The effects of proportional steering strategies on the behavior of controlled clocks

Two approaches to steering clocks to a reference standard via frequency steers have been explored in the literature, the pole placement (PP) approach and the linear quadratic Gaussian (LQG) approach. The PP method sets the response time of the controlled clock. 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). This paper unifies these techniques by developing an analysis that quantifies what time constants follow from the LQG-derived gains, and what costs are incurred by the PP-derived gains. With this analysis, one can compute how sensitive the outcomes would be to variations of the steering constants. Another outcome we present is a quantification of the degradation due to a common form of suboptimal state estimation, as well as that due to delays before steering decisions can be implemented into the system.