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