Investigation of Pole Placement Technique for Clock Steering

Abstract

The development of robust and accurate time scales is a key parameter for various future applications, i.e., in the global navigation satellite system sector. A promising concept is the composite clock approach which combines several clocks to produce a time scale which performs better than the individual inputs. One method to generate a composite time uses a Kalman filter to compute the Implicit Ensemble Mean (IEM). This produces only a software timescale but a physical realization may also be required, e.g. to create a Universal Coordinate Time contribution in a time lab. In a simplified manner, this can be achieved by combining the IEM with phase measurements of a real clock in a second Kalman filter. The second Kalman filter generates control values which can be applied to the real clock in turn steering its behavior to the generated IEM. To date, these control values are primarily calculated using the Linear Quadratic Gaussian (LQG) control technique. LQG control is a very flexible technique where the user can tune three different parameters to optimize the control values. However, this flexibility also makes it difficult to find the best parameter set for a given scenario. In this paper we investigate the use of an alternate technique to generate the aforementioned control values. This Pole Placement (PP) technique is designed for use in a closed loop system such as the one defined in the composite clock approach. One determines the poles of the system and moves them to desired pole locations. The poles are obtained by identifying the eigenvalues of the system’s state transition matrix. The benefit of this technique is that only one parameter, the desired pole location, must be fed into the system. This allows for significant simplification of the control value optimization. To evaluate this technique, we performed simulations in which two fictional clocks are steered against each other. We demonstrate sufficient steering performance using PP thus allowing for easier optimization of the control parameters in future applications.