  The Adaptive Smoothing Method (ASM) is a data-driven approach for traffic
state estimation. It interpolates unobserved traffic quantities by smoothing
measurements along spatio-temporal directions defined by characteristic traffic
wave speeds. The standard ASM consists of a superposition of two a priori
estimates weighted by a heuristic weight factor. In this paper, we propose a
systematic procedure to calculate the optimal weight factors. We formulate the
a priori weights calculation as a constrained matrix completion problem, and
efficiently solve it using the Alternating Direction Method of Multipliers
(ADMM) algorithm. Our framework allows one to further improve the conventional
ASM, which is limited by utilizing only one pair of congested and free flow
wave speeds, by considering multiple wave speeds. Our proposed algorithm does
not require any field-dependent traffic parameters, thus bypassing frequent
field calibrations as required by the conventional ASM. Experiments using NGSIM
data show that the proposed ADMM-based estimation incurs lower error than the
ASM estimation.
