Due to the limited frequency stability and poor accuracy of typical quartz oscillators built-in GNSS receivers, an additional receiver clock error has to be estimated in addition to the coordinates. This leads to several drawbacks especially in kinematic applications: At least four satellites in view are needed for navigation, high correlations between the clock estimates and the up-coordinates. This situation can be improved distinctly when connecting atomic clocks to GNSS receivers and modeling their behavior in a physically meaningful way (receiver clock modeling). Recent developments in miniaturizing atomic clocks result in so-called chip-scale atomic clocks and open up the possibility of using stable atomic clocks in GNSS navigation. We present two different methods of receiver clock modeling, namely in an extended Kalman filter and a sequential least-squares adjustment for codebased GNSS navigation using three different miniaturized atomic clocks. Using the data of several kinematic test drives, the benefits of clock modeling for GPS navigation solutions are assessed: decrease in the noise of the upcoordinates by up to 69 % to 20 cm level, decrease in minimal detectable biases by 16 %, and elimination of spikes and subsequently decrease in large position errors (35 %). Hence, a more robust position is obtained. Additionally, artificial partial satellite outages are generated to demonstrate position solutions with only three satellites in view.
Miniaturized atomic clocks with high frequency stability as local oscillators in global navigation satellite system (GNSS) receivers promise to improve real-time kinematic applications. For a number of years, such oscillators are being investigated regarding their overall technical applicability, i.e., transportability, and performance in dynamic environments. The short-term frequency stability of these clocks is usually specified by the manufacturer, being valid for stationary applications. Since the performance of most oscillators is likely degraded in dynamic conditions, various oscillators are tested to find the limits of receiver clock modeling in dynamic cases and consequently derive adequate stochastic models to be used in navigation. We present the performance of three different oscillators (Microsemi MAC SA.35m, Spectratime LCR-900 and Stanford Research Systems SC10) for static and dynamic applications. For the static case, all three oscillators are characterized in terms of their frequency stability at Physikalisch-Technische Bundesanstalt, Germany's national metrology institute. The resulting Allan deviations agree well with the manufacturer's data. Furthermore, a flight experiment was conducted in order to evaluate the performance of the oscillators under dynamic conditions. Here, each oscillator is replacing the internal oscillator of a geodetic-grade GNSS receiver and the stability of the receiver clock biases is determined. The time and frequency offsets of the oscillators are characterized with regard to the flight dynamics recorded by a navigation-grade inertial measurement unit. The results of the experiment show that the frequency stability of each oscillator is degraded by about at least one order of magnitude compared to the static case. Also, the two quartz oscillators show a significant g-sensitivity resulting in frequency shifts of − 1.2 × 10−9 and + 1.5 × 10−9, respectively, while the rubidium clocks are less sensitive, thus enabling receiver clock modeling and strengthening of the navigation performance even in high dynamics.
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