A Deep Learning Based Traffic State Estimation Method for Mixed Traffic Flow Environment

Table 1

Error comparison of different models in three cases (the results with the best performance are highlighted).

Case	Algorithm	RMSE	MRE	MAE
Case 1	KF	2.32031	0.15474	1.81752
	ACC-KF	2.27986	0.13954	1.74709
	LSTM	1.80295	0.09115	1.29157
	ACC-LSTM	1.62693	0.06925	1.17177
	P-LSTM	1.71519	0.07896	1.16926
	ACC-P-LSTM	1.54142	0.06452	1.05299
Case 2	KF	2.20117	0.10711	1.59424
	ACC-KF	2.17710	0.10660	1.58011
	LSTM	1.26577	0.06295	0.99065
	ACC-LSTM	1.25447	0.06122	0.98373
	P-LSTM	1.24782	0.06019	0.95079
	ACC-P-LSTM	1.24741	0.06022	0.96165
Case 3	KF	2.64087	0.16417	1.92558
	ACC-KF	2.52561	0.15863	1.78602
	LSTM	1.93180	0.09619	1.36391
	ACC-LSTM	1.92861	0.09618	1.34253
	P-LSTM	1.91543	0.09422	1.35214
	ACC-P-LSTM	1.91870	0.09661	1.33502

Note: KF = Kalman Filtering; ACC-KF = Kalman Filtering using KNN filling with fusion acceleration; LSTM = Long Short-Term Memory; ACC-LSTM = LSTM model using KNN filling with fusion acceleration; P-LSTM = LSTM model using penetration rate estimation; ACC-P-LSTM = LSTM model using KNN filling with fusion acceleration and penetration rate estimation; RMSE = Root Mean Square Error; MRE = Mean Relative Error; and MAE = Mean Absolute Error.