# Complete Systematic Error Model of SSR for Sensor Registration in ATC Surveillance Networks
## 8 Conclusions  
A complete model for radar biases in ATC has been developed in the paper considering both mechanical errors in the radar installation and errors in the physical propagation and atmospheric parameters. Typically only a basic bias model is considered in bias estimation and correction. As has \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **RMS Error** \\ \hline Without correction & 532.45 m \\ \([\Delta\rho,\alpha_{1},\Delta\theta]\) (basic model) & 286.60 m \\ \([\Delta\rho,\alpha_{1},\Delta\theta,s_{ant},\beta_{axis},\alpha_{axis}]\) & 260.65 m \\ \([\Delta\rho,\alpha_{1},\Delta\theta,s_{enc},\alpha_{enc},\Delta R/R,\ a_{ecc}]\) & 248.22 m \\ \([\Delta\rho,\alpha_{1},\alpha_{2},\alpha_{3},s_{ant},s_{axis},\alpha_{axis}, \Delta\theta,s_{enc},\alpha_{enc},\Delta R/R,\ a_{ecc},\Delta H_{p},\Delta T]\) & 242.19 m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Bias error deviation for different configuration of the model parameters. Figure 18: (**a**) Straight trajectory (**b**) Take off trajectory corrected with basic model (**c**) Several trajectories allocated at the upper-right corner of the scenario corrected with the complete model. been demonstrated with our results, with these simplified model parameters the major part of the errors can be corrected. In real scenarios the errors of the measures cannot be approximated only with the basic bias model. In online applications where the execution time is an important feature, the simple model reduces the major part of the errors. In offline applications (such as [30]) where the accuracy of the estimations is more relevant than the execution time, the number of estimated parameters can be increased reducing the final bias error. As the number of parameters is increased, the degrees of freedom to interpolate generic bias patterns is increased too. The bias estimation methods in general minimize the MSE and are better adjusted where the traffic density is bigger. With the basic model the biases are only adjusted to these higher density areas, leaving lower traffic density with badly corrected measures. With the complete biases model there are more degrees of freedom and the estimations will be better adjusted for areas where there is lower density. Analyzing the results using different bias configurations (estimation with different bias parameters) it can be observed that the basic biases will correct the major part of the systematic errors. The encoder eccentricity has a significant effect on the azimuth that does not depend on the target elevation and the use of this parameter will align the plots better than with the simple model. Also, trajectories near to one of the radars are highly affected by altitude errors. For future work two topics derived from this paper can be studied. On the one hand the distribution of the plots seems to be an important topic. An estimation method will be studied in order to try to make the density of the plots in a given area not so critical for the precision of the estimations. On the other hand, the parametrized model developed in this paper assumes that the atmospheric conditions are constant in all the airspace but the temperature and pressure at MSL change slowly with position. In the future we will also study the extension of the model with slow changing curves for pressure and temperature, and the potential associated improvements. Also, the estimation of transponder error, maybe exploiting ideas similar to the ones in [8] will be addressed. The research has been partially funded by UPM's project 'Tecnologias Avanzadas para la Monitorizacion y Gestion Remota del Trafico Aereo de Vehiculos Pilotados y no Pilotados' (RP1509550C02), by FUNDETEL project 'Tecnologias y Sistemas de Control y Gestion de Trafico Aereo' (GPDSJC.001), and by the Spanish Ministry of Economy and Competitiveness through grant TEC2014- 57022-C2-1-R.  
[PERSON] and [PERSON] performed the main part of the work-definiton of the bias model, design of estimation algorithms and proofs.