ICESat-2 ATBD:精确轨道确定与参数校准算法原理文档

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本篇文档是关于ICESat-2项目精确轨道确定、轨道设计以及地表参数校准的算法理论基础文档（ATBD），由NASA/GSFC的Scott Luthcke、Teresa Pennington和Bryant D. Loomis等人编撰，属于ICE, CLOUD, and Land Elevation Satellite（ICESat-2）的一部分。ICESat-2搭载的Advanced Topographic Laser Altimeter System (ATLAS) 仪器，包括其科学算法软件(ASAS) 和调度及数据管理系统(SDMS)，在科学处理系统(SIPS)上运行。该文档详述了从0级到4级的标准数据产品的生成过程，其中包括数据级处理算法的介绍，以及这些算法背后的理论基础。文档首先提供了简短的介绍，概述了本ATBD将涵盖的内容，如特定的数据产品、参数处理以及任何相关的辅助处理方法。它着重于用易于理解的语言解释算法的功能，包括其工作原理和支撑背景信息。这部分旨在使非专业读者也能理解算法的作用，便于公众事务办公室进行科普传播。第二部分提供了一个全面的概述和背景信息，可能涵盖了以下内容： 1. **算法概览**：描述算法如何通过测量地球表面反射回来的激光信号来获取冰川、云层和陆地的高度数据，以及这些数据如何转化为精确的地球物理参数。 2. **数据采集与处理流程**：详细阐述ATLAS接收和处理来自卫星的原始数据，包括激光回波信号的收集、噪声过滤、地面回波分类以及大气影响校正等步骤。 3. **轨道确定**：介绍使用精密的卫星姿态数据和地球重力场模型，如何计算并校正卫星的轨道参数，确保数据的准确性。 4. **地表参数校准**：讨论如何利用地面控制点和地形数据，对地表高度、反射率等参数进行校准，提高产品精度。 5. **数据质量控制与评估**：说明生成的标准数据产品如何经过严格的质量检查，包括数据一致性、可信度评估和错误检测，以确保用户可以依赖这些科学成果。 6. **版本更新与进度**：提到文档的版本历史，即从初步ATBD到R002版本的发布日期，以及未来可能的更新内容。 7. **用户指南与建议**：为科学家、工程师和数据使用者提供使用这些产品和算法的指南，包括可能遇到的问题及其解决方法。通过对这个ATBD的深入研究，科学家和应用者能够深入了解ICESat-2数据产品的生成过程，从而充分利用这些宝贵的地球观测数据进行科学研究和地球系统建模。

ICESat-2 Algorithm Theoretical Document for Precise Orbit Determination, Orbit Design &

Geolocation Parameter Calibration

Release 002

Release Date 28 October 2019

2.0 POD OVERVIEW AND CORE SOFTWARE

The geolocation of the laser altimeter surface return, or bounce point, relies on the precise

knowledge of several components. These include the position of the spacecraft center of mass,

the tracking point offsets of the instrument related to the spacecraft center of mass, the pointing

of the instrument, and the altimeter range observations.

The parameters defining the temporal history of the spacecraft center of mass position and

velocity, or the orbit, can be refined through the minimization of the spacecraft tracking data

residuals utilizing precise tracking data measurement models. This precision orbit determination

(POD) process is capable of estimating both dynamic parameters contributing to the force

modeling of the spacecraft, and measurement modeling parameters which can include a host of

geophysical parameters such as Earth orientation parameters, and tracking system specific

parameters such as antenna phase center offsets. The accuracy of the precision orbit solution

relies on the fidelity of the force and measurement models, and the quality of the tracking data.

The software program to be used in performing the ICESat-2 precise orbit determination is the

GEODYN-II program, which evolved from the original GEODYN program that was developed

at NASA GSFC in the 1960’s. This current version of the software has been operational since

1985, and has been extensively used for satellite orbit determination, altimeter geolocation,

geodetic parameter estimation, tracking instrument calibration, and orbit prediction, and is

capable of handling essentially all types of satellite tracking data.

GEODYN-II has been utilized on every NASA geodetic Earth and planetary altimeter mission

including TOPEX/Poseidon, Jason-1, Jason-2, Mars Global Surveyor, Shuttle Laser Altimeter I

& II, ICESat, GRACE, Lunar Reconnaissance Orbiter, MESSENGER, and GRAIL. Of note is

the use of the GEODYN-II program to achieve and confirm 1-centimeter radial orbit accuracy

for Jason-1 [Luthcke et al., 2003].

Solution strategy can also contribute to the final orbit and geolocation accuracy. For example,

the simultaneous processing of GPS and SLR tracking can provide a more accurate orbit solution

than is possible with either tracking data type alone [Rowlands, 1997]. Similarly, the

simultaneous estimation of altimeter instrument parameters, along with orbit and geophysical

parameters, is a robust solution strategy for improved geolocation accuracy [add reference].

Therefore, the implementation of the estimation process must include the ability to perform

simultaneous solutions for instrument, orbit and geophysical parameters through the reduction of

a combination of instrument range and spacecraft tracking data observations.

