The topic of this thesis deals with the implementation of a dynamic propagator usable for satellites in LEO (low Earth-orbit) based on the mathematical model SGP4 (Simplified General Perturbation model #4). This model exploits the theory of Two-Line Elements as propagator initialization approach. The project was developed at Deimos Space S.L.U., an aerospace company based in Madrid, Tres Cantos. At the end of the work, the propagator was included in the existing Flight Dynamics infrastructure of the company and, once the reliability was consolidated by carrying out targeted tests on the code, it found a positive response and operability. The mathematical model underlying the project was developed in the 1960s. This made it possible to use for the first time a new format, called TLE format, which allowed to express the initial state of the satellite in analysis and with which the model itself is initialized. From the model, it is possible to predict the position and velocity of the same satellite by providing a time interval. The TLE format was created by the North Aerospace Defense Command (NORAD) and called Two Line Elements (TLE) because of its specific format, composed by two lines containing all the necessary information to express the state of a satellite and to identify it. The use of the SGP4 model involves errors on the order of kilometers with respect to the real satellite orbit and implies an increment of 1 ÷ 2 kilometers per day. Despite these results may seem unreasonable with respect to what can be achieved today using a high-precision orbital propagator (HPOP), SGP4 is nowadays used because of its simplicity and computational efficiency. The work developed and the actual application is proof of this. The purpose of this document is to explain how the propagator was developed in compliance with the imposed requirements. The latter are partially set up to fit the software into the Flight Dynamics infrastructure above mentioned. The basic requirement is that it should be developed applying an object-oriented programming (OOP) approach. A SGP4 propagator, therefore based on the same mathematical model, was developed in the past by David Vallado using a functional programming approach. This was used as a reference software both to consolidate the knowledge inherent to the SGP4 model and above all to obtain reference values utilized to validate the developed software. The first chapter of this document is an introductory chapter which mainly deals with the state of the art, considered as the starting point from which the work was carried out, and the purpose and scope that has been sought to be achieved. Chapter 2 introduces all the useful concepts to facilitate the reader in understanding the elaborate. In addition, the SGP4 mathematical model is presented, highlighting the particularities and the steps to follow. The software architecture is presented in Chapter 3, starting with the architecture analysis of the reference software, which paves the way to the OOP TLE Propagator architecture, that represents the core of the section. Following the structure implemented, in Chapter 4 the tests carried out to validate the code are discussed. Finally, the possible applications to which the developed software could be submitted have been presented in Chapter 5. As said, under the computation efficiency aspect, the SGP4 model is very performing. Indeed, due to the high performance of the SGP4 propagation theory, an important application is inherent to collision risk assessment. This propagation theory is used to compute the collision risk with a large number of objects provided in the TLE catalogue. Other relevant applications are the orbit determination and the generation of synthetic TLEs. The knowledge areas involved in this project are: Orbital Mechanics, Software Engineering and Development, Functional programming paradigm, Object-Oriented programming paradigm and C++ Language.
Questa tesi tratta l'implementazione di un propagatore dinamico utilizzabile per i satelliti in LEO (Low Earth-orbit) basato sul modello matematico SGP4 (Simplified General Perturbation model #4). Il modello sfrutta la teoria dei Two-Line Elements come approccio di inizializzazione del propagatore. Il progetto è stato sviluppato presso Deimos Space S.L.U., una compagnia aerospaziale con sede a Madrid, Tres Cantos. Alla fine del lavoro, il propagatore è stato incluso nell'infrastruttura di Flight Dynamics dell'azienda e, una volta consolidata l'affidabilità, eseguendo test mirati sul codice, ha trovato un responso positivo in campo operazionale. Il modello matematico alla base del progetto è stato sviluppato negli anni '60. Ciò ha reso possibile l’utilizzo, per la prima volta, di un nuovo formato, chiamato formato TLE, che esprime lo stato iniziale del satellite in analisi e con il quale viene inizializzato il modello stesso. Dal modello, è possibile prevedere la posizione e la velocità del satellite dopo aver fornito un intervallo di tempo. Il formato TLE è stato creato dal North Aerospace Defense Command (NORAD) e chiamato Two Line Elements (TLE) a causa del suo formato specifico, composto da due linee contenenti tutte le informazioni necessarie per definire lo stato di un satellite e identificarlo. L'uso del modello SGP4 comporta errori nell'ordine dei chilometri rispetto all'orbita reale del satellite e implica un incremento di 1 ÷ 2 chilometri al giorno. Nonostante questi risultati possano sembrare irragionevoli rispetto a ciò che può essere raggiunto oggi utilizzando un propagatore orbitale di alta precisione (HPOP), SGP4 è comunque largamente utilizzato per la sua semplicità ed efficienza computazionale. Il lavoro sviluppato e l'applicazione che ne consegue ne sono la prova. Lo scopo di questo documento è spiegare come il propagatore è stato sviluppato in conformità con i requisiti richiesti. Questi ultimi sono parzialmente imposti per adattare il software all'infrastruttura di Flight Dynamics sopra menzionata. Il requisito di base è che sia sviluppato applicando un approccio di programmazione orientata agli oggetti (OOP). Un propagatore SGP4, quindi