Method for calculation the root mean square error of autonomous timescale keeping with a polynomial representation of clock correction in an autonomous navigation system

The article considers the problem of autonomous timescale keeping within an autonomous navigation system of a moving vehicle. The root-mean-square error of autonomous timescale keeping increases with the keeping duration and must be taken into account by the navigation system when processing primary navigation measurements and generating output navigation data. This article develops a method for real-time calculating the root-mean-square error of autonomous timescale keeping. This method is acceptable for implementation in a navigation system computer. The method was developed on the base of consideration of the random error of autonomous timescale keeping as the sum of random fl uctuations and systematic drift of the instrumental time scale relative to the reference one. Random fl uctuations are represented by the sum of fi ve independent random processes, for which analytical expressions for the dispersion and autocorrelation functions are obtained. The systematic drift is taken into account in the form of a clock correction described by a quadratic polynomial with unknown random coeffi cients. The polynomial coeffi cients are calculated using the least-squares method based on correlated measurements of the instants of reception of an external synchronization signal. This article examines the recurrent implementation of an algorithm for estimating coeffi cients in correlated measurements. Experimental results from applying the developed method to a thermostated frequency and time keeping device based on a compact rubidium oscillator are presented. The research results presented in this article can be used in the design of autonomous navigation systems for preliminary calculations of their accuracy characteristics and in the embedded software of such systems for real-time calculations of the root-mean-square error of autonomous timescale keeping.