# Transit Traffic Filtration Algorithm from Cleaned Matched License Plate Data
## 2 Literature Review
[PERSON] et al. in [12] introduced an algorithm based on the fuzzy c-line clustering method developed by [PERSON] [13]. The algorithm assigns a measure of membership to each travel time observation, which is then used to create a fuzzy line prototype. The weighted average of travel times is then calculated, with the weight being the degree of membership in the fuzzy line prototype. Nevertheless, a prior knowledge of outliers' values is required as input to this algorithm, rather than a result which is in contradiction to this study. [PERSON] and [PERSON] [14] used data from a Bluetooth detector instead of matching license plates to develop an outlier detection algorithm. Since license plates are used as unique vehicle identifiers, the use of the MAC address of the Bluetooth device seems viable. The proposed algorithm is based on creating a confidence interval that is determined by the expected mean and standard deviation in the current time interval evaluated, as well as the distribution of individual travel times in the preceding time interval. This leads to a complex quasi-prediction process to evaluate the expected mean and standard deviation based on the latest available travel time estimates. In 2016, [PERSON] [15] proposed an algorithm that evaluates the number of observations in the current time interval and then determines the confidence interval based on the previous time interval or the current. The algorithm utilizes the median absolute deviation to construct the confidence interval if the number of observations is greater than three. If the number of observations is not enough, the algorithm uses the confidence interval created from the previous time interval. Although similar to the [PERSON] et al. [6] MAD test, this approach introduces a new element by comparing the medians obtained from the current and previous time intervals to form the confidence interval. The weakness of this approach is the dependence on a large number of user-defined parameters, creating the necessity for robust manual calibration [16]. Finally, [PERSON] et al. [17] employed a wavelet analysis technique to clean the travel times acquired from the matched license plate data. This technique used Daubechies wavelets at level 4 to identify the approximation and detail coefficients. These coefficients were then used to reconstruct travel time series, which were further compared to the travel time data obtained. An observation of travel time was considered an outlier if the difference between the obtained and reconstructed travel times was larger than the standard deviation of these differences in the entire data set. [PERSON] et al. [17] discussed that this approach could depend on the type of wavelet or the level of decomposition. Despite advances, each method has its own set of assumptions, advantages, and disadvantages, summarized in Table 1. Based on a comprehensive analysis of existing methodologies, a critical need arises for a new algorithm that universally addresses a wide variety of travel time scenarios and enables the classification of through traffic without an extensive calibration process for each measurement site. Although the analyzed algorithms present a fairly powerful method to unravel the true underlying travel time on the analyzed routes, they are not free from certain drawbacks. Firstly, all of them aim to filter travel time by disregarding positive and negative outliers. This, in a natural way, assumes that there is some statistical mean value of the time needed to travel from the origin to the destination. As a consequence, vehicles traveling faster and slower than this mean value (and some tolerance value) are treated as error values (outliers). This approach is invalid for transit traffic filtration (identification and removal of vehicles traveling with some mid-stop between origin and destination), as it also eliminates vehicles that travel faster. By assumption, transit traffic has to travel slower. This difference in the philosophy of outlier treatment seems straightforward but has far-reaching consequences.