## Kalman Filter Explained With Python Code From Scratch

This snippet shows tracking mouse cursor with Python code from scratch and comparing the result with OpenCV. The CSV file that has been used are being created with below c++ code. A sample could be downloaded from here 1, 2, 3. Python Kalman Filter

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import numpy as np np.set_printoptions(threshold=3) np.set_printoptions(suppress=True) from numpy import genfromtxt #Notation used coming from: https://www.bzarg.com/p/how-a-kalman-filter-works-in-pictures/ def prediction(X_hat_t_1,P_t_1,F_t,B_t,U_t,Q_t): X_hat_t=F_t.dot(X_hat_t_1)+(B_t.dot(U_t).reshape(B_t.shape[0],-1) ) P_t=np.diag(np.diag(F_t.dot(P_t_1).dot(F_t.transpose())))+Q_t return X_hat_t,P_t def update(X_hat_t,P_t,Z_t,R_t,H_t): K_prime=P_t.dot(H_t.transpose()).dot( np.linalg.inv ( H_t.dot(P_t).dot(H_t.transpose()) +R_t ) ) print("K:\n",K_prime) X_t=X_hat_t+K_prime.dot(Z_t-H_t.dot(X_hat_t)) P_t=P_t-K_prime.dot(H_t).dot(P_t) return X_t,P_t acceleration=0 delta_t=1/20#milisecond groundTruth = genfromtxt('data/groundTruth.csv', delimiter=',',skip_header=1) #Observations: position_X, position_Y measurmens = genfromtxt('data/measurmens.csv', delimiter=',',skip_header=1) #Checking our result with OpenCV opencvKalmanOutput = genfromtxt('data/kalmanv.csv', delimiter=',',skip_header=1) #Transition matrix F_t=np.array([ [1 ,0,delta_t,0] , [0,1,0,delta_t] , [0,0,1,0] , [0,0,0,1] ]) #Initial State cov P_t= np.identity(4)*0.2 #Process cov Q_t= np.identity(4) #Control matrix B_t=np.array( [ [0] , [0], [0] , [0] ]) #Control vector U_t=acceleration #Measurment Matrix H_t = np.array([ [1, 0, 0, 0], [ 0, 1, 0, 0]]) #Measurment cov R_t= np.identity(2)*5 # Initial State X_hat_t = np.array( [[0],[0],[0],[0]] ) print("X_hat_t",X_hat_t.shape) print("P_t",P_t.shape) print("F_t",F_t.shape) print("B_t",B_t.shape) print("Q_t",Q_t.shape) print("R_t",R_t.shape) print("H_t",H_t.shape) for i in range(measurmens.shape[0]): X_hat_t,P_hat_t = prediction(X_hat_t,P_t,F_t,B_t,U_t,Q_t) print("Prediction:") print("X_hat_t:\n",X_hat_t,"\nP_t:\n",P_t) Z_t=measurmens[i].transpose() Z_t=Z_t.reshape(Z_t.shape[0],-1) print(Z_t.shape) X_t,P_t=update(X_hat_t,P_hat_t,Z_t,R_t,H_t) print("Update:") print("X_t:\n",X_t,"\nP_t:\n",P_t) X_hat_t=X_t P_hat_t=P_t print("=========================================") print("Opencv Kalman Output:") print("X_t:\n",opencvKalmanOutput[i]) |

C++ and OpenCV Kalman Filter Rapidcsv has been downloaded from …

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