NDLI: A stochastic framework for inequality constrained estimation

Content Provider	Springer Nature Link
Author	Roese Koerner, Lutz Devaraju, Balaji Sneeuw, Nico Schuh, Wolf Dieter
Copyright Year	2012
Abstract	Quality description is one of the key features of geodetic inference. This is even more true if additional information about the parameters is available that could improve the accuracy of the estimate. However, if such additional information is provided in the form of inequality constraints, most of the standard tools of quality description (variance propagation, confidence ellipses, etc.) cannot be applied, as there is no analytical relationship between parameters and observations. Some analytical methods have been developed for describing the quality of inequality constrained estimates. However, these methods either ignore the probability mass in the infeasible region or the influence of inactive constraints and therefore yield only approximate results. In this article, a frequentist framework for quality description of inequality constrained least-squares estimates is developed, based on the Monte Carlo method. The quality is described in terms of highest probability density regions. Beyond this accuracy estimate, the proposed method allows to determine the influence and contribution of each constraint on each parameter using Lagrange multipliers. Plausibility of the constraints is checked by hypothesis testing and estimating the probability mass in the infeasible region. As more probability mass concentrates in less space, applying the proposed method results in smaller confidence regions compared to the unconstrained ordinary least-squares solution. The method is applied to describe the quality of estimates in the problem of approximating a time series with positive definite functions.
Starting Page	1005
Ending Page	1018
Page Count	14
File Format	PDF
ISSN	09497714
Journal	Journal of Geodesy
Volume Number	86
Issue Number	11
e-ISSN	14321394
Language	English
Publisher	Springer-Verlag
Publisher Date	2012-04-11
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Stochastic framework Inequality constrained least-squares Monte Carlo method Quality description Sensitivity analysis Lagrange multipliers Geophysics/Geodesy Earth Sciences
Content Type	Text
Resource Type	Article
Subject	Geophysics Geochemistry and Petrology Computers in Earth Sciences

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

An Aggregate Constraint Method for Inequality-constrained Least Squares Problems

A Bayesian method for linear, inequality-constrained adjustment and its application to GPS positioning

Convex optimization under inequality constraints in rank-deficient systems

On the equivalence of Kalman filtering and least-squares estimation

The convergence problem of collocation solutions in the framework of the stochastic interpretation

On weighted total least-squares with linear and quadratic constraints

Integer least-squares theory for the GNSS compass

MLAMBDA: a modified LAMBDA method for integer least-squares estimation

The affine constrained GNSS attitude model and its multivariate integer least-squares solution

A stochastic framework for inequality constrained estimation

Similar Documents

An Aggregate Constraint Method for Inequality-constrained Least Squares Problems

A Bayesian method for linear, inequality-constrained adjustment and its application to GPS positioning

Convex optimization under inequality constraints in rank-deficient systems

On the equivalence of Kalman filtering and least-squares estimation

The convergence problem of collocation solutions in the framework of the stochastic interpretation

On weighted total least-squares with linear and quadratic constraints

Integer least-squares theory for the GNSS compass

MLAMBDA: a modified LAMBDA method for integer least-squares estimation

The affine constrained GNSS attitude model and its multivariate integer least-squares solution

A stochastic framework for inequality constrained estimation