# Transit Traffic Filtration Algorithm from Cleaned Matched License Plate Data
## 2 Literature Review  
The first references to the utilization of outlier filtering techniques to acquire valid travel time measurements in matched license plate data were made in 1983. [PERSON] [4] proposed a median and quartile statistic, mentioning that it is more robust to the detection of outliers than the mean and standard deviation. [PERSON] and [PERSON] [5] used a two-step process to eliminate outliers while researching variability in travel time on Leeds's arterial roads. In the beginning, a high cutoff value was established to remove any extreme values. Subsequently, median and quartile measures were applied to the cropped data to create a confidence interval in which valid travel time observations could be found. The main conclusion of this study was the necessity to effectively remove outliers from travel time data for their effective analysis. [PERSON] et al. [6] followed up on previous research by summarizing three statistical approaches to filtering travel times obtained from matched license plate data and aggregated in 5 min intervals. The first approach is based on the use of the first and ninth deciles to identify outlying travel times. The second involves the use of the mean absolute deviation (MAD) test. Travel times are considered valid if they are located within a confidence interval, which is set to be three times the MAD in the evaluated time period. However, [PERSON] and [PERSON] [7] argued that '_mean absolute deviation is sensitive to the presence of outliers, it may be preferable to use a more robust measure of range_, _such as the interquartile range_'. The final approach proposed a standardized normal z- or t-test using the median and quartile deviation. This approach uses a series of correction factors, as the standard tabulated multipliers are not appropriate, as variance of the median is not the same as that of the mean. [PERSON] et al. [6] discuss that the percentile approach is too extreme, since it always classifies 20% of the data as outliers. The MAD and the standardized test produce a similar percentage of detected outliers, but the standardized test is considered more robust to outliers. [PERSON] and [PERSON] [8] discuss the use of outlier detection methods in systems that provide travelers with real-time travel time estimates. Such systems include the TranStar system in Houston [9], the TransGuide system in San Antonio [10], or the Transmit system in the New York metropolitan area [11]. [PERSON] and [PERSON] [8] suggested that existing methods do not take into account sudden changes in travel times, so they proposed two versions of a low-pass filtering algorithm to estimate the average travel time on road links. This technique assumes that the travel times in the 5 min intervals have a log-normal distribution. The first version of the algorithm uses the mean and standard deviation to create a confidence interval in which the valid travel times are located. In addition to the aforementioned methods, [PERSON] and [PERSON] extended the method in the second version by considering that the third of three consecutive travel time observations is valid if the three observations are either above or below the range of the constructed confidence interval. [PERSON] and [PERSON] [7] proposed an overtaking rule method to clean matched license plate data. This approach is based on the assumption that vehicles with valid travel time are unlikely to pass on a single-lane road, and if on a multilane road, the difference in travel time between itself and the overtaking vehicles would not be too great. [PERSON] and [PERSON] used Vissim, a micro-simulation software, to collect their travel time data, which allowed them to calculate the population mean and standard deviation of valid travel times. However, the method is highly dependent on a parameter called tolerance time, which is hard to obtain since one is required to know the distribution of valid travel times. [PERSON] and [PERSON] [7] state that as the tolerance time increases, the number of vehicles falsely classified as valid will increase.