## 4 Results and Analyses
### Pedestrian Data in Urban Canyon
It can be observed from the above figures that the errors are smaller in the case of VB filters thus indicating the robustness of using the \(t\) distribution in environments with multipath laden GNSS measurements. The maximum horizontal error decreases by a factor of about 2.5 when using VB and VB Adaptive as compared to the standard filter. The accuracy seems to slightly degrade in the adaptive case. This is most likely due to subtle over-bounding of the assumed GNSS error distribution. Such over-bounding decreases the weight of the GNSS measurements. This de-weighting often leads to the dilution of unaffected measurements, thus degrading accuracy. However, the adaptive scheme leads to a highly reliable navigation solution as will be presented below. The above figures also include error plots for the GNSS only solution which was realized using an extended Kalman filter (EKF) that assumes a normal distribution for range and Doppler measurements. A standard residual based FDE was also implemented to detect and eliminate aberrant measurements. The error plots for the GNSS only solution gives an idea about the GNSS signal conditions in the test environment. It is observed from the above figures that there are few instances where the errors are in the range of around 200 m, thus leading to much higher RMSE as compared to the integrated GNSS/INS solutions. As discussed in Section 1, one of the most critical parameters for many applications using personal navigation devices is the reliability of the navigation solution. In this regard, the reliability of the navigation solution along the axes of the local plane for the three cases discussed above were computed as shown in Figure 11. It is observed that the reliability values are low for the standard filter. This is a common problem with standard Kalman filters, especially in integrated systems like GPS/INS, wherein the estimated accuracy of the navigation solution is often optimistic. However, the reliability values are found to improve with the VB filter and even further with the adaptive VB filter thus mitigating the problem of standard Kalman filters. These reliability results further indicate that, among the three filters, the adaptive VB filter best characterizes the true GNSS noise characteristics. Figure 10: **(a)** Horizontal errors (OEM6 + IMU)—urban canyon. **(b)** Vertical errors (OEM6 + IMU)—urban canyon. Avalability of GNSS measurements is another key parameter to be assessed in such signal deprived environment. Since the \(t\) distribution inherently tends to retain more measurements, the availability of GNSS measurements was found to increase when using the \(t\) distribution. The percentage of range measurements rejected by the FDE decreased from 0.78% to 0.51% when going from the standard filter to the adaptive VB filter. The standard approach identified 18% of the Doppler measurements as faults and subsequently rejected them. This indicates that the Doppler measurements had an optimistic variance associated with the observation in comparison to the internal solution. This statistic pointedly shows how the standard method is insufficient since the system is incapable of handling the increased variance in the degraded environment. The VB filter alternatively rejected only 0.26% of the Doppler measurements. If the personal navigation system is also required to provide GNSS integrity parameters such as horizontal and vertical integrity limit, then a certain minimum requirement in terms of GNSS measurement availability must be met. When using only GPS, as in this work, a minimum of 5 GPS measurements must be available. However, in signal challenged environments, the available GNSS measurements are often less than five due to signal masking. Moreover, improper assumption of measurement noise statistics can also add to this unavailability.