An Effective Method for Checking Consistency in Univariate Data-series with Multiple, Incomplete and Inconsistent Entries

Univariate time series is utilized in numerous scientific applications for a variety of purposes. They serve as the foundation for different statistical measurements and show how data evolves over time when viewed independently as real-time data series. Furthermore, binary data sets are frequently utilized in various fields, including health sciences, where each observation results in either a positive or negative outcome. The primary uses of time series analysis include: (a) Predicting future trends; (b) Determining characteristics like average, range, and standard deviation to comprehend the data's behavior; (c) Examining variations in means and variances among multiple time series using statistical methods like t-tests, F-tests, and Anova; and (d) Contrasting multiple time series to identify point-to-point discrepancies using different measures like root mean square error. This article suggests a straightforward yet successful method for comparing data from various time series that are not synchronized, have gaps in data, and require determining the error of the best match to ensure it falls within an acceptable range. We utilize this method for a challenging railway engineering issue to verify the consistency of laser and inertial sensor measurements within a specified error range.