全球定位系统精确点定位技术及其高效数据分析

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"Zumberg_JPL_1997 Precise point positioning" 这篇1997年的期刊文章“Zumberg_JPL_1997 Precise point positioning”主要探讨了全球定位系统（GPS）数据在大规模网络中的高效、稳健分析方法，即精密单点定位技术。该技术是针对由数十到数百个永久运行的高精度GPS接收器构成的网络，这些网络的地理覆盖范围从100到1000公里不等。文章由J.F. Zumberge、M.B. Heftin、D.C. Jefferson、M.M. Watkins和F.H. Webb等人发表在《地球物理学研究》期刊的B3卷第5005-5017页。他们来自美国加州理工学院的喷气推进实验室。摘要中提到，随着大量GPS接收器网络的出现，处理这些数据的计算负担变得日益繁重。为了解决这个问题，文章提出了一种策略：首先，利用全球分布的GPS接收器网络确定精确的GPS卫星位置和时钟校正。然后，对局部网络的数据进行分析时，估计每个接收器特有的参数，而卫星参数则固定在全球解决方案中确定的值。这种“精密单点定位”方法允许使用40-Mfiop（兆浮点运算每秒）级别的计算机每天处理数百至数千个站点的数据，并且结果与传统的基线解算方法相当。精密单点定位（PPP）技术的核心优势在于其效率和鲁棒性。通过将卫星轨道和钟差作为先验信息固定，可以大大减少局部网络数据分析的计算复杂性，使得处理大规模数据成为可能。这种方法对于监测地壳运动、气象学、地球动力学以及其他需要实时或近实时定位精度的应用具有重要意义。文章中可能涵盖了以下几点详细内容： 1. 精密单点定位的算法原理和实现步骤。 2. 全球和局部网络数据的处理差异及优化策略。 3. 不同规模网络的性能比较和实例应用。 4. 误差源分析，包括信号多路径效应、电离层延迟、对流层延迟等。 5. 精度评估和与其他定位方法的对比。 6. 计算机资源的需求和优化，以及未来计算能力的预测。 7. PPP技术的潜在改进和未来发展方向。这篇文章为GPS数据处理提供了一种经济高效的解决方案，尤其是在处理大规模GPS网络数据时，为科学研究和工程应用提供了强大的工具。

ZUMBERGE ET AL.' PRECISE POINT POSITIONING OF GPS DATA 5007

E o

o •

E• 0.1

0.01

10 100

number of receivers

Figure 1. Computational burden B as a function of the number of receivers R. The open circles

are actual total processing times on a 40-Mfiop computer and include three passes through the

parameter estimation module, as well as auxiliary programs. The dotted line is the theoretical

time required for three passes through the parameter estimation module only, assuming B =

2.68 n2m; the 2.68 is chosen so that Equations (3), (4), and (5) give the observed filter execution

time for the R = 48 and 49 cases. The units of B are the number of days required by a 40-Mfiop

computer to perform the analysis.

n2(nl q-n2) --n3(1 q- n) operations. The total cost )/,

relative to the n2m operations required for the analysis

of all data simultaneously, is thus

)/- (1+ n)

This can be generalized to

x-[lq-n(J-1)] [1 q-n(J-1) n

j2 q--- m

(7)

when the m measurements are divided equally into J

groups. Note that (7) approaches unity as n -• 1, as-

suming n/m is small. Thus, if all parameters are com-

mon, partitioning is ineffective.

With X - 24, f•/4•r = 0.25,A - 24 hours, (5 = 5 min,

d - 2, a - 29, b - 10, c - 5, and R - 40 receivers, we

have n - 1405 parameters of which

nn- bX + c- 245

are common (n • 0.174). There are m = 138240 mea-

surements, and the ratio of parameters to measurements

is n/m • 0.01. Equation (7) then shows a 64% reduc-

tion in burden for J = 2 and an 88% reduction for

J = 40. Clearly, partitioning is one effective means of

reducing CPU when n is small and has been demon-

strated by some analysis centers in the International

GPS Service for Geodynamics (IGS).

When many parameters are treated as stochastic, rig-

orous partitioning is difficult. We feel that the benefits

of using stochastics outweigh this disadvantage.

Double Differencing

For receivers q and r in view of satellites w and x at

time t, (1) can be used to show that the quantity

dLqrwxt -- Lqwt - Lrwt - Lqxt q- Lrxt (8)

is independent of all clock parameters. In practice, syn-

chronization of all measurements to GPS time is made

prior to the formation of the double difference. A sim-

ilar double difference can be formed for the pseudor-

ange. Least squares estimation of nonclock parameters

can be made based on double-difference measurements.

It is straightforward to form a measurement covariance

matrix that accounts for known correlations in double-

differenced data.

The technique has the advantage of a reduction in

both the measurement and parameter counts. One

need not.include the entire set of double-difference mea-

surements because it contains redundant information.

For R receivers in view of X transmitters at time t

there are (R - 1)(X - 1) independent double differ-

ences that form a complete measurement set. One

such set is dLqrwxt for q - w - 1, 2 _< r _< R, and

2 < x < X. Thus the measurement count m is reduced

by RX - (R- 1)(X - 1) - R + X - 1 compared to the

undifferenced case. An identical reduction in the pa-

rameter count n occurs because (R- 1)(X- 1) is also

the number of phase bias parameters to be estimated,

compared with RX in the undifferenced case. Finally,

receiver and transmitter clocks are no longer parame-

ters, so that the parameter count is further reduced by

R+X.

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