Session B4: GNSS Integrity and Augmentation

Initial Considerations About Alternative Approaches for Sigma Ground Processing in GAST E
Michael Nietlispach and Michael Felux, Zurich University of Applied Sciences
Location: Beacon B

In a Ground-Based Augmentation System (GBAS), carrier smoothing is applied to reduce noise and multipath in pseudorange measurements (Circiu et al., 2016). In GBAS Approach Service Type (GAST) C and D systems, the ground subsystem applies smoothing to the ground measurements. To ensure integrity of the position solution, residual noise and multipath after smoothing are accounted for by the parameter sigma ground. This parameter is a function of the applied smoothing time constant, as longer smoothing time constants mitigate noise and multipath more effectively over limited periods of time. Additionally, it is a function of satellite elevation, as noise and multipath generally decrease with increasing elevation. The GAST C and D ground subsystems are responsible for broadcasting sigma ground through the Very-high frequency Data Broadcast (VDB). In the airborne receiver, sigma ground is used to calculate protection levels. These conservative error bounds ensure that the GBAS service is only available as long as the errors due to ground and airborne noise and multipath as well as atmospheric errors are within a tolerable range. Finally, a reliable and accurate position solution can be computed by using the broadcast integrity parameters and corrections. In the future Dual-Frequency, Multi-Constellation (DFMC) GAST E, raw and 100 s smoothed pseudorange as well as carrier-phase measurements instead of corrections are planned to be uplinked to the airborne user (Murphy et al., 2023). The latter then smooths the ground measurements with a Divergence-Free (DFREE) variable-rate smoothing filter and smoothing time constants of up to 600 s. The DFREE mode avoids code-carrier divergence and for variable-rate smoothing it can be assumed that the smoothing filter converges after a period of time that is equal to twice the smoothing time constant (Murphy et al., 2022). As stated previously, it is expected that longer smoothing time constants mitigate noise and multipath more effectively over limited periods of time. However, to benefit from this improvement, a sigma ground that describes residual noise and multipath after smoothing with the applied smoothing time constant is required. In the current GAST E proposal it is suggested that the airborne subsystem derives the appropriate sigma ground as a function of the elapsed smoothing time from the broadcast 100 s smoothed sigma ground. This parameter is planned to be broadcast in the GAST E architecture to ensure backwards compatibility with previous GASTs. One advantage of this approach is that no additional parameters are required to be broadcast in the VDB (Murphy et al., 2023). In fact, the VDB capacity is limited and it is an open question whether any additional parameters will be broadcast in GAST E. The expression of sigma ground as a function of elapsed smoothing time allows to airborne user to compute a sigma ground for the smoothing filter transient state. Furthermore, it allows to compute a converged sigma ground for any applied smoothing time constant as the sigma ground that occurs after a smoothing period that is equal to twice the smoothing time constant. Nevertheless, this procedure assumes that both noise and multipath are modelled as white Gaussian noise, which is expected to be not sufficiently conservative. This paper addresses initial considerations about alternative approaches to process sigma ground which also account for time-correlated multipath in the GAST E airborne subsystem. As a first objective, we determined sigma ground for the L1/E1 signals as a function of satellite elevation and elapsed smoothing time experimentally from GPS and Galileo dual-frequency measurements. The second objective was to model the experimentally determined sigma ground with exponential models. To address the first objective, sigma ground after smoothing filter convergence was computed for various smoothing time constants between 50 s and 600 s. To that end, we used data from a choke-ring antenna located at Tenerife Norte Airport. The measurements were collected at a sampling time interval of 0.5 s over 63 days. The dependence on the elapsed smoothing time was introduced as follows. It was assumed that, as long as the elapsed smoothing time was below the time required for a smoothing filter applying a certain smoothing time constant to converge, the current sigma ground adopts the value of the converged sigma ground of the next smaller smoothing time constant. Repeating this procedure for each elevation bin yielded a time series of sigma ground for each elevation bin. The following describes the procedure of computing sigma ground for a certain smoothing time constant and is based on the work done by Felux et al. (2019). The data was cleaned from cycle slips and the DFREE Code-Minus Carrier (CMC) combinations were formed over contiguous intervals for each satellite. Then, the