# Performance Analyses of a RAIM Algorithm for Kalman Filter with GPS and NavIC Constellations
## 6 Simulation Studies  
In this section, various aspects of KF RAIM are analyzed using simulated GPS L1 and NavIC L5 signals for aircraft flight. For this purpose, a GNSS simulator from Accord Software and Systems is used [38]. It has a provision to load GPS and NavIC Yuma files, and configure user motion profiles and required error models (e.g., ionospheric and tropospheric errors). In the simulation, the ionospheric error is modeled by the Klobuchar model and the tropospheric error by RTCA98 [31]. Simulated signals are received by an IFEN receiver front end and digitized at 20 MHz. Stored 20 MHz IF data are processed by a developed GPS L1-NavIC L5 software receiver. Figure 4 shows the signal simulation and data collection setup. Performance is first analyzed in detail for a segment of an aircraft flight path during descent and approach, which is illustrated in Figure 5 along with GPS-NavIC satellite visibility.  
Figure 4: GNSS signal simulation and data collection setup.  
The IF data processing block diagram is depicted in Figure 6. A GPS L1-NavIC L5 software radio is developed in Matlab to perform all receiver operations. Following acquisition, it implements tracking of the visible satellites in parallel processing mode to speed up computation time. Tracking outputs are then sent to the navigation filter to estimate user position, velocity, and time. Relevant RAIM inputs are passed from the filter to the multi-constellation KF or WLS RAIM algorithm to carry out fault detection and PL computation.  
The receiver removes the ionospheric error using the Klobuchar model but uses a different model (modified Hopfield [39]) for the tropospheric error. The residual zenith tropospheric error is represented by an FOGM process in the navigation filter with a zero mean, standard deviation of 0.2 m, and time constant of 25 h. It bounds the actual error in the simulated measurements. There is no residual ionospheric error. Satellite orbit  
Figure 5: Simulated aircraft trajectory and skylpot of visible GPS and NavIC satellites. Aircraft height is shown above the WGS84 reference ellipsoid. In the skylpot, the circle marks the final position of a satellite in the trace. ‘G’ is for GPS, and ‘N’ is for NavIC.  
Figure 6: IF data processing block diagram.  
and clock error and multipath were not included in the simulation. They are, however introduced in the carrier-smoothed pseudorange measurements following the respective FOGM models. As a result, with each run, different positioning error results can be obtained. Range rate measurements, on the other hand, are generated from the Doppler frequencies of the carrier phase tracking loops. Only white noise with standard deviations obtained from the tracking loops of the receiver is modeled for range rate measurements. \(\mathcal{K}_{\text{min}}\) for KF RAIM is taken as 0.75\({}^{2}\) to be over conservative (see after Equation (34)).  
There is a provision for three different navigation filters in the receiver: WLS, SKF, and full-state EKF. WLS estimates error in the a priori ECEF position and velocity of the aircraft, and the receiver clock offsets and drifts for GPS and NavIC from respective truths. It calculates the measurement error standard deviation considering the residual tropospheric error, URA, multipath, and noise. Full-state EKF and SKF estimate error in the a priori acceleration states of the aircraft in ECEF apart from those mentioned for WLS. In addition, the full-state EKF estimates three states for the measurement error of each visible satellite (residual zenith tropospheric error, satellite clock and orbit error, and multipath and noise) using the corresponding FOGM models. The measurement update interval is 1 s. EKF and SKF position estimation errors in the NED frame and carrier-smoothed pseudorange measurement innovations are shown in Figure 7 for a simulation run. As the SKF treats residual errors, multipath, and noise as \"consider parameters\", its innovations remain biased, as opposed to those of full-state EKF.