B.1 Introduction

The principle of employing satellite navigation systems for position and time determination requires the satellite clocks to be in synchronism to a common timebase.

High-accuracy AFS are required to meet the stringent stability and drift rate requirements so that the common time base can be maintained. Stability is also important for the less accurate crystal-based oscillators that are typically employed in user equipment.

Frequency sources are subject to systemic errors, such as frequency offsets, aging, and random frequency errors. Random frequency errors are a primary concern, especially when characterizing the performance of an AFS. There are a number of important random frequency noise processes (i.e., frequency fluctuations): random walk frequency modulation, flicker frequency modulation, white frequency modulation, flicker phase modulation, and white phase modulation, as described in [1].

B.2 Frequency Standard Stability

The stability of a frequency source can be described by starting with an oscillator whose output voltage V( t), is given by:

where V ₀ and ? ₀ are the nominal amplitude and frequency, respectively, with corresponding errors ?( t) and ?( t).

The instantaneous phase is defined by

and the instantaneous frequency is defined by

A common method used to measure oscillator stability is based on the instantaneous fractional frequency deviation from the nominal frequency ? ₀ given by

The power-law spectral densities of the five random frequency noise processes mentioned in Section B.1 can be represented in the frequency...