【文章內(nèi)容簡介】 filter (KF2), and process these phase pseudo measurements with KF2 to obtain optimal sequential estimates and variances for the UECC. I have been successful with this approach. Figure 3 presents an ensemble of ―realistic‖ KF1 phase estimation errors, overlaid with ―realistic‖ KF2 sequential estimates of UECC in phase. (By ―realistic‖ I refer to realistic clock diffusion coefficient values.) . Observable error independent for each clock At each applicable time subtract the estimate of the UECC from the KF1 phase deviation estimate, for each particular GPS clock, to estimate the OEIC in phase for that clock. During measurement processing, the OEIC is contained within an envelope of a few parts of a nanosecond (see Figure 4). Figure 4 presents a graph of two cases of the OEIC for ground station clock S1. For the blue line of intervals of link visibility and KF1 range measurement processing are clearly distinguished from propagation intervals with no measurements. During measurement processing, the observable ponent of KF1 estimation error is contained within an envelope of a few parts of a nanosecond. Calculation of the sequential covariance for the OEIC requires a matrix value for the crosscovariance between the KF1 phase deviation estimation error and the UECC estimation error at each time. I have not yet been able to calculate this crosscovariance. 6. KALMAN FILTERS KF1 AND KF2 I have simulated GPS pseudorange measurements for two GPS ground station clocks S1 and S2, and for two GPS NAVSTAR clocks N1 and N2. Here I set simulated measurement time granularity to 30s for the set of all visible link intervals. Visible and nonvisible intervals are clearly evident in the blue line of Figure 4. I set the scalar rootvariance R for both measurement simulations and Kalman filter KF1 to R = 1 cm. Typically R ～1 m for GPS pseudorange, but when carrier phase measurements are processed simultaneously with pseudorange, the rootvariance is reduced by two orders of magnitude. So the use of R = 1cm enables me to quantify lower performance bounds for the simultaneous processing of both measurement types. . Create GPS clock ensemble Typically, one processes measurements with a Kalman filter to derive sequential estimates of a multidimensional observable state. Instead, here I imitate the GPS operational procedure and process simulated GPS pseudorange measurements with KF1 to create a sequence of unobservable multidimensional clock state estimates. Clock state ponents are unobservable from GPS pseudorange measurements. See Figure 2 for an example of an ensemble of estimated unobservable clock phase deviation state ponents created by KF1. . Sherman’s theorem GPS time, the unobservable GPS clock ensemble mean phase, is created by the use of Sherman’s theorem [1 18 ]in the USAF Kalman filter measurement update algorithm on GPS range measurements. Satisfaction of Sherman’s Theorem guarantees that the meansquared state estimate error on each observable state estimate ponent is minimized. But the meansquared state estimate error on each unobservable state estimate ponent is not reduced. Thus the unobservable clock phase deviation state estimate ponent mon to every GPS clock is isolated by application of Sherman’s theorem. An ensemble of unobservable state estimate ponents is thus created by Sherman’s theorem—see Figure 3for an example. . Initial condition errors A significant result emerges due to the modeling of Kalman filter (KF1) initial condition errors in phase and frequency. Initial estimated clock phase deviations are significantly displaced by the KF1 initial condition errors in phase. As time evolves estimated clock phase deviation magnitudes diverge continuously and increasingly when referred to true (simulated) phase deviations, and this is due to filter initial condition errors in frequency. See Figure 2for an example. 7. IDENTIFY NONCLOCK MODELING ERRORS My interest in the GPS NAVSTAR (SV) orbit determination problem, bined with that of the clock parameter estimation problem, has enabled the identification of a useful diagnostic tool: given realistic values for diffusion coefficients for each of the real GPS clocks, then quantitative upper bounds can be calculated on OEIC magnitudes. These calculations require the use of a rigorous simulator .Existence of significant crosscorrelations between GPS clock phase errors and other nonclock GPS estimation modeling errors enables significant aliasing into GPS clock phase estimates during operation of KF1 on re a l data. But given rigorous quantitative upper bounds on OEIC magnitudes, then significant violation of these bounds when processing real GPS pseudorange and carrier phase data identifies nonclock modeling errors related to the GPS estimation model. Modeling error candidates here include NAVSTAR orbit force modeling errors, ground antenna modeling errors (multipath), and tropospheric modeling errors. NAVSTAR orbit force modeling errors include those of solar photon pressure, albedo, thermal dump, and propellant outgassing. The accuracy of this diagnostic tool depends on the use of realistic clock diffusion coefficient values and a rigorous clock model simulation capability. 8. OBSERVABLE CLOCKS In an earlier version of my paper, I reported on KF1 validation results where clock S1 was specified as a TAI/UTC clock, external to the GPS clock ensemble consisting of S2, N1, and N2. This brought observability (see Sections 5 and 6 herein)to S2, N1, and N2 clock states from GPS pseudorange measurements, drove clocks S2, N1, and N2 immediately to the TAI/UTC timescale, and enabled a clean validation of my filter implementation.