Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
CA 02651077 2009-01-23
DECOUPLED CLOCK MODEL WITH AMBIGUITY DATUM FIXING
TECHNICAL FIELD
[0001]
A decoupled clock model with ambiguity datum fixing is provided. More
particularly, a method of processing carrier phase and pseudorange
measurements from,
consecutively, a network of receivers, and a single receiver is also provided.
BACKGROUND
[0002]
A key issue in Global Navigation Satellite Systems (GNSS), including the
original Global Positioning System (GPS), is the isolation and estimation of
the integer
ambiguity of the carrier phase measurements. Achieving integer ambiguity
resolution of
undifferenced carrier phase measurements has been a significant topic of
interest for the geodetic
and navigation communities for many years.
[0003]
The carrier phase signals of any GNSS are approximately two orders of
magnitude more precise than the primary pseudorange signals the systems
provide. However,
measurements of the carrier phases are ambiguous relative to those of the
pseudoranges by an
unknown number of integer cycles. Resolution of these ambiguities provides
centimeter to
millimeter-level pseudorange measurements compared to the decimeter to meter
level of the
inherent pseudoranges. The improvement in measurement precision is directly
carried into the
parameters estimated from the measurements.
[0004]
The ambiguities are currently only resolved as integers in so-called double
difference processing whereby dual-pairs of measurements (made for example
from two
receivers to the same two satellites) are differenced to produce one
measurement. The
differencing is carried out primarily to remove common transmitter and
receiver biases contained
in the measurements. The biases consist primarily of the oscillator-induced
time delays of both
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the satellite and the receiver. The existence of these biases is why the
measurements are
'pseudoranges' and not just 'ranges'.
[0005]
The primary disadvantage of double differencing is the requirement to have at
least two receivers, even for a single user who only requires his own
location. This essentially
turns point positioning into baseline, or relative, positioning. This
technique can be very limited
in baseline length if such error sources as orbits and ionosphere are required
to cancel out.
[0006]
As an alternative to double differencing, it is possible to process
undifferenced
measurements and estimate the biases explicitly. It can be shown that the two
solutions are
mathematically identical under certain circumstances. At the same time
however, it is not
possible to explicitly isolate the integer nature of the ambiguities due to
their exact linear
correlation with time delays due to the oscillators and other hardware. The
higher precision of
the carrier phase can still be accessed by estimating a random constant bias
in place of the
ambiguity; however, such a parameter requires an extended convergence period.
[0007]
The processing of undifferenced pseudorange and carrier phase observables from
a single receiver is referred to as Precise Point Positioning (PPP). PPP
returns in effect to the first
principles of GPS, where the focus is again placed on a single receiver. The
main challenge with
PPP is the significant convergence period required before a suitable solution
precision is
achieved. This convergence period is the most significant factor limiting
wider adoption of PPP.
If the ambiguity could be isolated and estimated as an integer value then, in
principle, the integer
nature represents more information that could be exploited to accelerate
convergence.
100081
Accordingly, integer ambiguity resolution of undifferenced carrier phase
observables has been an elusive goal in GPS processing, largely since the
advent of the PPP
method. Some recent advances in isolating integer ambiguities have been made
with techniques
that use single differences and undifferenced observables. However, it is not
clear that all
aspects of the problem have been addressed, particularly with respect to time-
varying code biases
that are not explicitly accounted for in those techniques.
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100091
The term 'code biases' generally refers to unmodelled common-mode errors of
the pseudoranges, usually considered to be hardware or local environment
delays, that are either
constant or believed to vary in a band-limited, quasi-random, manner. There
appears to be
general acceptance in the timing community that these biases are the cause of
the so-called 'day-
boundary clock jumps- highlighted by the time scale of the International GNSS
Service (IGS).
The term 'phase biases' refers to corresponding delays of the carrier phases.
100101
It is stated that the limiting factor in ambiguity resolution using
undifferenced
GPS observables is the presence of both code and phase biases in the estimates
of the
ambiguities. As parameterised in the "standard model" of undifferenced
pseudoranges and
carrier phases, the datum for the station and satellite clock parameters is
provided by the
pseudoranges. The consequence of this is that the estimated ambiguities
contain the time-
constant portions of both code and phase biases.
