Open Access

Erratum to: A Wald test with enhanced selectivity properties in homogeneous environments

EURASIP Journal on Advances in Signal Processing20152015:63

https://doi.org/10.1186/s13634-015-0252-8

Published: 24 July 2015

The original article was published in EURASIP Journal on Advances in Signal Processing 2013 2013:14

After publication of our work [1] we noticed the following mistakes:

Equation (3) should be
$$ \boldsymbol{I}\left(\boldsymbol{\theta} \right)=\mathrm{E}\left[\left(\frac{\partial \ln f\left(\boldsymbol{x},\boldsymbol{X};\boldsymbol{\theta} \right)}{\partial {\boldsymbol{\theta}}^{*}}\right)\left(\frac{\partial \ln f\left(\boldsymbol{x},\boldsymbol{X};\boldsymbol{\theta} \right)}{\partial {\boldsymbol{\theta}}^T}\right)\right] $$
(3)
Equation (5) should be
$$ {t}_{\mathrm{Wald}}={\left({\widehat{\boldsymbol{\theta}}}_{r_1}-{\boldsymbol{\theta}}_{r_0}\right)}^H{\left\{{\left[{\boldsymbol{I}}^{-1}\left({\widehat{\boldsymbol{\theta}}}_1\right)\right]}_{{\boldsymbol{\theta}}_r{\boldsymbol{\theta}}_r^{*}}\right\}}^{-1}\left({\widehat{\boldsymbol{\theta}}}_{r_1}-{\boldsymbol{\theta}}_{r_0}\right) $$
(5)

The notation “--“ in equations (6), (11), and (12) should be replaced by “-“, i.e., the minus sign.

Equations (17), (18), and (19) should be
$$ {\tilde{t}}_{\mathrm{ACE}}=\frac{{\tilde{\boldsymbol{x}}}^H{\boldsymbol{P}}_{\tilde{\boldsymbol{s}}}\tilde{\boldsymbol{x}}}{{\tilde{\boldsymbol{x}}}^H{\boldsymbol{P}}_{\tilde{\boldsymbol{s}}}^{\perp}\tilde{\boldsymbol{x}}}=\frac{{\left\Vert {\boldsymbol{P}}_{\tilde{\boldsymbol{s}}}\tilde{\boldsymbol{x}}\right\Vert}^2}{{\left\Vert {\boldsymbol{P}}_{\tilde{\boldsymbol{s}}}^{\perp}\tilde{\boldsymbol{x}}\right\Vert}^2} $$
(17)
$$ {t}_{\mathrm{Wald}}=\frac{1}{1+{\left\Vert \tilde{\boldsymbol{x}}\right\Vert}^2{\left\Vert {\boldsymbol{P}}_{\tilde{\boldsymbol{s}}}^{\perp}\tilde{\boldsymbol{x}}\right\Vert}^2/{\left\Vert {\boldsymbol{P}}_{\tilde{\boldsymbol{s}}}\tilde{\boldsymbol{x}}\right\Vert}^2} $$
(18)
and
$$ {\tilde{t}}_{\mathrm{Wald}}=\frac{{\left\Vert {\boldsymbol{P}}_{\tilde{\boldsymbol{s}}}\tilde{\boldsymbol{x}}\right\Vert}^2}{{\left\Vert {\boldsymbol{P}}_{\tilde{\boldsymbol{s}}}^{\perp}\tilde{\boldsymbol{x}}\right\Vert}^2{\left\Vert \tilde{\boldsymbol{x}}\right\Vert}^2} $$
(19)

respectively.

Notes

Authors’ Affiliations

(1)
College of Electronic Science and Engineering, National University of Defense Technology
(2)
Key Research Lab, Wuhan Radar Academy

References

  1. W Liu, W Xie, Y Wang, A Wald test with enhanced selectivity properties in homogeneous environments. EURASIP J Adv Signal Process 2013, 14 (2013)View ArticleGoogle Scholar

Copyright

© Liu et al. 2015

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.