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Parameters adjustment for PPP
| Fundamentals | |
|---|---|
| Title | Parameters adjustment for PPP |
| Author(s) | J. Sanz Subirana, JM. Juan Zornoza and M. Hernandez-Pajares, University of Catalunia, Spain. |
| Level | Medium |
| Year of Publication | 2011 |
The linear observation model [math]\displaystyle{ {\mathbf Y}={\mathbf G}\;{\mathbf X} }[/math] can be solved using Kalman Filter, considering the carrier phase bias [math]\displaystyle{ B^i }[/math] as "constants" along continuous phase arcs, and "white-noise" at the instants when cycle-slips occurs.
The following stochastic model can be used for the filter:
- Carrier phase biases ([math]\displaystyle{ B_C }[/math]) are taken as "constants" along continuous phase arcs, and "white-noise" when a cycle-slip happens (with [math]\displaystyle{ \sigma=10^4\,m }[/math], for instance, after a previous carrier-code alignment), see [[Kalman Filter}]].
- Wet tropospheric delay ([math]\displaystyle{ \Delta T_{z,wet} }[/math]) is taken as a random-walk process (a process noise with [math]\displaystyle{ d\sigma^2/dt= 1\,cm^2/h }[/math], initialised with [math]\displaystyle{ \sigma^2_0=0.25\, m^2 }[/math], can be used for most of the applications), see [[Kalman Filter}]].
- Receiver clock ([math]\displaystyle{ c\, \delta t }[/math]) is taken as a white noise process (with [math]\displaystyle{ \sigma= 3\, 10^5\; m }[/math], i.e, [math]\displaystyle{ 1 }[/math] millisecond, for instance.), see [[Kalman Filter}]].
- Receiver coordinates ([math]\displaystyle{ dx,dy,dz }[/math])
- For static positioning: the coordinates are taken as constants, see Kalman Filter.
- For kinematic positioning: the coordinates are taken as white noise or a random walk process as in Kalman Filter.
This solving procedure is called {\em to float} ambiguities. Floating in the sense that they are estimated by the filter "as real numbers". The bias estimations [math]\displaystyle{ B^i }[/math] will converge into a solution after a transition time that depends on the observation geometry, model quality and data noise. In general, one must expect errors at the decimetre level in pure kinematic positioning (i.e., coordinates [math]\displaystyle{ (x,y,z) }[/math] modelled as white-noise) and at the centimetre level in static PPP.