<abstract xmlns="http://www.w3.org/1999/xhtml"><p>The problem of integer or mixed integer/real valued parameter estimation in linear models is considered. It is a well-known result that for zero-mean additive Gaussian measurement noise the integer least-squares estimator is optimal in the sense of maximizing the probability of correctly estimating the full vector of integer parameters. In applications such as global navigation satellite system ambiguity resolution, it can be beneficial to resolve only a subset of all integer parameters. We derive the estimator that leads to the highest possible success rate for a given integer subset and compare its performance to suboptimal integer mappings via numerical studies. Implementation aspects of the optimal estimator as well as subset selection criteria are discussed.</p></abstract>

The problem of integer or mixed integer/real valued parameter estimation in linear models is considered. It is a well-known result that for zero-mean additive Gaussian measurement noise the integer least-squares estimator is optimal in the sense of maximizing the probability of correctly estimating the full vector of integer parameters. In applications such as global navigation satellite system ambiguity resolution, it can be beneficial to resolve only a subset of all integer parameters. We derive the estimator that leads to the highest possible success rate for a given integer subset and compare its performance to suboptimal integer mappings via numerical studies. Implementation aspects of the optimal estimator as well as subset selection criteria are discussed.

Optimal Estimation of a Subset of Integers with Application to GNSS

Artificial Satellites

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Optimal Estimation of a Subset of Integers with Application to GNSS"}

The problem of integer or mixed integer/real valued parameter estimation in linear models is considered. It is a well-known result that for zero-mean additive...

Optimal Estimation of a Subset of Integers with Application to GNSS

Publié en ligne: 23 déc. 2016

Pages: 123 - 134

Reçu: 25 mai 2016

Accepté: 02 nov. 2016

DOI: https://doi.org/10.1515/arsa-2016-0011

Mots clés
Integer estimation, GNSS ambiguity resolution, Partial fixing, Success rate

© 2016 Artificial Satellites

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Optimal Estimation of a Subset of Integers with Application to GNSS

Publié en ligne: 23 déc. 2016

Pages: 123 - 134

Reçu: 25 mai 2016

Accepté: 02 nov. 2016

DOI: https://doi.org/10.1515/arsa-2016-0011

Mots clésInteger estimation, GNSS ambiguity resolution, Partial fixing, Success rate

© 2016 Artificial Satellites

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
Integer estimation, GNSS ambiguity resolution, Partial fixing, Success rate