MULTILANE TRAFFIC DENSITY ESTIMATION AND TRACKING

As the number of vehicles in roads increases, information of traffic density becomes crucial to municipalities for making better decisions about road management and to the environment for reduced carbon emission. Here, the problem of traffic density estimation is addressed when there is continuous influx of vehicle data. First the traffic density is modeled by the clusters of the speed groups that are centered after Kernel Density Estimation technique is implemented for the probability density function of the speed data. Then, empirical cumulative distribution function of data is found by Kolmogorov-Smirnov Test. A peak detection algorithm is used to estimate speed centers of the clusters. Since the estimation model has linear and non-linear components, the estimation of variance values and kernel weights are found by a nonlinear Least Square approach with separation of parameters property. Finally, the tracking of former and latter estimations of a road is calculated by using Scalar Kalman Filtering with scalar state - scalar observation generality level. For all example data sets, the minimum mean square error of kernel weights is found to be less than 0.002 while error of mean values is found to be less than 0.261.

Keywords:

Traffic Density, Kernel Density Estimation, Kolmogorov-Smirnov Test Nonlinear Least Square, Scalar Kalman Filter.,

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[1] Laxhammar R., Falkman G., and Sviestins E., “Anomaly Detection in Sea Traffic - A Comparison of the Gaussian Mixture Model and the Kernel Density Estimator,” in Information Fusion, 2009, 12th International Conference on, July 2009, pp. 756–763.
[2] Murphy K. P., Machine Learning: A Probabilistic Perspective, MIT press, 2012.
[3] Tabibiazar A. and Basir O., “Kernel-Based Optimization for Traffic Density Estimation in ITS,” in Vehicular Technology Conference (VTC Fall), 2011 IEEE, Sept 2011, pp. 1–5.
[4] Yılan M. and Özdemir M. K., “Traffic Density Estimation via KDE and Nonlinear LS [submitted, pending],” in Turkish Journal of Electrical Engineering & Computer Sciences, 2016.
[5] Yılan M. and Özdemir M. K., “A Simple Approach to Traffic Density Estimation by using Kernel Density Estimation,” in Signal Processing and Communications Applications Conference (SIU), 2015 23th, May 2015, pp. 1865–1868.
[6] Jӓntschi L., Bolboaca S. D. et al., “Distribution Fitting 2. Pearson-Fisher, Kolmogorov-Smirnov, Anderson-Darling, Wilks-Shapiro, Kramer-von-Misses and Jarque-Bera statistics,” Bulletin UASVM Horticulture, vol. 66, no. 2, pp. 691–697, 2009.
[7] Kay S. M., Fundamentals of Statistical Signal Processing: Estimation Theory, Pearson Education, 2013, vol. 1.
[8] Botev Z. I., Grotowski J. F., Kroese D. P. et al., “Kernel Density Estimation via Diffusion,” The Annals of Statistics, vol. 38, no. 5, pp. 2916–2957, 2010.
[9] Xie Z. and Yan J., “Kernel Density Estimation of Traffic Accidents in a Network Space,” Computers, Environment and Urban Systems, vol. 32, no. 5, pp. 396–406, 2008.
[10] Djuric P. and Miguez J., “Model Assessment with Kolmogorov-Smirnov Statistics,” in Acoustics, Speech and Signal Processing, 2009, ICASSP 2009, IEEE International Conference on, April 2009, pp. 2973–2976.
[11] Song S., Lim J.-S., Baek S., and Sung K.-M., “Gauss Newton Variable Forgetting Factor Recursive Least Squares for Time Varying Parameter Tracking,” Electronics Letters, vol. 36, no. 11, pp. 988–990, May 2000.
[12] Vahidi A., Stefanopoulou A., and Peng H., “Recursive Least Squares with Forgetting for Online Estimation of Vehicle Mass and Road Grade: Theory and Experiments,” Vehicle System Dynamics, vol. 43, no. 1, pp. 31–55, 2005.
[13] DoD U., “Global Positioning System Standard Positioning Service Performance Standard,” Assistant Secretary of Defense for Command, Control, Communications, and Intelligence, 2008.
[14] Munoz L., Sun X., Horowitz R., and Alvarez L., “Traffic Density Estimation with the Cell Transmission Model,” in American Control Conference, 2003. Proceedings of the 2003, vol. 5, June 2003, pp. 3750–3755 vol.5.
[15] Sun X., Munoz L., and Horowitz R., “Highway Traffic State Estimation using Improved Mixture Kalman Filters for Effective Ramp Metering Control,” in Decision and Control, 2003. Proceedings, 42nd IEEE Conference on, vol. 6, Dec 2003, pp. 6333–6338 Vol. 6.