# A High-Efficiency Method of Mobile Positioning Based on Commercial Vehicle Operation Data
## 3 High-Efficiency Mobile Positioning Method
### Pre-Deployment Stage
#### 3.1.1 Input Data  
Input data are CVO data. Each record of CVO data includes the longitude Hive and latitude of an OBU, the ID of the current connected cell, and the RSSI of the connected cell. Each OBU can periodically send CVO data (_i.e._, longitude and latitude of the OBU, the ID of the current connected cell, and the RSSI of the connected cell) to CVO servers every 30 s. The RSSI and cell ID are paired and called the cell-RSSI pair. For example, the cell ID is presented as 10721_47366 when location area code (LAC) is 10721 and service area code (SAC) is 47366. The cell-RSSI pair is presented as 10721_47366_21 when the cell ID is 10721_47366 and the RSSI is \(-\)21 dBm [33].  
The notations of this study are summarized below:  
* There are \(n\) cells in CVO data, and the RSSI range of each cell is between 0 and \(m\) dBm. Therefore, there are \(n\)\(\times\)\(m\) cell-RSSI pairs, and all cells have the same RSSI range.
* The number of records of the \(i\)-th cell-RSSI pair is defined as \(r_{i}\).
* The longitude of the \(j\)-th record of the \(i\)-th cell-RSSI pair is defined as \(x_{ij}\), and the latitude of the \(j\)-th record of the \(i\)-th cell-RSSI is defined as \(y_{ij}\).
* The mean of \(x_{ij}\) is defined as \(\mu_{x,i}\), and the mean of \(y_{ij}\) is defined as \(\mu_{y,i}\).
* The standard deviation of \(x_{ij}\) is defined as \(\sigma_{x,i}\), and the standard deviation of \(y_{ij}\) is defined as \(\sigma_{y,i}\).
* After outlier filtering, the number of records of the \(i\)-th cell-RSSI pair is defined as \({r_{i}}^{{}^{\prime}}\).
* After outlier filtering, the longitude of the \(j\)-th record of the \(i\)-th cell-RSSI pair is defined as \({x_{ij}}^{{}^{\prime}}\), and the latitude of the \(j\)-th record of the \(i\)-th cell-RSSI is defined as \({y_{ij}}^{{}^{\prime}}\).
* The mean of \({x_{ij}}^{{}^{\prime}}\) is defined as \({\mu_{x,i}}^{{}^{\prime}}\), and the mean of \({y_{ij}}^{{}^{\prime}}\) is defined as \({\mu_{y,i}}^{{}^{\prime}}\).
* The longitude of the \(i\)-th cell-RSSI pair \(x_{i}\) is assumed to be normally distributed with mean \(\mu_{x,i}\) and standard deviation \(\sigma_{x,i}\). The probability density function (PDF) of its normal distribution is defined as \(f\left({x_{i}},{\mu_{x,i}},{\sigma_{x,i}}\right)=\frac{1}{{\sigma_{x,i}}\sqrt {2\pi}}e^{-\frac{{\left({x_{i}}-{\mu_{x,i}}\right)^{2}}}{{2{x_{i}}^{2}}}}\)[33,34].
* The latitude of the \(i\)-th cell-RSSI pair \(y_{i}\) is assumed to be normally distributed with mean \(\mu_{y,i}\) and standard deviation \(\sigma_{y,i}\). The PDF of its normal distribution is defined as \(f\left({y_{i}},{\mu_{y,i}},{\sigma_{y,i}}\right)=\frac{1}{{\sigma_{y,i}}\sqrt {2\pi}}e^{-\frac{{\left({y_{i}}-{\mu_{y,i}}\right)^{2}}}{{2{y_{i}}^{2}}}}\)[33,34].  
A study of cell-RSSI pair 10721_47366_21 helps to evaluate the assumptions of longitude and latitude distributions. The historical location data of this cell-RSSI pair were collected by the CVO system of Chunghwa Telecom from November 2013 to January 2014. The cumulative distribution functions (CDFs) of longitudes and latitudes based on 13,231 historical records were calculated and are illustrated in Figure 1. The chi-square goodness of fit test [26,35,36] is used to evaluate the distributions of practical data and normal distribution. Chi-square tests of these assumptions showed that \(\chi^{2}=0.653<\chi^{2}_{11,0.05}=19.675\) when \(\alpha=0.05\) for the longitude distribution and\(\chi^{2}=0.414<\chi^{2}_{11,0.05}=19.675\) when \(\alpha=0.05\) for the latitude distribution. No significant difference was observed, so the distributions of longitude and latitude were similar to normal distributions.