NOM
The standard GPS dual-frequency pseudorange (code) and carrier phase (phase)
observation equations are typically written in the form:
P, = p +T + + c(dtr - ) + b -b;,, +
+ N, )=
L, = p +T - + c(dt' - di' ) + b -b ; +1
(C1312 + N2)=
L, = p+T-q21+c(dt' -dt`)+1);-2-1);2+ 6.12
where P, is a pseudorange measurement made at frequency i and (I), is a
carrier phase
measurement made at frequency i. We write the integer ambiguity N, on the left
side to show
how it converts the ambiguous phase measurement cl), into a precise
pseudorange L. The factor
q represents the ratio of the primary and secondary GPS frequencies, c is the
vacuum speed of
light and 2, is the frequency-dependent wavelength of the carrier phase
measurements. Of the
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geometric parameters, p represents the geometric range between transmitter and
receiver
antennas, T is the range delay caused by signal propagation through the lower
atmosphere
(predominantly the Troposphere), and I is the range delay and apparent phase
advance on the
primary frequency caused by signal propagation through the upper atmosphere
(predominantly
the Ionosphere). The remaining, non-geometric, parameters are the oscillator
or 'clock' errors
for both the transmitter and receiver (di and dtr respectively), and common-
oscillator hardware
biases (1): ) for each observation. Unmodelled random or quasi-random errors
are represented by
E..
100121 The usual
practice when processing dual-frequency measurements is to take
advantage of the frequency-dependence of the ionospheric delay (to first
order) and linearly
combine two pseudoranges and two carrier phases to produce ionosphere-free
observables:
P3 = p +T + c(dtr - dt')+1)3-1);,, 1'3
L,= p+ 7' + c(dtr
where:
P-
(77' P -6O) (772L _602L7)
- = - I
(772 -602) 772 _602)
and the ionosphere-free ambiguity combination N3 = 77N1-60N2 is placed on the
right-hand side
to indicate that it is now treated as a parameter to be estimated from the
data.
100131 As they
stand, these equations are over-parameterised, and any system of normal
equations derived from them for the purposes of a least squares solution will
be singular. There
are two causes of deficiency. The first is that the clock errors are
inherently differenced and
cannot be uniquely separated. This is overcome in a network solution by fixing
one of the
station clocks, and in a single-receiver solution by fixing the satellite
clocks. The remaining
singularity is due to the presence of the hardware biases and their identical
functional behavior
with the associated clock parameters. Both these types of parameter represent
common-mode
time delays and having constant partial derivatives are not uniquely
separable.
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100141
To explicitly deal with this singularity, equivalent equations can be written
with
clock and code bias parameters combined. At the same time, due to the uniquely
ambiguous
nature of the carrier phase, the combined clock and bias parameter can be
carried over to the
phase observable:
P3 = p +T + c(dt - dt ;,3) +
L3 = p +T + c(dt - dt) + A1,3 g/ 3
where c = dip, = di* +1)*,,,, and compensating code biases plus the phase
biases and the
ambiguity are combined into one parameter:
= ¨¨+ h;,,¨ 23N,
which is sometimes referred to as the 'float ambiguity' because it is not
integer valued. The
justification for grouping these parameters is that they are all functionally
identical (constant
partial derivatives) and as a random bias. the integer ambiguity cannot be
independently
predicted a-priori.
[0015]
These equations will be referenced as the standard model for dual-frequency
undifferenced processing, despite being in what may appear to be a non-
standard form. These
equations correctly represent the combined effect of common-mode code-biases.
common-
observation clocks and random bias ambiguities. The net effect is that the
ambiguity parameter
of the standard model contains both phase and code time-constant biases.
0016]
It is re-stated that the standard model of undifferenced ionosphere-free
observables is sub-optimal. in that the estimated ambiguities contain the
constant code as well as
phase biases. Should the code or phase biases also vary over time, then the
standard model is
even less accurate, and any such variations must be accommodated by the other
estimated
parameters. For the standard model this will be primarily the clocks and
ambiguities.
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[0017]
Prior systems have not addressed this problem. For example, U.S. Patent No.
5,621,646 and U.S. Patent No. 5,828,336 both describe systems to compute GPS
user corrections
from wide-area ground networks. Both refer to using ionosphere-free
pseudoranges explicitly
smoothed with the carrier phase measurements, or averaged pseudoranges as
estimates for the
carrier ambiguity. The latter patent describes a process to explicitly
estimate the ionosphere
through which the measurements pass, wherein the existence of "instrumental
biases- in both the
receiver and satellite transmitter is acknowledged. The differing nature of
code biases versus
phase biases is not acknowledged and neither is the impact on standard model
processing for
positioning, etc. U.S. Patent No. 5.963.167 (which is a development of No.