The GEODYN-II precision orbit determination and geophysical parameter estimation program is

equipped with a full set of Multi-Beam Laser Altimeter (MBLA) range data processing

capabilities. The direct altimetry and dynamic crossover measurement model algorithms

(Geolocation ATBD, Section ?), along with the classic geolocation algorithms (ATL03g ICEsat-

2 Receive Photon Geolocation ATBD, Section 3.1), are fully implemented into the GEODYN-II

software. GEODYN-II supports the simultaneous estimation of orbit and instrument

measurement modeling parameters through the reduction of a combination of spacecraft tracking

ICESat-2 Algorithm Theoretical Document for Precise Orbit Determination, Orbit Design &

Geolocation Parameter Calibration

Release 002

Release Date 28 October 2019

3.0 ICESAT-2 DESIGN ORBIT AND REFERENCE GROUND TRACKS

3.1 Overview

The POD team developed the ICESat-2 orbit with the initial requirements of: (1) a 92°

inclination orbit for coverage of polar ice and sea ice while still producing orbit-crossings for

altimeter cross-over observations, (2) a frozen orbit to limit altitude variation at any given

latitude in order to maintain beam pattern geometry on the surface, (3) a ~91-day repeat to

sample seasonal variation with a ~30-day near repeat for temporal sampling of sea ice, (4) low

earth orbit for altimeter instrument radiometry considerations.

3.2 Orbit Design Procedure

The first step is to determine the number of nodal revolutions the satellite will complete by repeat,

N, and the number of Earth rotations performed with respect to the satellite’s orbital plane, D

(nodal days). Generally the science requirements will constrain these numbers. Altitude

requirements as well as track density (coverage) are typically known well enough to bound the

ratio N/D.

Given a satellite’s general altitude (semi-major axis) the period

, of a satellite is expressed by

Kepler’s 3

Law as:

!"#$%

(

)

######*+,$,-.

where a is the satellite’s semi-major axis and μ is the standard gravitational parameter for the

Earth.

N orbit periods should be approximately equal to the D nodal days to repeat. Further insight can

be gained from applying Bezout’s Theorem (Pie, 2008) expressed below as:

/012304"5

(3.2.2)

where m is the number of sub-cycle revolutions, d is sub-cycle nodal days, and k is the ground-

track nodal spacing deviation (integer 1,2…).

The closest sub-cycles,

5"6-

for ICESat-1 were important orbit design factors where these 2

sub-cycles ended up dividing the satellite’s 91 day repeat cycle into 3 nearly even periods where

the ground-track nearly repeated itself.

Once N and D are selected we can begin a more refined analysis involving some of the Earth’s

gravitational field zonal terms. The analysis also requires as input a mean orbit inclination, i

that

is typically determined from science or mission requirements. Again, the satellite’s mean semi-

major axis, a

can be initially estimated by calculating the period of the orbit and ensuring N orbit

periods approximately takes D days to complete. We can then look over a range of mean semi-

ICESat-2 Algorithm Theoretical Document for Precise Orbit Determination, Orbit Design &

Geolocation Parameter Calibration

Release 002

Release Date 28 October 2019

210* 7

."#9

(3.2.5)

where

is the Earth’s average rotation rate, and rates for mean anomaly, argument of perigee

and right ascension of ascending node (

) are theoretically calculated using zonal

coefficients as in Vallado, 2001 (9-38,9-40,9-42) and Roh et al., 2009 to account for the odd

zonal harmonics added to

In addition, the orbital period given in terms of general orbit perturbations can be expressed as:

!"#

######*+,$,V'.

With each orbit the resulting ground-track shift in longitude,

is given as:

de"!0*7

) (3.2.6b)

Given N longitude shifts, we should arrive back to where we first started for the orbit to be qualified

as an acceptable repeat candidate.

We can evaluate these conditions (equations 3.2.5 & 3.2.6) for every value of mean semi-major

axis in our search interval and its corresponding frozen eccentricity. The pair of values that gives

us the best repeat conditions is selected as the initial estimates of mean orbital elements with

=9>

#$?9>

. We can also validate the frozenness of our orbit by inspecting the value calculated

for

8. We expect that this value will be relatively small given the calculated frozen eccentricity.

We can next convert these mean elements into osculating elements using a GEODYN utility

program called C2GMEAN. The osculating elements are used to generate an orbit in GEODYN

that includes a larger gravity field expansion (70x70). Additionally, in the GEODYN runs the

non-conservative forces are turned off, as well as Earth nutation, precession and polar motion.

Earth rotation is fixed to a constant rate (mean over the time period of the mission).

Due to the higher gravity terms we expect to lose the repeat ground-track and lose some of the

frozen orbit characteristics. We wish to adjust the mean semi-major axis and eccentricity to

achieve repeat and frozen orbit conditions again with this more detailed geopotential model. We

can use an optimization procedure to adjust these mean values until the ground-track closure at

repeat is within a suitable tolerance and the altitude variation of the orbit has been effectively

minimized. A frozen orbit is essentially an orbit with minimal orbital element variation and this

leads to minimum altitude variation among each orbit pass. The optimization procedure

continuously changes between adjusted mean orbital elements and new osculating elements to start

the next GEODYN simulation. The procedure iterates until a successful repeat-frozen orbit has

been designed.

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