Efficient real time OD matrix estimation based on Principal Component Analysis

In this paper we explore the idea of dimensionality reduction and approximation of OD demand based on principal component analysis (PCA). First, we show how we can apply PCA to linearly transform the high dimensional OD matrices into the lower dimensional space without significant loss of accuracy. Next, we define a new transformed set of variables (demand principal components) that is used to represent the fixed structure of OD matrices in lower dimensional space. We update online these new variables from traffic counts in a novel reduced state space model for real time estimation of OD demand. Through an example we demonstrate the quality improvement of OD estimates using this new formulation and a so-called `colored' Kalman filter over the standard Kalman filter approach for OD estimation, when correlated measurement noise is accounted due to reduction of variables in state vector.