A GPS-based on-board orbit propagator for low earth-orbiting CubeSats
Rossouw, Nico Chris (2015-12)
ENGLISH ABSTRACT: On-board knowledge of satellite position is vital to all space missions. Due to the stringent power budgets of the CubeSat form factor, permanently active on-board GPS receivers for accurate navigation solutions are infeasible. Analytical techniques such as SGP4, which have been used since the 1970s, are often identified as the natural replacements. Unfortunately, due to inherent position errors of more than 1 km RMS, such techniques are unfit for some missions that prioritise precision. This emphasises the need for a new strategy for accurate on-board orbit determination and propagation. In an attempt to conserve power, it is proposed that the GPS receiver is activated intermittently such that a duty cycle of less than 15% (including the time-to-first-fix) is required. The orbit will be estimated during the activated period, after which navigation solutions will be obtained by means of propagation algorithms during the deactivated parts. Two approaches, one based on an analytical method and the other on numerical integration, are designed and implemented in the C programming language. These systems are simulated using actual on-board GPS datasets from SumbandilaSat and NigeriaSat missions. The analytical approach is based on SGP4. TLE parameter offsets are estimated by filtering the difference between the GPS and SGP4 output instantaneous Kepler elements, and an additional time offset is calculated for an in-track correction. Simulations revealed RMS and maximum 3D position errors of 200 m and 1 km, respectively, for a 12.5% duty cycle. The numerical approach employs an Extended Kalman Filter with a 4th order Runge-Kutta integrator for propagation. Reducing the propagator’s orbit dynamics model to only a 9th order JGM-3 geopotential and a Jacchia atmospheric density model for aerodynamic drag still produced fairly accurate results. Simulations revealed RMS and maximum 3D position errors of 60 m and 300 m, respectively, for a 10.7% duty cycle. The proposed system therefore delivers a remarkable accuracy improvement over standard analytical propagators at only a fraction of the power required by permanently active on-board GPS receivers.
AFRIKAANSE OPSOMMING: Dit is krities belangrik dat ’n satelliet ten alle tye kennis van sy eie posisie dra. Die streng kragverbruik begroting van ’n CubeSat veroorsaak dat akkurate navigasie d.m.v. ’n deurlopend geaktiveerde aanboord GPS ontvanger nie lewensvatbaar is nie. Analitiese metodes soos SGP4, wat al vanaf die 1970s gebruik word, is gewoonlik die naasbeste oplossing. Laasgenoemde se inherente wortel gemiddelde kwadraat (WGK) posisie afskattingsfoute van meer as 1 km is onaanvaarbaar vir sekere satelliet missies. ’n Nuwe strategie vir akkurate aanboord wentelbaan afskatting en voorspelling is dus nodig. Daar word voorgestel dat die GPS ontvanger sporadies aangeskakel word om krag te bespaar. ’n Dienssiklus van minder as 15% (met die tyd-tot-eerste-oplossing van GPS ontvanger ingesluit) word aanbeveel. Die wentelbaan sal gedurende die aangeskakelde periode afgeskat word, waarna algoritmes die posisie van die satelliet sal voorspel. Twee benaderings, een op ’n analitiese metode gebaseer en die ander een op numeriese integrasie, is ontwerp en in die C programmeringstaal geïmplementeer. Hierdie stelsels is gesimuleer met egte SumbandilaSat en NigeriaSat aanboord GPS data. Die analitiese metode is op SGP4 gebaseer. Aanpassingsveranderlikes vir die TLE parameters is bepaal deur die verskil tussen die GPS en SGP4 uittree se oombliklike Kepler elemente te gefiltreer. ’n Tydaanpassingsveranderlike is ook bereken om ’n finale in-spoor regstelling te maak. Simulasies het WGK en maksimum 3D posisiefoute van onderskeidelik 200 m en 1 km behaal met ’n 12.5% dienssiklus. Vir die numeriese benadering is ’n Uitgebreide Kalman Filter, met ’n 4de orde Runge-Kutta integreerder vir voorspelling, ontwikkel. Die dinamika model was beperk tot ’n 9de orde JGM-3 geopotensiaal en ’n Jacchia atmosferiese digtheidsmodel vir aërodinamiese sleur, en dit het steeds goeie resultate gelewer. Simulasies het WGK en maksimum 3D posisiefoute van onderskeidelik 60 m en 300 m behaal met ’n 10.7% dienssiklus. Die voorgestelde oplossing lewer dus ’n stelsel wat ’n merkwaardige akkuraatheid verbetering teenoor gewone analitiese metodes behaal teen slegs ’n fraksie van die kragverbruik van ’n deurlopend geaktiveerde aanboord GPS ontvanger.
Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/97908