5,828,336) describes
a more comprehensive analysis package for processing GPS observations. This
patent refers
briefly to the fixing of double-difference ambiguities in a network solution,
but without
significant detail and not for an isolated user.
[0018]
U.S. Patent No. 6,697.736 B2 relates to a positioning and navigation method
and
system combining GPS with an Inertial Navigation System. The objective of this
patent is to
provide a positioning and navigation method and system, in which the satellite
signal carrier
phase measurements, as well as the pseudoranges of the Global Positioning
System are used in a
Kalman filter, so as to improve the accuracy of the integrated positioning
solution. It is claimed
that carrier phase ambiguities can be fixed, but the existence and effect of
code and phase biases
in the underlying mathematical model is not recognised.
SUMMARY
[0019] To address the limitations and problems of the prior art, a new GPS
observation
model is presented herein called the -decoupled clock model". This model
rigorously
accommodates any synchronisation biases due to hardware delays (constant or
time-varying) that
may occur between common-frequency observables and facilitates the estimation
of integer
ambiguities without explicit differencing.
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10020]
The present invention provides a method for isolating and estimating the
integer
ambiguity of UPS carrier phase measurements. The method provides a solution
based on
arbitrarily biasing the carrier phase estimates of the oscillator errors
compared to those made
from the pseudorange measurements. Separate oscillator parameters are
specified for the carrier
phase and pseudorange measurements and the equations are solved by biasing the
carrier phase
estimates and at the same time constraining the remaining ambiguity parameters
to be integer-
valued.
10021]
Application of the decoupled clock model to both the standard model of
ionosphere-free code and phase observables and the well known widelane-
phase/narrowlane-
code combination leads to an "extended model- whereby simultaneous resolution
of 86cm and
11cm ambiguities is possible. The decoupled clock model is significantly more
general than the
standard model, requiring no assumption about the stability of code or phase
biases. Detailed
knowledge of the source of the biases is not required provided that each set
of received signals is
affected identically. Hence, the terms 'instrumental biases', 'hardware
biases', 'common-mode
biases', etc., are synonymous.
100221
The decoupled model can be applied to both network and single-user processing,
where the network solution provides the satellite clocks required to be fixed
by the user (one for
each observable used). General application of the decoupled clock model helps
explain some of
the remaining issues with GPS processing, such as the -day-boundary clock
jumps" identified by
the IGS time scale, and, under some circumstances, improves the convergence
time of Precise
Point Positioning.
100231 In
summary, therefore, the present invention provides a method of processing
undifferenced UPS carrier phase and pseudorange measurements, made at two
frequencies, by
one or more receivers, from a plurality of satellite transmitters, comprising
the steps of: defining
separate clock parameters for the carrier phase and pseudorange measurements;
arbitrarily
biasing phase estimates of oscillator errors with respect to the pseudorange
estimates; and
constraining the ambiguity parameters to be integer-valued.
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[0024]
Additionally, the present invention contemplates a method of determining
GPS
position information comprising the steps of: receiving GPS signals at one or
more GPS
receivers from a plurality of GPS satellite transmitters; obtaining from the
GPS signals
undifferenced GPS carrier phase and pseudorange measurements, made at two
frequencies, at the
one or more GPS receivers; defining separate clock parameters for the carrier
phase and
pseudorange measurements; arbitrarily biasing carrier phase estimates of
oscillator errors with
respect to pseudorange estimates; constraining the ambiguity parameters to be
integer-valued;
and determining the estimated position of the one or more GPS receivers based
on the constraint
of the estimated ambiguities.
[0025]
Furthermore, the present invention contemplates a system for determining
GPS
position information comprising: one or more GPS receivers for receiving GPS
signals from a
plurality of GPS satellite transmitters; means for obtaining from the GPS
signals undifferenced
GPS carrier phase and pseudorange measurements, made at two frequencies, at
the one or more
GPS receivers; means for defining separate clock parameters for the carrier
phase and
pseudorange measurements; means for arbitrarily biasing carrier phase
estimates of oscillator
errors with respect to pseudorange estimates; means for constraining the
ambiguity parameters to
be integer-valued; and means for determining the estimated position of the one
or more GPS
receivers based on the constraints of the estimated ambiguities.
BRIEF DESCRIPTION OF THE DRAWINGS
[0026]
Figure 1 is a flowchart showing the basic step to achieve integer
ambiguity fixed
estimates of position, time and atmosphere.
