1、 PDF外文：http:/ 4350 字 外文原文 Hindawi Publishing Corporation International Journal of Navigation and Observation Volume 2008, Article ID 261384,8 pages doi:10.1155/2008/261384 Research Article GPS Composite Clock Analysis James R. Wright Analytical Graphics, In c., 220 Valle y Creek Bl
2、vd, E x ton, PA 19341, USA Correspondence should be addressed to James R. Wright, Received 30 June 2007； Accepted 6 November 2007 Recommended by Demetrios Matsakis Copyright 2008 James R. Wright. This is an open access article distributed under the Creative Commons Attribution License,which p
3、ermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract The GPS composite clock defines GPS time, the timescale used today in GPS operations. GPS time is illuminated by examination of its role in the complete estimati
4、on and control problem relative to UTC/TAI. The phase of each GPS clock is unobservable from GPS pseudorange measurements, and the mean phase of the GPS clock ensemble (GPS time) is unobservable. A new and useful obs e r vabilit y definition is presented, together with new observabilit y theorems, t
5、o demonstrate explicitly that GPS time is unobservable. Simulated GPS clock phase and frequency deviations, and simulated GPS pseudorange measurements, are used to understand GPS time in terms of Kalman filter estimation errors. 1. INTRODUCTION GPS time is created by processing GPS pseud
6、orange measurements with the operational GPS Kalman filter. Brown 2refers to the object created by the Kalman filter as the GPS composite clock, and to GPS time as the implicit ensemble mean phase of the GPS composite clock. The fundamental goal by the USAF and the USNO is to control GPS time to wit
7、hin a specified bound of UTC/TAI. (I refer to TAI/UTC understanding that UTC has an accumulated discontinuity (a sum of leap seconds) when compared to TAI. But unique two-way transformations between TAI and UTC have been in successful operational use since 1972. I have no need herein to furthe
8、r distinguish between TAI and UTC.) I present here a quantitative analysis of the GPS composite clock, derived from detailed simulations and associated graphics. GPS clock diffusion coefficient values used here were derived from Allan deviation graphs presented by Oaks et al. 12 in 1998. I refer to
9、them as realistic, and in the sequel I claim realistic results from their use. Figure 1 presents their diffusion coefficient values and my derivation of associated Allan deviation lines. My interest in the GPS composite clock derives from my interest in performing real-time orbit determination for G
10、PS NAVSTAR spacecraft from ground receiver pseudorange measurements. (James R Wright is the architect of ODTK (Orbit Determination Tool Kit), a commercial soft-ware product offered by Analytical Graphics, Inc. (AGI).)The estimation of NAVSTAR orbits would be in complete without the simultaneous esti
11、mation of GPS clock parameters. I use simulated GPS clock phase and frequency deviations, and simulated GPS pseudorange measurements, to study Kalman filter estimation errors. This paper was first prepared for TimeNav07 20 . I am indebted to Charles Greenhall (JPL) for encouragement and help in this
12、 work. 2. THE COMPLETE ESTIMATION AND CONTROL P ROBLEM The USNO operates two UTC/TAI master clocks, each of which provides access to an estimate of UTC/TAI in real time(1 pps). One of these clocks is maintained at the USNO, and the other is maintained at Schriever Air Force Base in Color
13、ado Springs. This enables the USNO to compare UTC/TAI to the phase of each GPS orbital NAVSTAR clock via GPS pseudorange measurements, by using a UTC/TAI master clock in a USNO GPS ground receiver. Each GPS clock is a member of (internal to) the GPS ensemble of clocks, but the USNO master clock is e
14、xternal to the GPS ensemble of clocks. Because of this, the difference between UTC/TAI and the phase of each NAVSTAR GPS clock is observable. This difference can be (and is) estimated and quantified. The root mean square (RMS) on these differences quantifies the difference between UTC/TAI and GPS ti
15、me. Inspection of the differences between UTC/TAI and the phase of each NAVSTAR GPS clock enables the USNO to identify GPS clocks that require particular frequency-rate control corrections. Use of this knowledge enables the USAF to adjust frequency rates of selected GPS clocks. Currently, the USAF u
16、ses an automated bang-bang controller on frequency-rate. (According to Bill Feess, an improvement in control can be achieved by replacing the existing bang-bang controller with a proportional controller.) 3. STOCHASTIC CLOCK PHYSICS The most significant stochastic clock physics are under
17、stood in terms of Wiener processes and their integrals .Clock physics are characterized by particular values of clock-dependent diffusion coefficients, and are conveniently studied with aid of a relevant clock model that relates diffusion coefficient values to their underlying Wiener processes. For
18、my presentation here I have selected The clock model and its relationship with the Allan and related variances presented as an IEEE paper by Zucca and Tavella 19 in 2005.Except for FM flicker noise, this model captures the most significant physics for all GPS clocks. I simulate and validate GP
19、S pseudorange measurements using simulated phase deviations and simulated frequency deviations, according to Zucca and Tavella. 4. KALMAN FILTERS I present my approach for the optimal sequential estimation of clock deviation states and their error covariance functions. Sequential state e
20、stimates are generated recursively from two multidimensional stochastic update functions, the time update (TU) and the measurement update(MU). The TU moves the state estimate and covariance forward with time, accumulating integrals of random clock deviation process noise in the covariance. The
21、 MU is performed at a fixed measurement time where the state estimate and covariance are corrected with new observation information. The sequential estimation of GPS clock deviations re-quires the development of a linear TU and nonlinear MU. The nonlinear MU must be linearized locally to enable appl
22、ication of the linear Kalman MU. Kalmans MU derives from Shermans theorem, Shermans theorem derives from Andersons theorem 1, and Andersons theorem derives from the Brunn-Minkowki inequality theorem . The theoretical foundation for my linearized MU derives from these theorems. 4.1. Initial con
23、ditions Initialization of all sequential estimators requires the use of an initial state estimate column matrix 0|0 and an intial state estimate error covariance matrix 0|0P for time t0 . 4.2. Linear TU and nonlinear MU The simultaneous sequential estimation of GPS clock phase and freque
24、ncy deviation parameters can be studied with the development of a linear TU and nonlinear MU for the clock state estimate subset. This is useful to study clock parameter estimation, as demonstrated in Section 6 . Let ij| denote an n 1 column matrix of state estimate components, where the left subscr
25、ipt j denotes state epoch tj and the right subscript i denotes time-tag ti for the last observation processed, where i, j 0, 1, 2, .Let ijP|denote an associated n n square symmetric state estimate error co-variance matrix (positive eigenvalues). 4.2.1. Linear TU For k 0, 1, 2, 3,., M , the propagation of the true un-known n 1 matrix state KX is given by
