# A Real-Time On-Orbit Signal Tracking Algorithm for GNSS Surface Observations
## 6 Results: Statistical Geographic Performance Validation and Analysis of Resource Requirements
### Performance Evaluation Using On-Orbit CYGNSS Data  
The key evaluation parameters of the open loop tracker performance were the achieved accuracies of the predicted delay code phase and Doppler frequency. A total of 55 individual satellite days from the CYGNSS observatories was analyzed. For this statistical evaluation, the predicted code phase and Doppler from the tracking algorithms are compared with the precise estimates of delay and Doppler derived from the actual CYGNSS measurements. By processing a large set of CYGNSS data these errors can be mapped geographically to assess the algorithms performance as a function of location and geometry. The spatial distribution of the mean open loop tracking delay errors shown in Figure 7.  
Additionally, we will analyze the processing required using the same CYGNSS data set. The dominant resource demand in the tracking algorithm is during the estimation of the surface specular point location. However, the speed of the specular point estimation algorithm can be controlled by adjusting the correction factor \(K\) in Equation (7). The second key parameter determining convergence is the tolerance applied to the solution accuracy. In order to assess the performance of the specular point estimator and the resulting open loop tracking errors, the algorithm was tested using 35 total satellite days worth of CYGNSS data, providing repeated measurements over the CYGNSS coverage extent. The spatial distribution of the mean number of iterations in the specular point solution are shown in Figure 8.  
Figure 7: Open loop tracking errors in delay distributed spatially. Errors correspond to known variations between the Earth’s true surface and the WGS84 ellipsoid.  
The optimal configuration of the specular point estimation was determined by gradually increasing the value of the feedback gain \(K\) with respect to a predetermined tolerance _tol_ value which resulted in acceptable delay tracking error (based on the maximum path variation over the ellipsoid for a given Snell angle error). Table 1 shows the values of \(K\) and _tol_ and the resulting mean and max open loop tracking delay error and number of iterations. Notably, the specular point solution converged 100% of the time over the complete data set.  
For the configuration listed in Table 1, convergence results in maximum delay tracking errors of less than 0.56 chips in all cases, with mean errors of 0.13 chip globally. The mean Doppler error globally was 78 Hz, with a maximum error of 376 Hz (within the 500 Hz Doppler bin limit as per CYGNSS requirement).  
Essentially K acts as a linear feedback scale factor and the larger it is the faster the convergence of the solution, but with an important caveat: if the K is too large (with respect to the Snell angle tolerance), the solution will oscillate around the true specular point and not converge. Therefore, the tolerance must be small enough to represent a specular point region which results in low tracking errors, but not be too small as to require a small K factor to assure robust convergence.  
The number of iterations acts as a proxy for estimating the required computer resources. However, the actual computation time will depend on the specific computer configuration and is not explored in detail here.