My recent TRB paper employs a really simple circular fitting methods, i.e. Kasa’s method, to extract and measure the horizontal curves. This paper was motivated by the three-point method developed by Jeff Harpring at New Hampshire Department of Transportation (NHDOT), yet the robustness is dramatically improved. The philosophy behind this paper is straightforward. A roadway section consists of consecutive segments and is considered as the minimal unit sharing a unique radius. A curved segment has a radius of R, while a tangent segment has a radius of infinity. The objective of iterative circular fitting is to automatically partition the GPS trajectory data that represents the roadway into delineated segments. Each segment shares the same radius measurement. Instead of selecting a fixed number of neighboring points for fitting, an incremental number of neighboring points are attempted until arriving at the least fitting error. The number resulting in the least fitting error will be associated with this group of GPS points. The fitting error is measured by the fitness of the actual GPS points compared to the approximated circle. The error curve is monitored and recorded separately until the global minimum value is derived at among all the attempted iterations. Once the number of neighboring points is selected for the current group of GPS points, the next circular fitting will be started by skipping the current group of points. Hence, optimized numbers of GPS points are selected for each group of GPS points (i.e. segment) through iterations. Per the request from Tim from NHDOT, I post some sample codes of the iterative circular fitting in MATLAB for his assessment purpose [download].
Ai, C. and Tsai, Y. (2014). “An Automatic Horizontal Curve Radii Measurement Method for Roadway Safety Using GPS Data.” 93rd Transportation Research Board Annual Meeting, Washington D.C.
Later, this idea was further developed into a full technical paper that is recently published in the Journal of Transportation Engineering. Additional steps for identifying segment types, curve classification, and spiral curve update is added into the methodology. The detailed methods can be found in this paper. The sample codes for these additional steps will be released at a later time. Hopefully, this method can be of uses for researchers and agencies.
Ai, C. and Tsai, Y. (). “Automatic Horizontal Curve Identification and Measurement Method Using GPS Data.” J. Transp. Eng. ,10.1061/(ASCE)TE.1943-5436.0000740 , 04014078.