[0027]
Figure 2 is a flowchart showing the basic steps of implementing the
decoupled
clock model with ambiguity datum fixing in a network process.
[0028]
Figure 3 is a flowchart showing the basic steps of implementing the
decoupled
clock model with ambiguity datum fixing in a Precise Point Positioning (PPP)
process.
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DESCRIPTION OF THE PREFERRED EMBODIMENTS
100291 A process
for determining a mathematical model of the carrier phase and
pseudorange measurements is provided to isolate the integer ambiguity
parameter. The
"decoupled clock model" specifies separate oscillator parameters for carrier
phase and
pseudorange measurements. While this is known to be incorrect from a strictly
mechanical point
of view, it is known that the pseudorange measurements are subject to
oscillator-like errors that
do not occur on the carrier phases. At the same time it is likely that both
types of measurement
are transmitted and received at marginally different epochs of time,
differences that are
significant at the noise level of the carrier phases.
[0030]
The specification of separate oscillator parameters produces a system of
equations
that is under-determined and ill-posed. To address this, sufficient
mathematical constraints are
provided so that the system of equations can be solved. This is done by a
process of "ambiguity
datum fixing", which involves arbitrarily fixing a subset of the ambiguities
in the system of
equations. This is only possible because of the separate carrier phase and
pseudorange oscillator
parameters. The net result is that the carrier phase estimates of the
oscillator errors are arbitrarily
biased with respect to those made from the pseudoranges. At the same time the
remaining
ambiguity parameters are functionally constrained to be integer-valued.
[0031]
Neither the decoupling of the clock estimates nor the ambiguity datum fixing
directly impacts the estimates of position, time or atmosphere that are
usually of prime concern.
These parameters are only affected once a significant set of ambiguities are
resolved to their
correct integer values. Thus, in the present invention separate oscillator
parameters are
mathematically specified for the carrier phase and pseudorange measurements
and the resulting
under-determined system of equations is constrained by the fixing of a subset
of the ambiguity
parameters to arbitrary integer values. These two steps rigorously accommodate
all the
oscillator-like errors experienced by the two measurement types and
functionally isolate the
ambiguity parameters as integers.
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[0032]
To implement these steps. the ionosphere-free observation equations are
written
with separate code and phase satellite and station clock parameters:
1),= p +T +c(dt ¨ cit ;,, ) +
= p+T +c( ,)¨ 23A1 3+ s ,3
[0033]
Separating the code and phase clock parameters in this way naturally models
any
common-mode time-delay signals unique to the pseudoranges or carrier phases.
At the same
time, the code biases are explicitly isolated from the phases and. in
principle at least. the
ambiguity parameters are functionally integer valued.
[0034]
These equations represent a singular system and solving them is an example of
rank-defect integer least-squares. From an analytical point-of-view, the
primary implication of
formulating separate code and phase clock parameters is that the datum
provided by the
pseudoranges has been removed from the carrier phases and therefore an
alternative must be
provided.
[0035]
The effect of decoupling the code and phase estimates of the clock parameters
is
to make the system of equations singular again. However, the singular nature
of the clock
differences on the code and phases is now separate. and on the phases is
matched by the singular
nature of the ambiguities as well. The lack of a unique separation between the
phase clocks and
the ambiguities is exploited to provide enough constraints so that a least-
squares solution can be
solved at the first epoch of processing.
[0036] Even though it is the decoupling of the clock parameters that has
created a
singular solution, the overall singularity lies as much with the ambiguities
as with the phase
clocks. If the ambiguity parameters could be removed, the carrier phases would
be no more
singular than the pseudoranges. Fixing the ambiguities also enables provision
of a replacement
datum for the phase clocks by using the ambiguities to fill that role.
Consequently, all that is
CA 02651077 2009-01-23
required to provide a minimum-constraint least-squares solution when using the
decoupled clock
model is to arbitrarily fix one ambiguity associated with each estimated phase
clock.
[00371
In a network solution, one of the phase clocks must be fixed as a network
datum
in addition to one of the code clocks. In a single-user solution the fixing of
the satellite clocks
(code and phase) provides the network datum from which to estimate the
receiver clocks (code
and phase).
100381
The concept of fixing ambiguities as a datum is identical to the concept of
fixing
one of each clock as a network datum. In the same way that all clocks are then
estimated relative
to that clock, so with the decoupled clock model all the phase clocks are
computed with respect
to a network datum clock plus an ambiguity datum. Apart from an arbitrary
bias, the formal
nature of the phase clock estimates is unchanged relative to the standard
model clock estimates.