CMCs were smoothed with a variable-rate smoothing filter and the respective smoothing time constant. Independent smoothed CMC samples were selected at a rate that was equal to twice the smoothing time constant divided by the sampling time interval. The independent samples from all satellites were then sorted into elevation bins of 5°. In each bin, the standard deviations of the independent samples were calculated to yield a first estimate of sigma ground. These standard deviations were then adjusted for non-Gaussian distributions and limited sample sizes to yield the final sigma ground for the applied smoothing time constant. Within the scope of the second objective, we investigated how the experimentally determined sigma ground may be modelled. Because it was expected that sigma ground decays with increasing elapsed smoothing time, exponential models were used. The first model required one parameter that adjusts the slope of the model. The second model required two parameters, one that adjusts the slope of the fit and one that controls the value to which it converges. The parameters were determined by manually varying the respective parameters to obtain the best fit. As a result from addressing the first objective, the experimentally determined sigma ground was represented as a three-dimensional surface. It allows to obtain an estimate of sigma ground for each moment of smoothing since smoothing filter initialisation and satellite elevation and accounts for residual noise and multipath as it was derived from actual measurements. Furthermore, the results showed that increasing the smoothing time constant to more than 300 s provides only marginal additional reductions in sigma ground. Presumably, for longer smoothing time constants, antenna-induced errors become dominant and limit the theoretical improvements in noise and multipath mitigation through longer smoothing time constants. Regarding the second objective, it was shown that the one-parametric model depicts the experimentally determined sigma ground more accurately for shorter smoothing times. For longer smoothing times, the two-parametric model yielded a closer description of the experimentally determined sigma ground. It can be concluded that careful consideration is required about whether small improvements in sigma ground from longer smoothing time constants outweigh the longer convergence times that go in hand with longer smoothing time constants. Given that shorter smoothing time constants may also yield an acceptable performance, a one-parametric model may be a suited approach to model sigma ground. This would be beneficial in terms of VDB capacity, although it remains an open question whether additional capacity in the VDB will be available. Second, we modelled this sigma ground with exponential models that require one and two parameters per elevation bin. As a result, the experimentally determined sigma ground was represented as a three-dimensional surface. It allows to obtain an estimate of sigma ground for each moment of smoothing since smoothing filter initialisation and satellite elevation. The results also showed that increasing the smoothing time constant to more than 300 s provides only marginal additional reductions in sigma ground. Furthermore, the one-parametric model generated a closer depiction of the experimentally determined sigma ground for shorter smoothing times, whereas the two-parametric model fitted sigma ground for longer smoothing times more accurately. Given the marginal improvements from applying smoothing time constants of 300 s or more, the one-parametric model may be an alternative approach to GAST E airborne processing of sigma ground. Nevertheless, the question whether additional capacity in the very-high frequency data broadcast is available to uplink the model parameters remains open.
REFERENCES
Circiu, M.-S., Felux, M., Gerbeth, D., Caamano, M., & Meurer, M. (2016). Assessment of Different Dual-frequency Dual-constellation GBAS Processing Modes Based on Flight Trials. Proceedings of the 29th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2016), 3197–3207. https://doi.org/10.33012/2016.14697
Felux, M., Circiu, M.-S., Caizzone, S., Enneking, C., Fohlmeister, F., & Rippl, M. (2019). Towards Airborne Multipath Models for Dual Constellation and Dual-frequency GNSS. Proceedings of the 2019 International Technical Meeting of The Institute of Navigation, 62–68. https://doi.org/10.33012/2019.16683
Murphy, T., Harris, M., Balvedi, G., McGraw, G., Wichgers, J., Lavik, L., Topland, M., Tuffaha, M., & Saito, S. (2022). Ionospheric Gradient Monitoring for Dual Frequency Multi-Constellation GBAS. Proceedings of the 2022 International Technical Meeting of The Institute of Navigation, 1075–1097. https://doi.org/10.33012/2022.18178
Murphy, T., Harris, M., Balvedi, G., McGraw, G., Wichgers, J., Lavik, L., Topland, M., Tuffaha, M., & Saito, S. (2023). Managing Long Time Constant and Variable Rate Carrier Smoothing for DFMC GBAS. Proceedings of the 36th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2023), 925–946. https://doi.org/10.33012/2023.19433