On a unified framework for linear nuisance parameters

On a unified framework for linear nuisance parameters

Hu, Y. (TU Delft Signal Processing Systems)
Leus, G.J.T. (TU Delft Signal Processing Systems)

2017

Estimation problems in the presence of deterministic linear nuisance parameters arise in a variety of fields. To cope with those, three common methods are widely considered: (1) jointly estimating the parameters of interest and the nuisance parameters; (2) projecting out the nuisance parameters; (3) selecting a reference and then taking differences between the reference and the observations, which we will refer to as “differential signal processing.” A lot of literature has been devoted to these methods, yet all follow separate paths. Based on a unified framework, we analytically explore the relations between these three methods, where we particularly focus on the third one and introduce a general differential approach to cope with multiple distinct nuisance parameters. After a proper whitening procedure, the corresponding best linear unbiased estimators (BLUEs) are shown to be all equivalent to each other. Accordingly, we unveil some surprising facts, which are in contrast to what is commonly considered in literature, e.g., the reference choice is actually not important for the differencing process. Since this paper formulates the problem in a general manner, one may specialize our conclusions to any particular application. Some localization examples are also presented in this paper to verify our conclusions.

Best linear unbiased estimator (BLUE)
Differential signal processing
Joint estimation
Linear nuisance parameters
Orthogonal subspace projection (OSP)
Source localization

http://resolver.tudelft.nl/uuid:045ff678-d64b-4e01-aa1b-b07f7e331a8f

https://doi.org/10.1186/s13634-016-0438-8

1687-6172

Eurasip Journal on Advances in Signal Processing, 2017 (1), 1-14

Institutional Repository

journal article

© 2017 Y. Hu, G.J.T. Leus