Unbiased Estimation Methods of Nonlinear Transport Models Based on Linearly Projected Data

Abstract

Linear data projection is widely used for unbiased traffic data estimation. Nevertheless, recent studies have proven that direct model estimation based on linearly projected data that ignores the scaling factor variability may lead to systematically biased parameters. Adjustment factors were derived for a generalised multivariate polynomial (GMP) function with fixed exponents to remove such biases. However, the methods have not been extended to generic nonlinear transport models necessitating nonlinear regressions. This paper scrutinises the mechanism of systematic data point distortion resulting from linear data projection and identifies the practical difficulties of the adjustment factor approach to other nonlinear models. To reduce such biases in nonlinear transport models, a generic mean value restoration (MVR) method, requiring only the first two moments of the scaling factor, and an extended MVR (EMVR) method, further incorporating higher-order moments by assuming a scaling factor distribution, are proposed. Simulation studies are conducted for both GMP functions with relaxed exponents and multivariate exponential decay functions, which are the most commonly adopted nonlinear functions for modeling traffic flow, to examine the effectiveness and robustness of the proposed methods for recovering the assumed true model parameters. Results reveal that the EMVR method generally can achieve higher level of accuracy.