کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4974655 | 1365544 | 2016 | 31 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Reduced-rank estimation for ill-conditioned stochastic linear model with high signal-to-noise ratio
ترجمه فارسی عنوان
تخمین زده شده برای مدل خطی تصادفی نامناسب با نسبت سیگنال به نویز بالا
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موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
پردازش سیگنال
چکیده انگلیسی
Reduced-rank approach has been used for decades in robust linear estimation of both deterministic and random vector of parameters in linear model y=Hx+ϵn. In practical settings, estimation is frequently performed under incomplete or inexact model knowledge, which in the stochastic case significantly increases mean-square-error (MSE) of an estimate obtained by the linear minimum mean-square-error (MMSE) estimator, which is MSE-optimal among linear estimators in the theoretical case of perfect model knowledge. However, the improved performance of reduced-rank estimators over MMSE estimator in estimation under incomplete or inexact model knowledge has been established to date only by means of numerical simulations and arguments indicating that the reduced-rank approach may provide improved performance over MMSE estimator in certain settings. In this paper we focus on the high signal-to-noise ratio (SNR) case, which has not been previously considered as a natural area of application of reduced-rank estimators. We first show explicit sufficient conditions under which familiar reduced-rank MMSE and truncated SVD estimators achieve lower MSE than MMSE estimator if singular values of array response matrix H are perturbed. We then extend these results to the case of a generic perturbation of array response matrix H, and demonstrate why MMSE estimator frequently attains higher MSE than reduced-rank MMSE and truncated SVD estimators if H is ill-conditioned. The main results of this paper are verified in numerical simulations.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of the Franklin Institute - Volume 353, Issue 13, September 2016, Pages 2898-2928
Journal: Journal of the Franklin Institute - Volume 353, Issue 13, September 2016, Pages 2898-2928
نویسندگان
Tomasz Piotrowski, Isao Yamada,