10039] The practical impact of fixing ambiguity datums ensures that any
phase biases are
associated with the underlying oscillator error to form a 'phase clock-
parameter. At the same
time fixing to integer values ensures the remaining ambiguities are
functionally integer in nature.
The effect can be considered as an implicit differencing effect.
100401 Straightforward processing of ionosphere-free dual-frequency data
with the
decoupled clock model and ambiguity datum fixing provides solutions where the
estimated
ambiguities are functionally integer valued. However, for GPS La2 processing
explicit
ambiguity fixing is not practicable because the ionosphere-free wavelength is
too short
(2,3-6mm) relative to the phase noise. In addition, the phase clock estimates
will drift due to the
inability to maintain datum continuity. Datum continuity becomes an issue when
a datum
ambiguity drops out of the solution and a new one must be chosen in its place.
Strict datum
continuity can only be maintained when the new datum ambiguity has converged
to, or been
fixed at, its correct integer value.
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[0041]
For GPS L1/L2 processing therefore. the widelane-phase/narrowlane-code
combination is used to first fix the widelane ambiguity (wavelength -86cm)
which in turn
amplifies the ionosphere-free wavelength to that of the narrowlane (-11cm).
This step produces
a model referred to as the -extended model", and is mandatory for integer
ambiguity resolution
with UPS 1.1/L2 processing. For I.2/L; processing with UPS-Ill for example,
this step will not
provide any benefit, because the ionosphere-free combination wavelength is
already at 12.5cm
and widelane substitution has no effect.
100421
The widelane-phase/narrowlane-code combination (also known as the Melbourne-
Wilbbena observable) is defined as:
A, = L,- = +
where L, = (77L1 - 60L2)117 is the widelane phase combination and p, = (77P, +
60P2)/137 is
the narrowlane code combination. It is usual when using this combination to
consider the station
and satellite biases as constant. however this cannot generally be justified.
Therefore, the
decoupled clock model will be invoked and these biases will be treated as time-
varying. At the
same time ambiguity datum and network bias fixing is applied to introduce
redundancy into the
system. As a third step, this observable is processed simultaneously with P3
and L3 to provide a
homogeneous system of equations. In theory this step should only be undertaken
with rigorous
error propagation from the raw P1, 132, Li and L2 observables. however the
relative correlation
between A4 and P3 and L3 is theoretically small enough that it is possible to
ignore it in practice.
[0043)
Since the decoupled clock model is a generic processing model, it can be
applied
directly to Precise Point Positioning with the advantage that it facilitates
Ambiguity Resolution
(PPP-AR). Just as for standard PPP. PPP-AR requires precise orbit and clock
corrections for
each observed satellite, but in this case each observable requires its own
satellite clock
parameter, namely a carrier phase clock, a pseudorange clock, and a widelane
(clock-like) bias.
The source of such corrections can only be a network solution using the
decoupled clock model.
Standard model clock corrections, such as those provided by the IGS, cannot
facilitate PPP-AR
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because they contain constant code biases and do not contain the phase biases.
Because time
synchronisation alone is the key to undifferenced ambiguity resolution,
regular orbit corrections
can be used.
[0044] Due to
the relative stability of the satellite code biases, the provision of the
corrections can be simplified by providing the pseudorange minus carrier phase
clock difference.
However, the least squares estimates of the satellite code biases are affected
by station code
noise mapped to the satellites, and so both these and the widelane biases may
be smoothed a-
posteriori. For real-time correction distribution, this is likely to be the
optimum method to
minimize the bandwidth required to deliver corrections to a user.
[0045]
Thus. the provision of decoupled satellite clock corrections permits carrier
phase
ambiguity resolution of a single-receiver user of GPS. With ambiguity
resolution possible, PPP-
AR with the decoupled clock model has the capability to drastically reduce the
observation time
required for precise positioning.
[0046]
The foregoing dissertation respecting the invention can be further understood
with
reference to the drawings which discussed hereinbelow.
[0047] Figure 1 is a flowchart showing the basic steps to achieve integer
ambiguity fixed
estimates of position, time and atmosphere (step 70) from single station data
(step 50). Single
station solutions are computed in a PPP process (step 60) and depend on
explicit satellite
positions (ephemeris) and clock estimates (step 40). The only source of such
estimates is a
multiple station solution (step 30) where data from a plurality of widely
spread receivers (step
20) are processed. In principle the satellite positions can be estimated at
the same time as the
satellite clocks, but suitable values from publicly available sources are
available (step 10), and
can be used in both the multiple- and single-station solutions.
