Simulating Future GPS Clock Scenarios with Two Composite Clock Algorithms

Abstract

Using the GPS Toolkit, the GPS constellation is simulated using 31 satellites (SV) and a ground network of 17 monitor stations (MS). At every 15-minute measurement epoch, the monitor stations measure the time signals of all satellites above a parameterized elevation angle. Once a day, the satellite clock estimates are uploaded to the satellites. Two composite clock algorithms are applied to estimate the station and satellite clocks. The first composite clock (B) is based on the Brown algorithm [1], and is now used by GPS. The second one (G) is based on the Greenhall algorithm [2]. The composite clock of G and B performances are investigated using three ground-clock models. Model C simulates the current GPS configuration, in which all stations are equipped with cesium clocks, except for masers at USNO and Alternate Master Clock (AMC) sites. Model M is an improved situation in which every station is equipped with active hydrogen masers. Finally, Models F and O are future scenarios in which the USNO and AMC stations are equipped with fountain clocks instead of masers. Model F is a rubidium fountain, while Model O is a more precise but futuristic Optical Fountain. Each model is evaluated using three performance metrics. The timing-related user range error having all satellites available is the first performance index (PI1). The second performance index (PI2) relates to the stability of the broadcast GPS system time itself. The third performance index (PI3) evaluates the stability of the time scales computed by the two composite clocks. A distinction is made between the "Signal-in-Space" accuracy and that available through a GNSS receiver.

A robust Kalman filter time scale algorithm with data anomaly

“…The reference clock is taken as the fountain clock. The diffusion coefficients of noises are tabulated in table 1 as described in [19]. According to the noise diffusion coefficients of the clocks, the atomic clocks are simulated and their stabilities are calculated.…”

Combined covariance reductions for Kalman filter composite clocks

“…The combination maintains the ensemble estimates of the Greenhall algorithm and the covariance entries grow more slowly than those of the two separate methods. The result was observed by the simulation of a GPS like clock scenario comparing the composite clocks of the two reduction methods [4].…”

“…Within [4], it is found by numerical simulations that the Brown and Greenhall reductions can be combined and that the combination gives the same estimates of the ensemble offset as using Greenhall reduction alone. The equivalence relation is applied to prove that the combination of the reduction methods gives the same Kalman gains as the series of Greenhall reductions (corollary 5.1, figure 2).…”

“…Motivated by [4], in which the performances of the introduced composite clock algorithms are compared, the time offset representation error and the time offset synchronization error of both algorithms are contrasted.…”

“…The simulation evaluates the trace of the series of normal C k , Brown C B,k , Greenhall C G,k and Greenhall-Brown C GB,k (Brown-Greenhall C BG,k ) reduced covariances of an ensemble of three clocks: caesium, active hydrogen maser (AHM) and rubidium atomic frequency standard (RAFS). The stochastic parameters of the clock offsets are given in table 1 and relate to [4]. The clock offset model is based on three states and given in appendix B.…”