NDLI: Integer parameter estimation in linear models with applications to GPS

Content Provider	IEEE Xplore Digital Library
Author	Hassibi, A. Boyd, S.
Copyright Year	1991
Abstract	We consider parameter estimation in linear models when some of the parameters are known to be integers. Such problems arise, for example, in positioning using carrier phase measurements in the global positioning system (GPS), where the unknown integers enter the equations as the number of carrier signal cycles between the receiver and the satellites when the carrier signal is initially phase locked. Given a linear model, we address two problems: (1) the problem of estimating the parameters and (2) the problem of verifying the parameter estimates. We show that with additive Gaussian measurement noise the maximum likelihood estimates of the parameters are given by solving an integer least-squares problem. Theoretically, this problem is very difficult computationally (NP-hard); verifying the parameter estimates (computing the probability of estimating the integer parameters correctly) requires computing the integral of a Gaussian probability density function over the Voronoi cell of a lattice. This problem is also very difficult computationally. However, by using a polynomial-time algorithm due to Lenstra, Lenstra, and Lovasz (1982), the LLL algorithm, the integer least-squares problem associated with estimating the parameters can be solved efficiently in practice; sharp upper and lower bounds can be found on the probability of correct integer parameter estimation. We conclude the paper with simulation results that are based on a synthetic GPS setup.
Sponsorship	IEEE Signal Processing Society
Starting Page	2938
Ending Page	2952
Page Count	15
File Size	628820
File Format	PDF
ISSN	1053587X
Volume Number	46
Issue Number	11
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1998-11-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Parameter estimation Global Positioning System Additive noise Phase measurement Equations Satellites Noise measurement Gaussian noise Maximum likelihood estimation Probability density function
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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

Estimating the Probability Density Function of a Nonstationary Non-Gaussian Noise

Estimating statistical properties of Eddy-current signals from steam generator tubes

On Tests for Global Maximum of the Log-Likelihood Function

Parameter estimation for autoregressive Gaussian-mixture processes: the EMAX algorithm

Maximum-likelihood array processing in non-Gaussian noise with Gaussian mixtures

Cauchy Estimation for Linear Scalar Systems

GPS positioning in a multipath environment

Blind Maximum-Likelihood Identification of Wiener Systems

The Absolute Maximum of the Likelihood Function of the Rice Distribution: Existence and Uniqueness

Integer parameter estimation in linear models with applications to GPS

Similar Documents

Estimating the Probability Density Function of a Nonstationary Non-Gaussian Noise

Estimating statistical properties of Eddy-current signals from steam generator tubes

On Tests for Global Maximum of the Log-Likelihood Function

Parameter estimation for autoregressive Gaussian-mixture processes: the EMAX algorithm

Maximum-likelihood array processing in non-Gaussian noise with Gaussian mixtures

Cauchy Estimation for Linear Scalar Systems

GPS positioning in a multipath environment

Blind Maximum-Likelihood Identification of Wiener Systems

The Absolute Maximum of the Likelihood Function of the Rice Distribution: Existence and Uniqueness

Integer parameter estimation in linear models with applications to GPS