  The performance of Neyman-Pearson detection of correlated stochastic signals
using noisy observations is investigated via the error exponent for the miss
probability with a fixed level. Using the state-space structure of the signal
and observation model, a closed-form expression for the error exponent is
derived, and the connection between the asymptotic behavior of the optimal
detector and that of the Kalman filter is established. The properties of the
error exponent are investigated for the scalar case. It is shown that the error
exponent has distinct characteristics with respect to correlation strength: for
signal-to-noise ratio (SNR) >1 the error exponent decreases monotonically as
the correlation becomes stronger, whereas for SNR <1 there is an optimal
correlation that maximizes the error exponent for a given SNR.
