  The optimal power adaptation problem is investigated for vector parameter
estimation according to various Fisher information based optimality criteria.
By considering an observation model that involves a linear transformation of
the parameter vector and an additive noise component with an arbitrary
probability distribution, six different optimal power allocation problems are
formulated based on Fisher information based objective functions. Via
optimization theoretic approaches, various closed-form solutions are derived
for the proposed problems. Also, the results are extended to cases in which
nuisance parameters exist in the system model or certain types of nonlinear
transformations are applied on the parameter vector. Numerical examples are
presented to investigate performance of the proposed power allocation
strategies.
