Kalman_Filtering_Example = function(n) { ##### Establishing Sigma Values sigma_V = .2; sigma_W = .1; ##### Creating storage vectors for X, Y, X_pred, X_filt, Omega, Delta and Theta X = rep(0, n); Y = rep(0, n); X_hat_pred = rep(0, n); X_hat_filt = rep(0, n); Omega = rep(0, n); Delta = rep(0, n); Theta = rep(0, n); ###### Starting everything with t = 1 X[1] = rnorm(1, 0, sigma_V); Y[1] = X[1] + rnorm(1,0, sigma_W); X_hat_pred[1] = .2; Omega [1] = . 04; Delta [1] = Omega [1] + sigma_W^2; Theta [1] = Omega [1] for (j in 2:n) { ######### doing prediction ########## X_hat_pred[j] = X_hat_pred[j-1] + (Theta[j-1]/Delta[j-1])*(Y[j-1] - X_hat_pred[j-1]); Omega[j] = Omega[j-1] + sigma_V^2 - Theta[j-1]^2/Delta[j-1]; Delta[j] = Omega[j] + sigma_W^2; Theta[j] = Omega [j]; ######## simulating next value of X and Y ########### X[j] = X[j-1] + rnorm(1, 0, sigma_V); Y[j] = X[j] + rnorm(1, 0, sigma_W); ####### filtering ############ X_hat_filt[j] = X_hat_pred[j] + (Omega[j]/Delta[j])*(Y[j] - X_hat_pred[j]); plot (X, type = "1") lines(X_hat_pred, type = "1", col = "red"); Lines(X_hat_filt, type = "1", col = "blue"); legend(x = "topleft", legend=c("True X", "Predicted X", "Filtered X"), col=c("black", "red", "blue"), Ity = c(1, 1,1)) print(X_hat_pred [70: 85]); print(X_hat_filt [70: 85])