[0048]
Figure 2 is a flowchart showing the basic steps of implementing the decoupled
clock model with ambiguity datum fixing in a network process. The minimum
purpose of this
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process is to produce decoupled satellite clock estimates (step 40), for
subsequent single-station
(PPP) processes (step 60). In the current invention, data from multiple
stations is gathered (step
20) and combined into ionosphere-free pseudorange (code), ionosphere-free
carrier phase
(phase) and widelane/narrowlane observables (step 22). The combinations are
formed
independently of the processing epoch and other stations, i.e. they are
undifferenced in the
standard terminology. One oscillator in the system (usually a ground receiver)
is designated as a
reference station and its code, phase and widelane decoupled clock parameters
are held fixed
(step 24). For each remaining oscillator in the system. an ambiguity for both
the phase and
widelane clocks is identified and fixed to an arbitrary integer value (step
26). This fixing
procedure allows a minimum constraint least-squares solution to be formed
(step 28). Such a
solution is not limited to estimating satellite and station clocks and can
include, depending on the
geometry, station and satellite positions, local atmospheric parameters and
other physical
parameters not fixed a-priori to suitably precise values. The iterative nature
of a least-squares
solution permits continual processing with subsequent data from step 22. The
result of the least
squares solution includes ambiguity parameters that can be fixed to integer
values with standard
techniques (step 32) to improve the estimates of the other parameters.
100491
Figure 3 is a flowchart showing the basic steps of implementing the decoupled
clock model with ambiguity datum fixing in a Precise Point Positioning (PPP)
process. The
typical purpose of such a process is to produce precise estimates of position.
time and
atmosphere (step 70). In the current invention, data from a single station is
gathered (step 50)
and combined into ionosphere-free pseudorange (code), ionosphere-free carrier
phase (phase)
and widelane/nan-owlane observables (step 52). The decoupled satellite clock
estimates from a
network solution (step 40) are subtracted from these observables (step 54) to
provide the
necessary clock datum for a single-station solution. For the remaining station
oscillator, an
ambiguity for both the phase and widelane clocks is identified and fixed to an
arbitrary integer
value (step 56). This fixing procedure allows a minimum constraint least-
squares solution to be
formed (step 58). Such a solution is not limited to estimating the station
clocks and usually
includes the station position and local atmospheric parameters. The iterative
nature of a least-
squares solution permits continual processing with subsequent data from step
52. The result of
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the least squares solution includes ambiguity parameters that can be fixed to
integer values with
standard techniques (step 32) to produce improved estimates of the other
parameters (step 70).
[0050]
One benefit of the decoupled clock model compared to other recently introduced
ambiguity resolution techniques, is that accommodating receivers measuring a
different
pseudorange type on either frequency (e.g. Coarse/Acquisition and not Precise
on 1 ) is
straightforward. requiring the user to correct for the constant satellite code
bias with values
which are publicly available, or supplied through an associated correction
stream. In a similar
manner, any carrier phase quadrature bias can also be corrected.
[0051]
From a philosophical point of view, the decoupled clock model conforms to the
original principles of PPP. and in fact GPS, whereby purely undifferenced
observables are used.
and all the user-required information is contained in satellite-only
corrections. However, it
should be stressed that in practice. the decoupled clock model represents a
significantly more
rigorous model of the GPS observations, and, even without explicit ambiguity
resolution,
provides more consistent solutions over those provided by the standard
undifferenced
observation model.
[0052]
The principle of the decoupled clock model can be extended to the processing
of
measurements from other, and multiple, Global Navigation Satellite Systems.
The requirement
for observation-dependent clock parameters is determined by the differing
signal structure of
each system and the consequent hardware implementations of both the
transmitters and the
receivers.
[0053]
Applications of this process involve, for example. use by commercial providers
of
GPS augmentation services to create a GPS correction stream that could
eventually provide near-
instant centimeter-level real-time positioning globally. Centimeter-level
global positioning can
be used in a wide range of applications in positioning, navigation, Earth and
atmospheric
sciences, from engineering and mapping to machine and missile guidance.
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[0054] In addition, the new level of performance in navigation
provided by the present
process has the potential to be used in many government agencies for
applications such as
atmospheric sounding. water surveys (Environment), precision farming
(Agriculture), air/marine
navigation, vehicular guidance, (Transport), mapping, geo-hazards (Natural
Resources), and lidar
and bathymetry surveys (Fisheries and Ocean).
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