Optimal and unbiased fir estimates of clock state for space and ground applications

It is commonly accepted [2] that clocks forming time scales in electronic systems have three states: time interval error (TIE), fractional frequency offset, and linear frequency drift rate. All other states are included to the model noise part. If the clock state is estimable, then its behavior can be predicted that is required for many applications. To estimate clock state optimally, several algorithms have been examined for decades. The state space strategy was originally proposed for clocks by Allan and Barnes [2] in order to exploit facilities of Kalman filtering [3]. A description of the clock model was then given by Tryon and Jones in [4] and Chaffee in [5]. Thereafter, the Kalman algorithm has been investigated by many authors [6]-[9] and its applications to timescales were outlined in [10]. The main problem we meet here is associated with clock noise that is inherently colored, whereas Kalman claims the noise to be white sequence. Moreover, the Kalman estimate may diverge [11] in the presence of model uncertainties and high order states and temporary measurement uncertainties caused by the Global Positioning System (GPS), for example.