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# Parameters adjustment for PPP

Fundamentals | |
---|---|

Title | Parameters adjustment for PPP |

Author(s) | J. Sanz Subirana, J.M. Juan Zornoza and M. Hernández-Pajares, Technical University of Catalonia, Spain. |

Level | Basic |

Year of Publication | 2011 |

The linear observation model [math]{\mathbf Y}={\mathbf G}\;{\mathbf X}[/math] can be solved using Kalman Filter, considering the carrier phase bias [math]B_{C}^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]B_C[/math]) are taken as "constants" along continuous phase arcs, and "white-noise" when a cycle-slip happens (with [math]\sigma=10^4\,m[/math], for instance), see Kalman Filter.

**Wet tropospheric delay**([math]\Delta T_{z,wet}[/math]) is taken as a random-walk process (a process noise with [math]d\sigma^2/dt= 1\,cm^2/h[/math], initialised with [math]\sigma^2_0=0.25\, m^2[/math], can be used for most of the applications), see Kalman Filter.

**Receiver clock**([math]c\, \delta t[/math]) is taken as a white noise process (with [math]\sigma= 3\, 10^5\; m[/math], i.e, [math]1[/math] millisecond, for instance.), see Kalman Filter.

**Receiver coordinates**([math]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 *to float* ambiguities. Floating in the sense that they are estimated by the filter "as real numbers". The bias estimations [math]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](x,y,z)[/math] modelled as white-noise) and at the centimetre level in static PPP.