Adjustment of sampling locations in rail‐geometry datasets: Using dynamic programming and nonlinear filtering

Abstract

AbstractA track inspection car, which measures the shape of railway tracks (hereafter, rail geometry) while it is running on rails, discretizes the measurement results at nearly fixed spatial intervals. However, the distance between the discretized locations (spatial sampling intervals) may shorten or lengthen locally due to slipping or sliding of the car wheel, and this prevents the sampling locations from aligning with those of a dataset obtained with another measuring run. The authors developed an algorithm for approximately aligning the sampling locations of the measurement datasets obtained with different runs. First, they considered this problem as the selection of the series of data corresponding to each supervised data from a training dataset, which was constructed by interpolation in order to minimize the evaluation function of a number sequence representing data points. Next, they used the maximum likelihood method to identify the unknown parameters contained in the evaluation function. This problem uses two features of the evaluation function. The first is that the evaluation function is minimized by dynamic programming, and the obtained optimum sequence is equivalent to a maximum a posteriori (MAP) estimate in the Bayesian framework. The second is that by converting the evaluation function to a general state space representation, the log likelihood of the model that includes the parameters is obtained by a nonlinear filtering method. Also, to simplify the search for the identification, they devised a parameter search procedure for the parameters in the autoregressive (AR) model. © 2005 Wiley Periodicals, Inc. Syst Comp Jpn, 37(1): 61–70, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.20313