PPP Fundamentals

Fundamentals
Title	PPP Fundamentals
Author(s)	GMV
Level	Basic
Year of Publication	2011

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.

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.