Group-Based Dimensionality Reduction and Estimation for Heterogeneous Large-Scale Traffic Networks

State estimation for traffic networks is a particularly challenging problem in view of their large dimensionality, and since models are often inaccurate and the interaction patterns unpredictable. In this article, we approach the problem by mixing aggregation-based complexity reduction and nonlinear filtering. We subdivide vehicles into groups and derive a lower-dimensional approximate model where vehicles belonging to the same group are represented by a unique random variable matching their average characteristics. Then, we propose a procedure to estimate the statistical properties of the group variables from partial measurements. Connections to car-following models are discussed, and the developed methodology is illustrated through numerical simulations.