Orbital Elements Ephemerides and Interfaces Design of LEO Satellites

doi:10.11947/j.JGGS.2019.0405

Abstract

Abstract:

Low earth orbit satellites, with unique advantages, are prosperous types of navigation augmentation satellites for the GNSS satellites constellations. The broadcast ephemeris element needs to be designed as an important index of the augmented LEOs. The GPS ephemerides of 16/18 elements cannot be directly applied to the LEOs because of the poor fitting accuracies in along-track positional component. Besides, the ill-conditioned problem of the normal-matrix exists in fitting algorithm due to the small eccentricity of the LEO orbits. Based on the nonsingular orbital elements, 5 sets of ephemerides with element numbers from 16 to 19 were designed respectively by adding or modifying orbital elements magnifying the along-track and radial positional components. The fitting experiments based on the LEO of 300 to 1500km altitudes show that the fitting UREs of the proposed 16/17/18/18 ^*/19-element ephemerides are better than 10/6/4/5/2.5cm, respectively. According to the dynamical range of the fitting elements, the interfaces were designed for the 5 sets of ephemerides. The effects of data truncation on fitting UREs are at millimeter level. The total bits are 329/343/376/379/396, respectively. 29/15 bits are saved for the 16/17-element ephemerides compared with the GPS16 ephemeris, while 64/61/41 bits can be saved for the 18/18 ^*/19-element ephemerides compared with the GPS18 elements ephemeris.

Key words: LEO satellites; broadcast ephemeris; nonsingular orbital elements of the first kind; quantization unit

Shanchuan FANG,Lan DU,Yunpeng GAO,Peiyuan ZHOU,Zejun LIU. Orbital Elements Ephemerides and Interfaces Design of LEO Satellites[J]. Journal of Geodesy and Geoinformation Science, 2019, 2(4): 44-52.

Figures/Tables 10

Tab.1

Fig.1

Tab.2

Secular perturbations in tangent and radial directions of orbits"

Number of elements	16	17	18	18^*	19
Long-term perturbationelements along track direction	Δn	ΔnΔ $n ·$	ΔnΔ $n ·$	ΔnΔ $n ·$ Δ $n · ·$	ΔnΔ $n ·$ Δ $n · ·$
Long-term Perturbationelements in Radial direction	—	—	$a ·$	—	$a ·$

Tab.2

Tab.3

Methods for calculating the semi-major axis and the mean angular velocity"

Number of elements	Orbital Semi-Length Axis	Average angular velocity of satellite
16	A= $(A) 2$	n= $μ$ / $(A) 3$ +Δn
17	A= $(A) 2$	n= $μ$ / $(A) 3$ +Δn+ $12$ Δ $n ·$ t
18	A=A_ref+ΔA+ $A ·$ t	n= $μ / (A ref + Δ A) 3$ +Δn+ $12$ Δ $n ·$ t
18^*	A=A_ref+ΔA	n= $μ / (A ref + Δ A) 3$ +Δn+ $12$ Δ $n ·$ t+ $16$ Δ $n · ·$ t²
19	A=A_ref+ΔA+ $A ·$ t	n= $μ / (A ref + Δ A) 3$ +Δn+ $12$ Δ $n ·$ t+ $16$ Δ $n · ·$ t²

Tab.3

Fig.2

Fig.3

Fig.4

Fig.5

Tab.4

The interface design of 16~19 elements ephemerides"

Elements	16 elements										18^* elements									Units
Elements	LSB	bits		LSB		bits		LSB		bits		LSB	bits		LSB		bits			Units
t_oe	2⁴		16		2⁴		16		2⁴		16			2⁴		16		2⁴	16	s
$A$ /ΔA	2^-17		29		2^-5		±18		2^-5		±22			2^-5		±19		2^-6	±19	$m$
e	2^-28		23		2^-29		19		2^-29		24			2^-29		22		2^-30	22	—
i₀	2^-29		±29		2^-30		±28		2^-30		±30			2^-30		±28		2^-30	±28	π
Ω₀	2^-29		±29		2^-30		±31		2^-30		±30			2^-30		±31		2^-30	±31	π
ω	2^-29		±29		2^-30		±31		2^-30		±30			2^-30		±31		2^-31	±32	π
M₀	2^-29		±29		2^-30		±31		2^-30		±30			2^-30		±31		2^-31	±32	π
$A ˙$	—		—		—		—		2^-14		±18			—		—		2^-14	±19	m/s
$n · ·$	—		—		—		—		—		—			2^-56		±18		2^-38	±15	π/s³
i_dot	2^-37		±15		2^-37		±14		2^-38		±15			2^-38		±15		2^-39	±15	π/s
$Ω ˙$	2^-37		±17		2^-38		±17		2^-38		±18			2^-38		±17		2^-39	±18	π/s
Δn	2^-38		±17		2^-39		±19		2^-38		±17			2^-39		±22		2^-47	±18	π/s
$n ·$	—		—		2^-48		±17		2^-46		±17			2^-48		±17		2^-54	±19	π/s²
C_uc	2^-27		±14		2^-28		±15		2^-28		±16			2^-28		±18		2^-28	±17	π
C_us	2^-27		±14		2^-28		±16		2^-28		±17			2^-28		±18		2^-28	±16	π
C_rc	2^-4		±15		2^-5		±16		2^-5		±17			2^-5		±17		2^-5	±17	m
C_rs	2^-4		±13		2^-5		±14		2^-5		±16			2^-5		±16		2^-5	±17	m
C_ic	2^-27		±14		2^-27		±13		2^-27		±13			2^-27		±13		2^-28	±14	rad
C_is	2^-27		±14		2^-27		±13		2^-28		±14			2^-28		±14		2^-28	±14	rad
Total Bit Number (Contains symbolic bits)	—		329		—		343		—		376			—		379		—	396	—

Tab.4

Fig.6

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System	Orbcomm	Iridium	Globalstar	OneWeb	SpaceX	Hongyan	Hongyun
Operator	America Orbcomm	America Motorola	America LQSS	France OneWeb	America SpaceX	China CASC	China CASIC
Orbit type	Circle	Circle	Circle	Circle	Circle	Circle	Circle
Orbital altitude (km)	835/725	785	1414	1200	1127	1200	1000
Number of satellites	36	66+6	48	648	4425	60	156
Orbit inclination angle(°)	0/45/70/108	86.4	52	88	—	—	—
Coverage area	Global	Global	±70°	Global	Global	Global	Global
Service time	1997	1998	1999	2019	2020	2020	2022