The Unification of the Pole Placement and Linear Quadratic Gaussian Techniques

Two approaches to steering clocks to a reference standard via frequency steers have been explored in the literature, the Linear Quadratic Gaussian (LQG) approach and the Pole Placement (PP) approach. LQG minimizes a user-selected cost function, which is a linear combination of the expected variances of the phase, frequency, and control effort (frequency steers). The PP method sets the response time of the controlled clock. We unify these techniques by developing an analysis that quantifies what time constants are in fact determined by LQG-derived gains, and what total costs would be incurred under PP-derived gains. We also explore the effects of suboptimal state estimation, and of delays between the time measurements are made and when the steering decisions based upon them are incorporated into the system.