  This work investigates the task of estimating a real valued parameter vector
based on complex valued measurements in a classical set-up. The application of
standard estimators in general results in complex valued estimates of the real
valued parameter vector. To avoid this systematic error, widely linear
classical estimators that produce real valued estimates are investigated. One
of these estimators is the widely linear least squares (WLLS) estimator
proposed in this work, which does not utilize any noise statistics. Further, we
introduce the best widely linear unbiased estimator (BWLUE) for real valued
parameter vectors. The proposed estimators in general outperform their standard
counterparts LS estimator and BWLUE, respectively, and they only require half
as many complex valued measurements. We compare the novel approaches to
standard classical estimators in two application scenarios. One of these
applications considers the estimation of a real valued impulse response based
on noisy measurements of the system's magnitude and phase response. For this
problem, we propose a novel two-step approach based on the introduced widely
linear concepts that outperforms standard estimators.
