  In this paper, we consider the detection of a small change in the frequency
of sinusoidal signals, which arises in various signal processing applications.
The generalized likelihood ratio test (GLRT) for this problem uses the maximum
likelihood (ML) estimator of the frequency, and therefore suffers from high
computational complexity. In addition, the GLRT is not necessarily optimal and
its performance may degrade for non-asymptotic scenarios that are characterized
by close hypotheses and small sample sizes. In this paper we propose a new
detection method, named the generalized locally most powerful unbiased (GLMPU)
test, which is a general method for local detection in the presence of nuisance
parameters. A closed-form expression of the GLMPU test is developed for the
detection of frequency deviation in the case where the complex amplitudes of
the measured signals are unknown. Numerical simulations show improved
performance over the GLRT in terms of probability of detection performance and
computational complexity.
