  In this paper, we discover that the trace of the division of the optimal
output estimation error covariance over the noise covariance attained by the
Kalman-Bucy filter can be explicitly expressed in terms of the plant dynamics
and noise statistics in a frequency-domain integral characterization. Towards
this end, we examine the algebraic Riccati equation associated with Kalman-Bucy
filtering using analytic function theory and relate it to the Bode integral.
Our approach features an alternative, frequency-domain framework for analyzing
algebraic Riccati equations and reduces to various existing related results.
