 detImuTime*sind(X_ekf(4,i-1)) 0 0;
|
||||
% 0 0 0 0 0;
|
||||
% 0 0 0 0 0;
|
||||
% 0 0 0 0 0;];
|
||||
if w<WW
|
||||
vtx = detD*cosd(theta_imu(i));
|
||||
vty = detD*sind(theta_imu(i));
|
||||
else
|
||||
vtx = v/w*(sind(theta_imu(i))-sind(theta_imu(i-1)));
|
||||
vty = v/w*(-cosd(theta_imu(i))+cosd(theta_imu(i-1)));
|
||||
end
|
||||
x_imu(i) = x_imu(i-1)+vtx;
|
||||
y_imu(i) = y_imu(i-1)+vty;
|
||||
errUwb(i) = norm([x_uwb(i);y_uwb(i)]-[xt(i);yt(i)]);
|
||||
errImu(i) = norm([x_imu(i);y_imu(i)]-[xt(i);yt(i)]);
|
||||
X_next = [vtx;vty;detV;detTheta;detW];
|
||||
if (x_uwb(i) == x_uwb(i-1))&&(y_uwb(i) == y_uwb(i-1))
|
||||
X_ukf(:,i) = X_ukf(:,i-1)+X_next;
|
||||
errUKf(i) = norm(X_ukf(1:2,i)-[xt(i);yt(i)]);
|
||||
theta_ukf(i) = X_ukf(4,i);
|
||||
continue
|
||||
end
|
||||
|
||||
xestimate = X_ukf(:,i-1);
|
||||
Xx = repmat(xestimate, 1, length(xestimate));
|
||||
Xsigma = [xestimate, ( Xx + ukf_gamma * Pu ), ( Xx - ukf_gamma * Pu )];
|
||||
|
||||
%第二步：对Sigma点集进行一步预测
|
||||
[Xsigmapre]=fun1(Xsigma,detImuTime);
|
||||
%第三步：估计预测状态
|
||||
Xpred = ukf_W0_m * Xsigmapre(:,1) + ukf_Wi_m * sum(Xsigmapre(:,2:end), 2);
|
||||
%第四步：均值和方差
|
||||
Xx = repmat(Xpred, 1, length(xestimate)*2);
|
||||
[~, R] = qr([sqrt(ukf_Wi_c) * ( Xsigmapre(:,2:end) - Xx ), Qu]', 0);
|
||||
Ppred = cholupdate(R, sqrt(ukf_W0_c) * (Xsigmapre(:,1) - Xpred), '-')';
|
||||
|
||||
%第5步：根据预测值，再一次使用UT变换，得到新的sigma点集
|
||||
Xx = repmat(Xpred, 1, length(xestimate));
|
||||
Xsigmapre = [Xpred, ( Xx + ukf_gamma * Ppred ), ( Xx - ukf_gamma * Ppred )];
|
||||
|
||||
%第6步：观测预测
|
||||
Zsigmapre=H*Xsigmapre;
|
||||
|
||||
%第7步：计算观测预测均值和协方差
|
||||
Zpred = ukf_W0_m * Zsigmapre(:,1) + ukf_Wi_m * sum(Zsigmapre(:,2:end), 2);
|
||||
|
||||
Yy = repmat(Zpred, 1, length(xestimate)*2);
|
||||
[~, Rz] = qr([sqrt(ukf_Wi_c) * (Zsigmapre(:,2:end) - Yy), Ru]', 0);
|
||||
Pzz = cholupdate(Rz, sqrt(ukf_W0_c) * (Zsigmapre(:,1) - Zpred), '-')';
|
||||
|
||||
Xd = Xsigmapre - repmat(Xpred, 1, length(xestimate)*2 + 1);
|
||||
Zd = Zsigmapre - repmat(Zpred, 1, length(xestimate)*2 + 1);
|
||||
|
||||
Pxz = ( ukf_W0_c* Xd(:,1) * Zd(:,1)' ) + ( ukf_Wi_c * Xd(:,2:end) * Zd(:,2:end)' );
|
||||
|
||||
%第七步：计算kalman增益
|
||||
Kukf= (Pxz / Pzz') / Pzz;
|
||||
%第八步：状态和方差更新
|
||||
Z = [x_uwb(i);y_uwb(i);theta_uwb(i)];
|
||||
Xpred=Xpred+Kukf*(Z-Zpred);
|
||||
U = Kukf * Pzz;
|
||||
Rp = Ppred';
|
||||
for ii=1:size(U, 2)
|
||||
