# Intelligent Environment-Adaptive GNSS/INS Integrated Positioning with Factor Graph Optimization
## 3 Adaptive GNSS Uncertainty Estimation by CNN
### Features Related to GNSS Measurement Quality  
During each available epoch, the eight proposed features that are discussed in the following will be extracted and then utilized as the inputs for the subsequent CNN model.  
* **Feature 1: Ratio of number of received satellite signals to the total number of available satellite signals** The ephemeris data obtained from reference stations provides the PRN codes of all existing satellites in the sky. However, the received satellite number is always lower due to the blockage of GNSS signals by buildings. Therefore, the ratio of the number of received satellite signals to the total number of satellites in ephemeris data can indicate the obstruction level from buildings (i.e., the measurement quality).
* **Feature 2: Mean elevation angles of satellites** Research [42] has shown that when the elevation angle of a transmitter is lower than 15 degrees, 97% of the signals are blocked by the buildings in an urban environment. Signals are less likely to be blocked or reflected by buildings with high elevation angles, thus proving the mean elevation angle to be a critical feature for filtering NLOS signals.
* **Feature 3 and 4: Mean and standard deviation of carrier-to-noise Ratio \(C/N_{0}\)** \(C/N_{0}\) represents the received signal strength, which is largely attenuated by reflection and blockage. A higher value of mean \(C/N_{0}\) indicates less likelihood of an NLOS signal and thus better positioning performance. Given that the standard deviation shows the outlier signal, both the average and standard deviation of \(C/N_{0}\) among the satellites could be adopted as features to identify the signal quality in each epoch.
* **Feature 5 and 6: Mean and standard deviation of pseudo-range residuals** A pseudo-range residual is used to provide information about the fitness of the least squares method [43], and a smaller pseudo-range residual reveals higher consistency between the measurement and the estimated positioning results. The pseudo-range residual (\(\epsilon\)) is defined as the differences between the estimated pseudo-range (\(\hat{\rho}\)) and the measured pseudo-range (\(\rho\)). The equation is: \[\epsilon=\rho-\hat{\rho}=\rho-G\hat{x}\] (23) where \(G\) is a matrix consisting of the unit vector along LOS from user to satellites and \(\hat{x}\) is the converged state vector of users calculated by least squares estimation: \[\hat{x}=(C^{T}G)^{-1}G^{T}\rho\] (24)
* **Feature 7 and 8: Mean and standard deviation of pseudo-range rate consistency** Pseudo-range rate consistency is defined as the difference between the delta pseudo-range and the product of the pseudo-range rate and a unit time. Its mean and standard deviation can reflect the positioning performance of the receiver. The equation of pseudo-range rate consistency (\(\delta\)) is written as: \[\delta=\mid\Delta\rho_{t}^{i}-\hat{\rho}^{i}\cdot\Delta t\mid\] (25) Delta pseudo-range is the difference of the pseudo-range between two epochs, and it is measured through the code tracking loop. The equation is expressed as: \[\Delta\rho_{t}^{i}=\rho_{t}^{i}-\rho_{t-1}^{i}\] (26) The pseudo-range rate is computed using the Doppler shift as: \[\hat{\rho}^{i}=-\frac{c}{f_{L1}}\cdot f_{Doppler}^{i}\]where \(c\) is speed of light, \(f_{L1}\) is the GPS L1 band frequency (1575.42 MHz), and \(f_{Doppler}^{i}\) is the Doppler frequency obtained by the carrier tracking loop.