TY - GEN
T1 - PDF Evaluation of Elliptically Contoured GNSS Integer Ambiguity Residuals
AU - Teunissen, Peter J.G.
AU - Verhagen, Sandra
PY - 2023
Y1 - 2023
N2 - In this contribution we will present and evaluate the joint probability density function (PDF) of the multivariate integer GNSS carrier phase ambiguity residuals, thereby assuming that the GNSS data belong to the very general class of elliptically contoured (EC) distributions. Examples of distributions belonging to this class are the multivariate normal distribution, the t-distribution and the contaminated normal distribution. Since the residuals and their properties depend on the integer estimation principle used, we will present the PDF of the ambiguity residuals for the whole class of admissible integer estimators. This includes the estimation principles of integer rounding, integer bootstrapping, and integer least squares. The probabilistic properties of these estimators vary with the distributions from the EC-class. In order to get a better understanding of the various features of the joint PDF of the ambiguity residuals we will use a step-by-step construction aided by graphical means.
AB - In this contribution we will present and evaluate the joint probability density function (PDF) of the multivariate integer GNSS carrier phase ambiguity residuals, thereby assuming that the GNSS data belong to the very general class of elliptically contoured (EC) distributions. Examples of distributions belonging to this class are the multivariate normal distribution, the t-distribution and the contaminated normal distribution. Since the residuals and their properties depend on the integer estimation principle used, we will present the PDF of the ambiguity residuals for the whole class of admissible integer estimators. This includes the estimation principles of integer rounding, integer bootstrapping, and integer least squares. The probabilistic properties of these estimators vary with the distributions from the EC-class. In order to get a better understanding of the various features of the joint PDF of the ambiguity residuals we will use a step-by-step construction aided by graphical means.
KW - Ambiguity success-rate
KW - GNSS
KW - Integer ambiguity resolution
KW - Integer least-squares (ILS)
KW - Pull-in region
KW - Z-transformation
UR - https://www.scopus.com/pages/publications/85195510861
U2 - 10.1007/1345_2023_204
DO - 10.1007/1345_2023_204
M3 - Conference contribution
AN - SCOPUS:85195510861
SN - 9783031553592
T3 - International Association of Geodesy Symposia
SP - 57
EP - 63
BT - X Hotine-Marussi Symposium on Mathematical Geodesy
A2 - Freymueller, Jeffrey T.
A2 - Sánchez, Laura
PB - Springer
T2 - 10th Hotine-Marussi Symposium on Mathematical Geodesy, 2022
Y2 - 13 June 2022 through 17 June 2022
ER -