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==PPP Algorithm==
==PPP Algorithm==


Precise Point Positioning (PPP) is a global precise positioning service, since it requires the availability of precise reference satellite orbit and clock products in real-time using a network of GNSS reference stations distributed worldwide.
The PPP algorithm uses as input code and phase observations from a dual-frequency receiver, and precise satellite orbits and clocks, in order to calculate precise receiver coordinates and clock. The dual frequency observables are used undifferenced, and combined into the so-called ionosphere-free combination. The highlights of the algorithm are described next.
At a given epoch, and for a given satellite, the simplified observation equations are presented next:


Combining the precise satellite positions and clocks with a dual-frequency GNSS receiver (to remove the first order effect of the ionosphere), PPP is able to provide position solutions at centimetre to decimetre level<ref>M.D. Laínez Samper et al, [http://mycoordinates.org/multisystem-real-time-precise-point-positioning/ Multisystem real time precise-point-positioning], Coordinates, Volume VII, Issue 2, February 2011</ref>. PPP differs from double-difference [[Real Time Kinematic|Real Time Kinematic (RTK)]] positioning in the sense that it does not require access to observations from one or more close reference stations accurately-surveyed. PPP just requires data from reference stations from a relatively sparse station network (thousands of km apart would suffice). This makes PPP a very attractive alternative to RTK for those areas where RTK coverage is not available. On the contrary, the PPP technique is still not so much consolidated as RTK and requires a longer convergence time to achieve maximum performances (in the order of tenths of minutes).  
l_P=ρ+c(b_Rx-b_Sat )+Tr+ε_P (1)
l_∅=ρ+c(b_Rx-b_Sat )+Tr+〖Nλ+ε〗_∅ (2)
 
Where:
lP is the ionosphere-free combination of L1 and L2 pseudoranges
l is the ionosphere-free combination of L1 and L2 carrier phases
bRx is the receiver clock offset from the reference (GPS) time
bSat is the satellite clock offset from the reference (GPS) time
c is the vacuum speed of light
Tr is the signal path delay due to the troposphere
 is the carrier combination wavelength
N is the ambiguity of the carrier-phase ionosphere-free combination (it is not an integer number)
P and  are the measurement noise components, including multipath and other effects
is the geometrical range between the satellite and the receiver, computed as a function of the satellite (xSat, ySat, zSat) and receiver (xRx, yRx, zRx) coordinates as:
 
ρ=√(〖(x_Sat-x_Rx)〗^2+〖(y_Sat-y_Rx)〗^2+〖(z_Sat-z_Rx)〗^2 )  (3)
 
The observations coming from all the satellites are processed together in a filter that solves for the different unknowns, namely the receiver coordinates, the receiver clock, the zenith tropospheric delay and the phase ambiguities.


The [[PPP Fundamentals|PPP algorithm]] uses as input code and phase observations from a dual-frequency receiver, and precise satellite orbits and clocks, in order to calculate precise receiver coordinates and clock. The observations coming from all the satellites are processed together in a filter that solves for the different unknowns, namely the receiver coordinates, the receiver clock, the zenith tropospheric delay and the phase ambiguities.


The accuracy of the satellite clocks and orbits is one of the most important factors affecting the quality of the PPP. Another relevant factor that affects the PPP performances is the amount and quality of the observations. Like any GNSS technique, PPP is affected by satellite line-of-sight obstructions. Even the most precise orbit and clock data is useless if the user cannot track particular satellites. When satellite visibility is partially obstructed, a best possible service can be ensured by using the full range of satellites from both the GPS and GLONASS systems.


The trend clearly lies towards increasing availability of GNSS satellites on orbit; many studies predict the future benefits of combining the constellations of GPS and Galileo. There is no need, however, to wait for future constellations to reap the immediate benefits of access to additional GNSS satellites. The current GLONASS constellation may not have all the features of future GNSS systems, but it is available here and now. Recently, the Russian government has proven its commitment to enhancing the GLONASS constellation. Many receiver manufacturers have also acknowledged this fact and now provide combined GPS and GLONASS receivers.


==Notes==
==Notes==

Revision as of 16:08, 13 May 2011


FundamentalsFundamentals
Title PPP Fundamentals
Author(s) GMV
Level Basic
Year of Publication 2011
Logo GMV.png


Precise point positioning (PPP) is a global precise positioning service using current and coming GNSS constellations. PPP requires the availability of precise reference satellite orbit and clock products in real-time using a network of GNSS reference stations distributed worldwide. Combining the precise satellite positions and clocks with a dual-frequency GNSS receiver (to remove the first order effect of the ionosphere), PPP is able to provide position solutions at centimetre to decimetre level[1].

PPP Algorithm

The PPP algorithm uses as input code and phase observations from a dual-frequency receiver, and precise satellite orbits and clocks, in order to calculate precise receiver coordinates and clock. The dual frequency observables are used undifferenced, and combined into the so-called ionosphere-free combination. The highlights of the algorithm are described next. At a given epoch, and for a given satellite, the simplified observation equations are presented next:

l_P=ρ+c(b_Rx-b_Sat )+Tr+ε_P (1) l_∅=ρ+c(b_Rx-b_Sat )+Tr+〖Nλ+ε〗_∅ (2)

Where: lP is the ionosphere-free combination of L1 and L2 pseudoranges l is the ionosphere-free combination of L1 and L2 carrier phases bRx is the receiver clock offset from the reference (GPS) time bSat is the satellite clock offset from the reference (GPS) time c is the vacuum speed of light Tr is the signal path delay due to the troposphere  is the carrier combination wavelength N is the ambiguity of the carrier-phase ionosphere-free combination (it is not an integer number) P and  are the measurement noise components, including multipath and other effects  is the geometrical range between the satellite and the receiver, computed as a function of the satellite (xSat, ySat, zSat) and receiver (xRx, yRx, zRx) coordinates as:

ρ=√(〖(x_Sat-x_Rx)〗^2+〖(y_Sat-y_Rx)〗^2+〖(z_Sat-z_Rx)〗^2 ) (3)

The observations coming from all the satellites are processed together in a filter that solves for the different unknowns, namely the receiver coordinates, the receiver clock, the zenith tropospheric delay and the phase ambiguities.



Notes


References

  1. ^ M.D. Laínez Samper et al, Multisystem real time precise-point-positioning, Coordinates, Volume VII, Issue 2, February 2011
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