Rp = cholupdate(Rp, U(:,ii), '-');
|
||||
end
|
||||
Ppred = Rp';
|
||||
X_ukf(:,i)=Xpred;
|
||||
|
||||
errUKf(i) = norm(X_ukf(1:2,i)-[xt(i);yt(i)]);
|
||||
theta_ukf(i) = X_ukf(4,i);
|
||||
end
|
||||
plot(errUKf);
|
||||
mean(errUKf)
|
||||
155
Code/Matlab/AOA-IMU/script_kf.m
Normal file
155
Code/Matlab/AOA-IMU/script_kf.m
Normal file
@ -0,0 +1,155 @@
|
||||
clear
|
||||
clc
|
||||
close all
|
||||
load('data1.mat');
|
||||
nn = size(imuPosX,1);
|
||||
%% lightHouse坐标系转换
|
||||
x = lightHousePosX * 100;
|
||||
y = -lightHousePosZ * 100;
|
||||
|
||||
% 定义误差函数，即均方根误差
|
||||
errorFunction = @(params) sqrt(mean((x(1:500) * cos(params(1)) - y(1:500) * sin(params(1)) + params(2) - imuPosX(1:500)).^2 + (x(1:500) * sin(params(1)) + y(1:500) * cos(params(1)) + params(3) - imuPosY(1:500)).^2));
|
||||
|
||||
% 使用 fminsearch 优化误差函数，找到使误差最小的旋转角和位移
|
||||
initialGuess = [0, 10, 10]; % 初始猜测值，[旋转角, 位移]
|
||||
optimizedParams = fminsearch(errorFunction, initialGuess);
|
||||
|
||||
% 输出优化后的旋转角和位移
|
||||
rotationAngle = optimizedParams(1);
|
||||
xOffset = optimizedParams(2);
|
||||
yOffset = optimizedParams(3);
|
||||
% 旋转坐标
|
||||
xt = x * cos(rotationAngle) - y * sin(rotationAngle) + xOffset;
|
||||
yt = x * sin(rotationAngle) + y * cos(rotationAngle) + yOffset;
|
||||
%%
|
||||
tagN = 4;
|
||||
%标签坐标
|
||||
XN(:,1)=[-300;-300];
|
||||
XN(:,2)=[-300;300];
|
||||
XN(:,3)=[300;300];
|
||||
XN(:,4)=[300;-300];
|
||||
sim2=6;
|
||||
Q=diag(repmat(sim2,1,2*tagN));%协方差矩阵
|
||||
measure_AOA = zeros(4,nn);
|
||||
measure_d = zeros(4,nn);
|
||||
measure_AOA(1,:) = aoa1';
|
||||
measure_AOA(2,:) = aoa2';
|
||||
measure_AOA(3,:) = aoa3';
|
||||
measure_AOA(4,:) = aoa4';
|
||||
measure_d(1,:) = d1';
|
||||
measure_d(2,:) = d2';
|
||||
measure_d(3,:) = d3';
|
||||
measure_d(4,:) = d4';
|
||||
%% uwb解算
|
||||
x_uwb(1) = 0;
|
||||
y_uwb(1) = 0;
|
||||
theta_uwb=zeros(nn,1);
|
||||
for i=2:nn
|
||||
if measure_d(1,i) == 0
|
||||
x_uwb(i) = x_uwb(i-1);
|
||||
y_uwb(i) = y_uwb(i-1);
|
||||
continue;
|
||||
end
|
||||
[t1,theta] = WLS(XN,measure_AOA(:,i),measure_d(:,i),Q);
|
||||
x_uwb(i) = t1(1);
|
||||
y_uwb(i) = t1(2);
|
||||
theta_uwb(i) = 90-theta;
|
||||
theta_uwb(i) = mod(theta_uwb(i)+180,360)-180;
|
||||
derr_WLS(i)=norm(t1-[xt(i);yt(i)]);
|
||||
end
|
||||
thetat=zeros(nn,1);
|
||||
for i=2:nn
|
||||
detx=xt(i)-xt(i-1);
|
||||
dety=yt(i)-yt(i-1);
|
||||
thetat(i)=atan2d(detx,dety);
