Accession Number : ADA316640
Title : Interactive Computer-Aided Control System Design.
Descriptive Note : Final rept. 1 Jun 93-31 May 96,
Corporate Author : STANFORD UNIV CA
Personal Author(s) : Boyd, Stephen ; Hassibi, Arash
PDF Url : ADA316640
Report Date : 14 OCT 1996
Pagination or Media Count : 10
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 phase measurements in th global positioning system (GPS). Given a linear model, we address two problems: The problem of estimating the parameters; the problem of verifying the parameter estimates. Under Gaussian measurement noise: maximum likelihood estimates of the parameters are given by solving an integer least-square problem. Theoretically, this problem is very difficult to solve. Verifying the parameter estimates (computing the probability of correct integer parameter estimation) is related to computing the integral of a Gaussian PDF over the Voronol cell of a lattice. This problem is also very difficult computationally. However, by using a polynomial-time algorithm due to Lenstra, Lenstra, and Lovasz (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 GPS setup.
Descriptors : *COMPUTER AIDED DESIGN, *GLOBAL POSITIONING SYSTEM, MATHEMATICAL MODELS, ALGORITHMS, LINEAR SYSTEMS, SIMULATION, MEASUREMENT, PARAMETERS, MAXIMUM LIKELIHOOD ESTIMATION, INTEGER PROGRAMMING, GAUSSIAN NOISE, ESTIMATES, LINEARITY, LEAST SQUARES METHOD, NUMBERS.
Subject Categories : Computer Programming and Software
Construction Equipment, Materials & Supplies
Distribution Statement : APPROVED FOR PUBLIC RELEASE