A divide and conquer approach to least-squares estimation
- 1 March 1990
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Aerospace and Electronic Systems
- Vol. 26 (2) , 423-427
- https://doi.org/10.1109/7.53453
Abstract
The problem of estimating parameters theta which determine the mean mu ( theta ) of a Gaussian-distributed observation X is considered. It is noted that the maximum-likelihood (ML) estimate, in this case the least-squares estimate, has desirable statistical properties but can be difficult to compute when mu ( theta ) is a nonlinear function of theta . An estimate formed by combining ML estimates based on subsections of the data vector X is proposed as a computationally inexpensive alternative. The main result is that this alternative estimate, termed here the divide-and-conquer (DAC) estimate, has ML performance in the small-error region when X is appropriately subdivided. As an example application, an inexpensive range-difference-based position estimator is derived and shown by means of Monte-Carlo simulation to have small-error-region mean-square error equal to the Cramer-Rao lower bound.Keywords
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