- Title
- Large sample properties of separable nonlinear least squares estimators
- Creator
- Mahata, K.; Soderstrom, T.
- Relation
- IEEE Transactions on Signal Processing Vol. 52, Issue 6, p. 1650-1658
- Publisher Link
- http://dx.doi.org/10.1109/TSP.2004.827227
- Publisher
- Institute of Electrical and Electronics Engineers
- Resource Type
- journal article
- Date
- 2004
- Description
- In this paper, the large sample properties of the separable nonlinear least squares algorithm are investigated. Unlike the previous results in the literature, the data are assumed to be complex valued, and the whiteness assumption on the measurement noise sequence has been relaxed. Convergence properties of the parameter estimates are established. Asymptotic accuracy analysis has been carried out, in which the assumptions used are relatively weaker than the assumptions in the previous related works. It is shown under quite general conditions that the parameter estimates are asymptotically circular. Conditions for asymptotic complex normality are also established. Next, a bound on the deviation of the asymptotic covariance matrix from the Crame/spl acute/r-Rao bound (CRB) is derived. Finally, a sufficient condition for the nonlinear least squares estimate to achieve the Crame/spl acute/r-Rao lower bound is established. The results presented in this paper are general and can be applied to any specific application where separable nonlinear least squares is employed.
- Subject
- nonlinear least squares; consistency; Rao bound; variable projection problem
- Identifier
- uon:966
- Identifier
- http://hdl.handle.net/1959.13/26603
- Identifier
- ISSN:1053-587X
- Rights
- Copyright © 2004 IEEE. Reprinted from IEEE Transactions on Signal Processing, 52, 6, 1650-1658. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Newcastle's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.
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