Global Positioning System Reference
In-Depth Information
estimate both the ephemeris and clock errors. However, any error common to all of
the clocks remains unobservable. Essentially, given a system of n clocks, there are
only equivalently n - 1 separable clock observables, leaving one unobservable state.
An early CS Kalman filter design avoided this unobservablity by artificially forcing
a single monitor station clock as the master and referencing all CS clock estimates to
that station. Based on the theory of composite clocks, developed in [25], the CS
Kalman filter was upgraded to exploit this unobservability and established GPS sys-
tem time as the ensemble of all active AFSs. At each measurement update, the com-
posite clock reduces the clock estimate uncertainties [20]. Also with the composite
clock, GPS time is steered to UTC (USNO) absolute time scale for consistency with
other timing services. Common view of the satellites from multiple monitor stations
is critical to the estimation process. This closure of the time-transfer function pro-
vides the global time scale synchronization necessary to achieve submeter estima-
tion performance. Given such advantages of the composite clock, the International
GPS Service (IGS) has recently transitioned its products to IGS system time along
the lines of the composite clocks [26].
The CS Kalman filter has several unique features. First, the CS Kalman filter is
decomposed into smaller minifilters, known as partitions. The CS partitioned
Kalman filter was required due to computational limitations in the 1980s. In a sin-
gle partition, the Kalman filter estimates up to six satellites and all ground states,
with logic across partitions to coordinate the alignment of the redundant ground
estimates. Second, the CS Kalman filter has constant state estimates (i.e., filter states
with zero covariance). (This feature is used in the cesium and rubidium AFS models,
which are linear and quadratic polynomials, respectively). Classically, Kalman the-
ory requires the state covariance to be positive-definite. However, given the U - D
time update in (3.8) and its associated Gram-Schmidt factorization [19], the a poste-
riori covariance factors,
~ (), ~ ()
, are constructed to be positive semidefinite with
selected states having zero covariance. Third, the CS Kalman filter supports Kalman
backups. The CS Kalman backup consists of retrieving prior filter states and
covariances (up to the past 24 hours) and reprocessing the smoothed measurement
under different filter configurations. This backup capability is critical to 2SOPS for
managing satellite, ground station, or operator-induced abnormalities. The CS
Kalman filter has various controls available to 2SOPS to manage special events,
including AFS runoffs, autonomous satellite jet firings, AFS reinitializations and
switchovers of AFSs, reference trajectories, and Earth orientation parameter
changes. The CS Kalman filter has been continuously running since the early 1980s
with no filter restarts.
UD
MCS Upload Message Formulation
The MCS upload navigation messages are generated by a sequence of steps. First,
the CS generates predicted ECEF satellite antenna phase center positions, denoted
as [ ~
, using the most recent Kalman filter estimate at time, t k . Next, the CS
performs a least squares fit of these predicted positions using the NAV Data mes-
sage ephemeris parameters. The least squares fits are over either 4-hour or 6-hour
time intervals, also known as a subframe. (Note that the subframe fitting intervals
are longer for the extended operation uploads.) The 15 orbital elements (see Section
2.3.1, Table 2.2) can be expressed in vector form as
r
(| )]
t
sa
k
E
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