近年來，自動駕駛與智慧城市的發展漸漸的藉由龐大的資料實踐，而對交通流的預測與模擬需要更精準、更大範圍且更長期的預測。基本上，現行的交通流預測模型來至於兩種方法，第一是有交通流理論基礎的數學模型方法，優點是在理想狀態及環境下能穩定的給出長遠而準確的結果；第二是基於大量的數據分析及對模型的訓練而得出的機器學習模型，優點在於可適應部分非理想狀態的多變性。為了結合兩方的優點進而得出更接近真相的預測，我們藉由資料同化技術將多方的預測資料導入模型中。本研究將結合宏觀的交通流數學模型 LWR 模型 (Lighthill-Whitham-Richards model) 及描述固定環境中車輛速度與車輛密度的 MacNicholas 模型建立數值上的預測，在此一數學預測模型上搭建擴展型卡爾曼濾波器(extended Kalman Filter)以達到資料同化中降低觀測誤差的效果，進而得到更完美的起始值。同時，因 Godunov schem 離散過後的 LWR 模型對邊界資料的需求，我們導入了遞歸神經網路 (RNN) 中常用於預測問題的長短期記憶模型 (LSTM) 以協助取得未來出、入口的邊界資料，也將 LSTM 所得的多次全範圍預測同化入卡爾曼濾波器中，藉此獲得兩個預測模型各自的優點，也同時將卡爾曼濾波器降低觀測誤差的效果導入 LSTM 所給出的預測結果中，借此校正被觀測誤差所影響的預測結果，將此預測方法命名為 LSTM-EKF 方法。實驗中使用基本的 Riemann Problem 為測試問題，對我們所建立的卡爾曼濾波器與數學模型進行分析，並且使用高速公路局公開的交通資料庫做實際數據的實驗，用以檢驗及分析我們所提出的方法在真實世界的應用。實驗結果可以看出數學模型與機器學習模型在預測問題中的優缺點與差異之外，我們提出的 LSTM-EKF 方法也可以成功的過濾部分觀測誤差所產生的影響。;In recent years, the developments of self-driving cars and smart cities have been studied. The prediction and simulation of traffic flow require more accurate, larger-scale, and longer-term forecasts. The current traffic flow prediction model comes from two classes: One is a mathematical model based on the theory of traffic flow, which can stably give long-term and accurate results under ideal conditions. The other one is a machine learning model based on training a model and analysis of data, which can give us some information beyond the theory of traffic. To take advantage of the methods from these classes to obtain a better prediction, we develop a hybrid method, namely the EKF-LSTM method, under the framework of the data assimilation system. The key ingredients of the proposed technique include a numerical prediction method based on the Godunov scheme for the Lighthill-Whitham-Richards equation with the MacNicholas model. We build an extended Kalman Filter (EKF) with the prediction model to reduce the observation error and obtain a better initial value. At the same time, due to the requirement of boundary data for the Godunov scheme′s discretization, we introduce the long short-term memory (LSTM) method, which is a deep learning method commonly used in prediction problems, to find the boundary data. The multiple full-range predictions given by LSTM are also assimilated into the Kalman filter to obtain the advantages of two prediction models. The Kalman filter can reduce the effect of observation error in the prediction of LSTM. In the experiment, %the Riemann Problem is used as the test case to analyze the extended Kalman filter and the numerical model that we build. In addition, we use the data published by the Ministry of Transportation and Communications in Taiwan to build real-world experiments to test and analyze the EKF-LSTM method we develop. The results show the differences between the numerical model and the machine learning model in the prediction problem. Also, the LSTM-EKF method can successfully filter out the noise from observation errors and perform better than the traditional EKF and LSTM alone methods.
