A Discrete/Continuous Minimization Method in Interferometric Image Processing
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
A Chebyshev Inequality For Multivariate Normal Distribution
Probability in the Engineering and Informational Sciences
EURASIP Journal on Applied Signal Processing
Integer least squares: sphere decoding and the LLL algorithm
Proceedings of the 2008 C3S2E conference
Rigorous and Efficient Short Lattice Vectors Enumeration
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Radius selection algorithms for sphere decoding
C3S2E '09 Proceedings of the 2nd Canadian Conference on Computer Science and Software Engineering
Solving Ellipsoid-Constrained Integer Least Squares Problems
SIAM Journal on Matrix Analysis and Applications
Algorithms for the shortest and closest lattice vector problems
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Ps-LAMBDA: Ambiguity success rate evaluation software for interferometric applications
Computers & Geosciences
Useful tools for non-linear systems: Several non-linear integral inequalities
Knowledge-Based Systems
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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