├── .gitattributes ├── EKF.m ├── EKF_Scilab.sce ├── README.md ├── Radar_Lidar_Data1.csv ├── Radar_Lidar_Data2.csv ├── Result1.png └── Result2.png /.gitattributes: -------------------------------------------------------------------------------- 1 | # Auto detect text files and perform LF normalization 2 | * text=auto 3 | -------------------------------------------------------------------------------- /EKF.m: -------------------------------------------------------------------------------- 1 | clear; 2 | clf; 3 | dt = 0.1; 4 | Data = csvread('Radar_Lidar_Data1.csv',1,1); 5 | % Data = csvread('Radar_Lidar_Data2.csv',1,1); 6 | Radar_Measurement = []; 7 | Lidar_Measurement = []; 8 | EKF_Path = []; 9 | 10 | F = [[1, 0, dt, 0]; 11 | [0, 1, 0, dt]; 12 | [0, 0, 1, 0]; 13 | [0, 0, 0, 1]]; 14 | 15 | u = 0; 16 | B = [(dt^2)/2 (dt^2)/2 dt dt]'; 17 | 18 | P = [[1, 0, 0, 0]; 19 | [0, 1, 0, 0]; 20 | [0, 0, 1000, 0]; 21 | [0, 0, 0, 1000]]; 22 | 23 | 24 | R_l = [[0.0025, 0]; 25 | [0, 0.0025]]; 26 | 27 | R_r = [[0.09, 0, 0]; 28 | [0, 0.005, 0]; 29 | [0, 0, 0.09]]; 30 | 31 | 32 | Q = [(dt^2)/4 0 (dt^3)/2 0; 33 | 0 (dt^2)/4 0 (dt^3)/2; 34 | (dt^3/2) 0 (dt^2) 0; 35 | 0 (dt^3)/2 0 (dt^2)]; 36 | 37 | 38 | H = [[1, 0, 0, 0]; 39 | [0, 1, 0, 0]]; 40 | 41 | I = eye(4); 42 | 43 | if (Data(1,1) == 1) 44 | x = [Data(1,2); Data(1,3); 0; 0]; 45 | else 46 | x = [Data(1,2); Data(1,3); Data(1,4); 0]; 47 | end 48 | 49 | for n = 1:length(Data) 50 | 51 | if (Data(n,1) == 2) 52 | 53 | %prediction 54 | x = F * x + B*u; 55 | P = F * P * transpose(F) + Q; 56 | 57 | %measurement update 58 | Z = Data(n,2:4); 59 | X = Z(1)*cos(Z(2)); 60 | Y = Z(1)*sin(Z(2)); 61 | VX = Z(3)*cos(Z(2)); 62 | VY = Z(3)*sin(Z(2)); 63 | 64 | c1 = X^2 + Y^2; 65 | c2 = sqrt(c1); 66 | c3 = c1 * c2; 67 | if (c1==0 || c2==0 || c3==0) 68 | H_Jac = [[0, 0, 0, 0]; 69 | [0, 0, 0, 0]; 70 | [0, 0, 0, 0]]; 71 | else 72 | H_Jac = [[X/c2, Y/c2, 0, 0]; 73 | [-Y/c1, X/c1, 0, 0]; 74 | [(Y*(VX*Y-VY*X))/c3, (X*(X*VY-Y*VX))/c3, X/c2, Y/c2]]; 75 | end 76 | Z_Car = [X; Y; VX; VY]; 77 | y = transpose(Z) - (H_Jac * Z_Car); 78 | S = H_Jac * P * transpose(H_Jac) + R_r; 79 | K = P * transpose(H_Jac) * inv(S); 80 | x = Z_Car + (K * y); 81 | P = (I - (K * H_Jac)) * P; 82 | EKF_Path = [EKF_Path;[x(1),x(2)]]; 83 | Radar_Measurement = [Radar_Measurement; Data(n,2:4)]; 84 | 85 | else 86 | 87 | %prediction 88 | x = (F * x) + B*u; 89 | P = F * P * transpose(F) + Q; 90 | 91 | %measurement update 92 | Z = Data(n,2:3); 93 | y = transpose(Z) - (H * x); 94 | S = H * P * transpose(H) + R_l; 95 | K = P * transpose(H) * inv(S); 96 | x = x + (K * y); 97 | P = (I - (K * H)) * P; 98 | EKF_Path = [EKF_Path;[x(1),x(2)]]; 99 | Lidar_Measurement = [Lidar_Measurement; Data(n,2:3)]; 100 | end 101 | 102 | end 103 | 104 | for i = 1:length(Radar_Measurement) 105 | Radar_Measurement_Cart(i,:) = [[Radar_Measurement(i,1),0];[0, Radar_Measurement(i,1)]]*[cos(Radar_Measurement(i,2));sin(Radar_Measurement(i,2))]; 106 | end 107 | 108 | hold on; 109 | 110 | plot(Data(:,6),Data(:,7),'linewidth', 2); 111 | scatter(EKF_Path(:,1),EKF_Path(:,2),25,'filled','r'); 112 | scatter(Lidar_Measurement(:,1),Lidar_Measurement(:,2),5,'filled','blue'); 113 | scatter(Radar_Measurement_Cart(:,1),Radar_Measurement_Cart(:,2),5,'filled','g'); 114 | 115 | legend('Grundtruth','EKF Path result','Lidar Measurement','Radar Measurement','Location','northwest'); 116 | axis square; 117 | hold off; 118 | -------------------------------------------------------------------------------- /EKF_Scilab.sce: -------------------------------------------------------------------------------- 1 | clear; 2 | clf; 3 | dt = 0.1; 4 | Data = csvRead('Radar_Lidar_Data1.csv',[], [], "double", [], [], [2 2 1225 10]);//Omit the header and the first column. 5 | Radar_Measurement = []; 6 | Lidar_Measurement = []; 7 | EKF_Path = []; 8 | F = [[1, 0, dt, 0]; 9 | [0, 1, 0, dt]; 10 | [0, 0, 1, 0]; 11 | [0, 0, 0, 1]]; 12 | 13 | u = 0; 14 | B = [(dt^2)/2 (dt^2)/2 dt dt]'; 15 | 16 | P = [[1, 0, 0, 0]; 17 | [0, 1, 0, 0]; 18 | [0, 0, 1000, 0]; 19 | [0, 0, 0, 1000]]; 20 | 21 | 22 | R_l = [[0.0025, 0]; 23 | [0, 0.0025]]; 24 | 25 | R_r = [[0.09, 0, 0]; 26 | [0, 0.005, 0]; 27 | [0, 0, 0.09]]; 28 | 29 | 30 | Q = [(dt^2)/4 0 (dt^3)/2 0; 31 | 0 (dt^2)/4 0 (dt^3)/2; 32 | (dt^3/2) 0 (dt^2) 0; 33 | 0 (dt^3)/2 0 (dt^2)]; 34 | 35 | 36 | H = [[1, 0, 0, 0]; 37 | [0, 1, 0, 0]]; 38 | I = eye(4,4); 39 | 40 | if (Data(1,1) == 1) 41 | x = [Data(1,2); Data(1,3); 0; 0]; 42 | else 43 | x = [Data(1,2); Data(1,3); Data(1,4); 0]; 44 | end 45 | for n = 1:size(Data)(1,1) 46 | 47 | if (Data(n,1) == 2) 48 | 49 | //prediction 50 | x = F * x + B*u; 51 | P = F * P * F' + Q; 52 | 53 | //measurement update 54 | Z = Data(n,2:4); 55 | X = Z(1)*cos(Z(2)); 56 | Y = Z(1)*sin(Z(2)); 57 | VX = Z(3)*cos(Z(2)); 58 | VY = Z(3)*sin(Z(2)); 59 | 60 | c1 = X^2 + Y^2; 61 | c2 = sqrt(c1); 62 | c3 = c1 * c2; 63 | if (c1==0 || c2==0 || c3==0) 64 | H_Jac = [[0, 0, 0, 0]; 65 | [0, 0, 0, 0]; 66 | [0, 0, 0, 0]]; 67 | else 68 | H_Jac = [[X/c2, Y/c2, 0, 0]; 69 | [-Y/c1, X/c1, 0, 0]; 70 | [(Y*(VX*Y-VY*X))/c3, (X*(X*VY-Y*VX))/c3, X/c2, Y/c2]]; 71 | end 72 | Z_Car = [X; Y; VX; VY]; 73 | y = Z' - (H_Jac * Z_Car); 74 | S = H_Jac * P * H_Jac' + R_r; 75 | K = P * H_Jac' * inv(S); 76 | x = Z_Car + (K * y); 77 | P = (I - (K * H_Jac)) * P; 78 | EKF_Path = [EKF_Path;[x(1),x(2)]]; 79 | Radar_Measurement = [Radar_Measurement; Data(n,2:4)]; 80 | 81 | else 82 | 83 | //prediction 84 | x = (F * x) + B*u; 85 | P = F * P * F' + Q; 86 | 87 | //measurement update 88 | Z = Data(n,2:3); 89 | y = Z' - (H * x); 90 | S = H * P * H' + R_l; 91 | K = P * H' * inv(S); 92 | x = x + (K * y); 93 | P = (I - (K * H)) * P; 94 | EKF_Path = [EKF_Path;[x(1),x(2)]]; 