|
||||
end
|
||||
% Uwb.x=x_uwb;
|
||||
% Uwb.y=y_uwb;
|
||||
% Uwb.alpha=theta_uwb;
|
||||
|
||||
|
||||
% 角速度校准
|
||||
detW = mean(wZ(1:200));
|
||||
wZ = wZ - detW;
|
||||
|
||||
x_imu(1) = 0;
|
||||
y_imu(1) = 0;
|
||||
Z=zeros(3,1);
|
||||
WW = 0.05;
|
||||
theta_imu(1) = 0;
|
||||
|
||||
|
||||
%
|
||||
% Imu.x=x_imu;
|
||||
% Imu.y=y_imu;
|
||||
% Imu.v=v_imu;
|
||||
% Imu.alpha=alpha_imu;
|
||||
% Imu.omega=omega_imu;
|
||||
|
||||
%% KF
|
||||
R = diag([1 1 1]);
|
||||
% qq = 1;
|
||||
qq = 0.005;
|
||||
Q1 = diag([qq qq qq qq qq]);
|
||||
P0 = diag([0 0 0 0 0]);
|
||||
H = [1 0 0 0 0;
|
||||
0 1 0 0 0;
|
||||
0 0 0 1 0];
|
||||
I = eye(5);
|
||||
JF = zeros(5,5);
|
||||
X_pre = zeros(5,nn);
|
||||
X_kf(:,1) = [imuPosX(1);imuPosY(1);vXY(1)*100;0;wZ(1)];
|
||||
for i=2:nn
|
||||
% 计算IMU和里程计的时间差值
|
||||
detImuTime = imuDataRxTime(i) - imuDataRxTime(i-1);
|
||||
detOdomTime = odomDataRxTime(i)-odomDataRxTime(i-1);
|
||||
% 获得此时Z轴角速度
|
||||
w = wZ(i);
|
||||
% 获得小车的水平速度
|
||||
v = vXY(i)*100;
|
||||
% 计算速度增量
|
||||
detV=(vXY(i)-vXY(i-1))*100;
|
||||
% 计算位置增量
|
||||
detD = v*detImuTime;
|
||||
% 计算角度增量
|
||||
detTheta = w*180/pi*detImuTime;
|
||||
% 计算角速度的变化量
|
||||
detW = w-wZ(i-1);
|
||||
% 积分计算IMU的航位角
|
||||
theta_imu(i) = theta_imu(i-1)+detTheta;
|
||||
% 航向约束
|
||||
theta_imu(i) = mod(theta_imu(i)+180,360)-180;
|
||||
|
||||
% 状态更新方程
|
||||
F = [1 0 detImuTime*cosd(X_kf(4,i-1)) 0 0;
|
||||
0 1 detImuTime*sind(X_kf(4,i-1)) 0 0;
|
||||
0 0 0 0 0;
|
||||
0 0 0 0 0;
|
||||
0 0 0 0 0;];
|
||||
% 获得水平和垂直方向的位置增量
|
||||
vtx = detD*cosd(theta_imu(i));
|
||||
vty = detD*sind(theta_imu(i));
|
||||
|
||||
x_imu(i) = x_imu(i-1)+vtx;
|
||||
y_imu(i) = y_imu(i-1)+vty;
|
||||
|
||||
X_next = [vtx;vty;detV;detTheta;detW];
|
||||
if (x_uwb(i) == x_uwb(i-1))&&(y_uwb(i) == y_uwb(i-1))
|
||||
X_kf(:,i) = X_kf(:,i-1)+X_next;
|
||||
errKf(i) = norm(X_kf(1:2,i)-[xt(i);yt(i)]);
|
||||
theta_kf(i) = X_kf(4,i);
|
||||
continue
|
||||
end
|
||||
X_pre(:,i) = X_kf(:,i-1)+X_next;
|
||||
% 观测矩阵: UWB的位置、UWB的航向角
|
||||
Z = [x_uwb(i);y_uwb(i);theta_uwb(i)];
|
||||
P = F*P0*F'+Q1;
|
||||
Kg_kf = P*H'*inv(H*P*H'+R);
|
||||
X_kf(:,i) = X_pre(:,i)+Kg_kf*(Z-H*X_pre(:,i));
|
||||
P0 = (I-Kg_kf*H)*P;
|
||||
|
||||
errKf(i) = norm(X_kf(1:2,i)-[xt(i);yt(i)]);
|
||||
theta_kf(i) = X_kf(4,i);
|
||||
end
|
||||
plot(errKf);
|
||||
mean(errKf)
|
||||
Loading…
x
Reference in New Issue
Block a user