Advanced receiver autonomous integrity monitoring using triple frequency data with a focus on treatment of biases

doi:10.1016/j.asr.2017.01.037

Advances in Space Research

Volume 59, Issue 8, 15 April 2017, Pages 2148-2157

https://doi.org/10.1016/j.asr.2017.01.037 Get rights and content

Abstract

Most current Advanced Receiver Autonomous Integrity Monitoring (ARAIM) methods are designed to use dual-frequency ionosphere-free observations. These methods assume that receiver bias is absorbed in the common receiver clock offset and bound satellite biases by nominal values. However, most multi-constellation Global Navigation Satellite Systems (GNSS) can offer triple frequency data that can be used for civilian applications in the future, which can improve observation redundancy, solution precision and detection of faults. In this contribution, we explore the use of this type of observations from GPS, Galileo and BeiDou in ARAIM. Nevertheless, the use of triple frequency data introduces receiver differential biases that have to be taken into consideration. To demonstrate the significance of these additional biases we first present a method to quantify them at stations of known coordinates and using available products from the International GNSS service (IGS). To deal with the additional receiver biases, we use a between-satellite single difference (BSSD) observation model that eliminates their effect. A pilot test was performed to evaluate ARAIM availability for Localizer Performance with Vertical guidance down to 200 feet (LPV-200) when using the triple-frequency observations. Real data were collected for one month at stations of known coordinates located in regions of different satellite coverage characteristics. The BSSD triple-frequency model was evaluated to give early indication about its feasibility, where the implementation phase still requires further comprehensive studies. The vertical position error was always found to be bounded by the protection level proven initial validity of the proposed integrity model.

Introduction

The presence of multiple GNSS constellations that provide a global coverage with multiple frequency observations led to the development of Advanced Receiver Autonomous Integrity Monitoring (ARAIM) methods for aircraft localizer performance with vertical guidance. For example, integration of GPS with Galileo in ARAIM has been shown in Rippl et al. (2011), and in Choi et al., 2012, Walter et al., 2013 using GPS and GLONASS. Integration of GPS with BeiDou in ARAIM has been demonstrated in Lijun et al., 2012, Liu and Zhu, 2014; and El-Mowafy (2016).

The current proposed ARAIM methods use dual-frequency observations. Nevertheless, Galileo, BeiDou and GPS block III satellites provide triple-frequency observations. The additional use of a third frequency can improve positioning accuracy compared to the dual-frequency case (Elsobeiey, 2015, Duong et al., 2016) and can enhance the fault detection capability (Guo et al., 2011), which is a fundamental task in integrity monitoring. Another advantage of the use of a third frequency is that in case of unavailability of observation from one frequency, the remaining data of the satellite can still be used without excluding this satellite. Nevertheless, aviation requires the use of signals operating in designated safety-of-life aeronautical radionavigation service (ARNS) band. At present, the International Civil Aviation Organisation (ICAO) has not published the required navigation standards for Galileo and BeiDou, and the standards for dual-frequency use. However, these standards are expected to be available in the near future. Naturally, the implementation phase of a third frequency still requires a long road until the three signals are operationally available and regulations and policies are developed.

Although the use of multi-constellation GNSS signals can enhance positioning accuracy and integrity monitoring (IM), such improvement requires proper handling and bounding of biases not only for satellite observations from each constellation but also among different constellations. The observation biases are dependent on the receiver and the individual satellite signal characteristics. They are mainly caused by signal distortion in the analogue and digital parts of the signal chain, which produces distortions in the chip shape that cause the receiver’s correlation function to deviate from its ideal triangular shape leading to a shift in the tracking point, and thus causes a bias in the measured pseudorange (Hauschild and Montenbruck, 2016). Additional biases are attributed to satellite orbit and clock navigation message miss-modelling, antenna phase centre offsets, inter-frequency biases, code-carrier incoherence, in addition to signal path through the antenna, splitter, cabling and amplifier (Phelts, 2007). It is typically assumed that the signal characteristics of the satellites from the same GNSS constellation on the same spectral band are identical. Hence, in the current ARAIM dual-frequency methods, the receiver biases are assumed absorbed into the common receiver clock offset and the satellite biases are bounded by a nominal value. However, differential receiver biases will be introduced when a third civilian frequency is used due to the fact that receiver biases are frequency dependent, which then require a proper treatment.