95 | Lidar_Measurement = [Lidar_Measurement; Data(n,2:3)]; 96 | end 97 | 98 | end 99 | for i = 1:size(Radar_Measurement)(1,1) 100 | Radar_Measurement_Cart(i,:) = [[Radar_Measurement(i,1),0];[0, Radar_Measurement(i,1)]]*[cos(Radar_Measurement(i,2));sin(Radar_Measurement(i,2))]; 101 | end 102 | 103 | set(gca(),"auto_clear","off") 104 | plot(Data(:,6),Data(:,7),'r','linewidth', 2); 105 | scatter(gca(),EKF_Path(:,1),EKF_Path(:,2),,'scilabred3'); 106 | scatter(gca(),Lidar_Measurement(:,1),Lidar_Measurement(:,2),,'scilabgreen3'); 107 | scatter(Radar_Measurement_Cart(:,1),Radar_Measurement_Cart(:,2),,'skyblue'); 108 | legend(gca(),['Grundtruth';'EKF Path result';'Lidar Measurement';'Radar Measurement'],2); 109 | //axis square; Not Implemented yet. 110 | set(gca(),"auto_clear","on") 111 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Lidar-and-Radar-sensor-fusion-with-Extended-Kalman-Filter 2 | Most autonomous driving cars are equipped with Lidar and Radar. However the outputs of those two are different, the output of Lidar is positions of objects in cartesian coordinates whereas Radar gives out the position and velocity of the objects in polar coordinates. The Extended Kalman Filter is utilized as it can fuse non-linear data, in this case the data from cartesian coordinates and polar coordinates. To estimate the non-linear measurement, the Jacobian matrix is introduced. 3 | 4 | 5 | As the results below, the EKF functions fuses linear Lidar with non-linear Radar data. 6 | 7 | 8 | ![alt text](https://github.com/paulyehtw/Lidar-and-Radar-sensor-fusion-with-Extended-Kalman-Filter/blob/master/Result1.png) 9 | ![alt text](https://github.com/paulyehtw/Lidar-and-Radar-sensor-fusion-with-Extended-Kalman-Filter/blob/master/Result2.png) 10 | 11 | The code is written from scratch. 12 | 13 | Data source is from Udacity course Self-Driving Car 14 | 15 | -------------------------------------------------------------------------------- /Radar_Lidar_Data1.csv: -------------------------------------------------------------------------------- 1 | Column1,Column12,Column2,Column3,Column4,Column5,Column6,Column7,Column8,Column9 2 | R,2,8.46642,0.0287602,-3.04035,1.47701E+15,8.6,0.25,-3.00029,0 3 | L,1,8.44818,0.251553,,1.47701E+15,8.45,0.25,-3.00027,0 4 | 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https://raw.githubusercontent.com/paulyehtw/Lidar-and-Radar-sensor-fusion-with-Extended-Kalman-Filter/089d3160ce73453640c501dfbb561f0885ef1b64/Result1.png -------------------------------------------------------------------------------- /Result2.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/paulyehtw/Lidar-and-Radar-sensor-fusion-with-Extended-Kalman-Filter/089d3160ce73453640c501dfbb561f0885ef1b64/Result2.png --------------------------------------------------------------------------------