Traffic density estimation via KDE and nonlinear LS

Authors: MİKAİL YILAN, MEHMET KEMAL ÖZDEMİR

Abstract: With increasing population, the determination of traffic density becomes critical in managing urban city roads for safer driving and low carbon emissions. In this study, kernel density estimation is utilized in order to estimate traffic density more accurately when the speeds of vehicles are available for a given region. For the proposed approach, as a first step, the probability density function of the speed data is modeled by kernel density estimation. Then the speed centers from the density function are modeled as clusters. The cumulative distribution function of the speed data is then determined by Kolmogorov--Smirnov test, whose complexity is less when compared to the other techniques and whose robustness is high when outliers exist. Then the mean values of clusters are estimated from the smoothed density function of the distribution function, followed by a peak detection algorithm. The estimates of variance values and kernel weights, on the other hand, are found by a nonlinear least square approach. As the estimation problem has linear and nonlinear components, the nonlinear least square with separation of parameters approach is adopted, instead of dealing with a high complexity nonlinear equation. Simulations are carried out in order to assess the performance of the proposed approach. It is observed that the error between cumulative distribution functions is less than $1\% $, an indication that the traffic densities are estimated accurately. For an assumed traffic condition that bears five speed clusters, the minimum mean square error of kernel weights is found to be less than 0.00004. The proposed approach was also applied to real data from sample road traffic, and the speed center and the variance were accurately estimated. By using the proposed approach, accurate traffic density estimation is realized, providing extra information to the municipalities for better planning of their cities.

Keywords: Traffic density estimation, kernel density estimation, Kolmogorov-Smirnov tests, nonlinear least square

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