basato sullo stesso modello matematico, è stato sviluppato in passato da David Vallado usando un approccio di programmazione funzionale. Quest’ultimo è stato utilizzato come software di riferimento sia per consolidare le conoscenze inerenti al modello SGP4 sia, soprattutto, per ottenere valori di riferimento utilizzati per validare il software sviluppato. Il primo capitolo di questo documento è un capitolo introduttivo che si occupa principalmente dello stato dell'arte, da considerarsi sia come punto di partenza per il lavoro svolto che l’obiettivo ultimo che si è cercato di conseguire. Il capitolo 2 introduce tutti i concetti utili per facilitare il lettore nella comprensione dell'elaborato. Inoltre, viene presentato il modello matematico SGP4 evidenziandone le particolarità e i passaggi da seguire. Il software sviluppato è presentato nel capitolo 3 partendo dall'analisi dell'architettura del software di riferimento. Questo è necessario per la comprensione del OOP TLE Propagator, che rappresenta il nucleo della sezione. Seguendo la struttura implementata, nel Capitolo 4 vengono discussi i test effettuati per validare il codice. Infine, le possibili applicazioni per le quali il software sviluppato potrebbe essere utilizzato sono state presentate nel Capitolo 5. Come detto, sotto l'aspetto dell'efficienza computazionale, il modello SGP4 è molto performante. Infatti, grazie alle elevate prestazioni della teoria di propagazione SGP4, un'applicazione importante è inerente alla collision risk assessment. Questa teoria viene utilizzata per calcolare il rischio di collisione con un gran numero di oggetti forniti dal catalogo TLE. Altre applicazioni rilevanti sono la determinazione dell'orbita e la generazione di TLE sintetici. Le aree di conoscenza coinvolte in questo progetto sono: Meccanica orbitale, Ingegneria e sviluppo software, paradigma di programmazione funzionale, paradigma di programmazione orientata agli oggetti e linguaggio C ++.
Development of SGP4 propagator using object-oriented programming
D'ANDREA, BIAGIO
2019/2020
Abstract
The topic of this thesis deals with the implementation of a dynamic propagator usable for satellites in LEO (low Earth-orbit) based on the mathematical model SGP4 (Simplified General Perturbation model #4). This model exploits the theory of Two-Line Elements as propagator initialization approach. The project was developed at Deimos Space S.L.U., an aerospace company based in Madrid, Tres Cantos. At the end of the work, the propagator was included in the existing Flight Dynamics infrastructure of the company and, once the reliability was consolidated by carrying out targeted tests on the code, it found a positive response and operability. The mathematical model underlying the project was developed in the 1960s. This made it possible to use for the first time a new format, called TLE format, which allowed to express the initial state of the satellite in analysis and with which the model itself is initialized. From the model, it is possible to predict the position and velocity of the same satellite by providing a time interval. The TLE format was created by the North Aerospace Defense Command (NORAD) and called Two Line Elements (TLE) because of its specific format, composed by two lines containing all the necessary information to express the state of a satellite and to identify it. The use of the SGP4 model involves errors on the order of kilometers with respect to the real satellite orbit and implies an increment of 1 ÷ 2 kilometers per day. Despite these results may seem unreasonable with respect to what can be achieved today using a high-precision orbital propagator (HPOP), SGP4 is nowadays used because of its simplicity and computational efficiency. The work developed and the actual application is proof of this. The purpose of this document is to explain how the propagator was developed in compliance with the imposed requirements. The latter are partially set up to fit the software into the Flight Dynamics infrastructure above mentioned. The basic requirement is that it should be developed applying an object-oriented programming (OOP) approach. A SGP4 propagator, therefore based on the same mathematical model, was developed in the past by David Vallado using a functional programming approach. This was used as a reference software both to consolidate the knowledge inherent to the SGP4 model and above all to obtain reference values utilized to validate the developed software. The first chapter of this document is an introductory chapter which mainly deals with the state of the art, considered as the starting point from which the work was carried out, and the purpose and scope that has been sought to be achieved. Chapter 2 introduces all the useful concepts to facilitate the reader in understanding the elaborate. In addition, the SGP4 mathematical model is presented, highlighting the particularities and the steps to follow. The software architecture is presented in Chapter 3, starting with the architecture analysis of the reference software, which paves the way to the OOP TLE Propagator architecture, that represents the core of the section. Following the structure implemented, in Chapter 4 the tests carried out to validate the code are discussed. Finally, the possible applications to which the developed software could be submitted have been presented in Chapter 5. As said, under the computation efficiency aspect, the SGP4 model is very performing. Indeed, due to the high performance of the SGP4 propagation theory, an important application is inherent to collision risk assessment. This propagation theory is used to compute the collision risk with a large number of objects provided in the TLE catalogue. Other relevant applications are the orbit determination and the generation of synthetic TLEs. The knowledge areas involved in this project are: Orbital Mechanics, Software Engineering and Development, Functional programming paradigm, Object-Oriented programming paradigm and C++ Language.| File | Dimensione | Formato | |
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https://hdl.handle.net/10589/164715