In this paper, we explore the feasibility of using a third frequency in ARAIM by creating two dual frequencies ionosphere-free (IF) observations, expecting the presence of these signals for civilian use in the future. To this end, instead of making assumptions on the differential receiver biases between the two IF observations, or trying to estimate them, where both approaches have a degree of uncertainty, we use a between-satellite single difference (BSSD) observation model in place of the traditional undifferenced observation model. This approach eliminates receiver clock offset as well as receiver hardware biases and therefore solves the problem at hand.

In the following sections, integrity monitoring using the triple-frequency data is presented. A method for estimation of biases at stations of known coordinates is discussed to show the significance of the differential code biases and that they should be considered when using triple frequency observations. The implementation of the BSSD model in ARAIM using triple-frequency data to cancel these biases is next discussed. Then, results of experimental evaluation of ARAIM availability is presented and analysed at representative sites using data from multiple-constellations, including GPS, Galileo and BeiDou.

Section snippets

The triple-frequency observation model

In this study we use triple frequency data in the form of two ionosphere-free (IF) combinations. The IF observation equation of the pseudorange code measurements for satellite m from a GNSS constellation, such as Galileo, to receiver r for signals $c_{i}$ and $c_{j}$ on frequencies f_i and f_j in length units can be expressed as (El-Mowafy, 2014): $p {({IF}_{c_{i, j}})}_{r}^{m} = ρ_{r}^{m} + C (d {\overset{ˇ}{t}}_{r} - {dt}^{m}) + T^{m} + {Cd}^{m} ({IF}_{c_{i, j}}) + ε_{P {({IF}_{c_{i, j}})}_{r}^{m}}$ where $d {\overset{ˇ}{t}}_{r} = {dt}_{r} + d_{r} ({IF}_{c_{i, j}}), d_{r} ({IF}_{c_{i, j}}) = a_{i, j} d_{r} (c_{i}) - b_{i, j} d_{r} (c_{j})$ $d^{m} ({IF}_{c_{i, j}}) = a_{i, j} d^{m} (c_{i}) - b_{i, j} d^{m} (c_{j})$ with $a_{i, j} = \frac{f_{i}^{2}}{f_{i}^{2} - f_{j}^{2}}$

Receiver DCBs due to the use of a third frequency

To demonstrate the significance of the DCBs when using two IF combinations of triple-frequency data, we estimate in this section the DCBs at IGS stations of known coordinates and using available IGS products. Note here that this estimation method of DCBs is not a part of the proposed ARAIM approach.

Let us first re-parameterize the IF combination of phase observations for $c_{i}$ and $c_{j}$ in the form: $ϕ {({IF}_{c_{i, j}})}_{r}^{m} = {\tilde{ρ}}_{r}^{m} + M^{m} ({IF}_{c_{i, j}}) + ε_{P {({IF}_{c_{i, j}})}_{r}^{m}}$ where ${\tilde{ρ}}_{r}^{m} = ρ_{r}^{m} + C ({dt}_{r} - {dt}^{m}) + T^{m}$ and $M^{m}$ denotes the phase ambiguities.

Between-satellite single difference (BSSD) of triple observations model in ARAIM

In this study, triple-frequency BSSD model is presented restricting our focus to the integrity evaluation process. The fault detection and exclusion (FDE) process will be discussed in detail in a separate study.

Testing

In this section, a pilot experiment was carried out to evaluate performance of the triple frequency observations using the BSSD model in ARAIM. At the time of the test, there were 31 GPS satellites, 20 BeiDou satellites and 12 satellites in Galileo. Their full constellations will be operational within a few years. The test gives an initial indication about possible future performance.

Conclusion

A pilot study on the feasibility of triple-frequency data for ARAIM is presented. In the current ARAIM dual-frequency methods, the receiver biases are assumed absorbed with the common receiver clock offset. However, with the use of a third frequency, significant receiver DCBs will appear since receiver biases are frequency dependent. Such DCBs are cancelled when BSSD observations are used. An ARAIM method implementing the BSSD approach is presented.

A pilot test was carried out to evaluate

Acknowledgments

The Institute for Geoscience Research (TIGeR), Curtin University, is acknowledged for partially funding this research. The data used in this study was downloaded from the International GNSS Service (IGS) open-source streams. We would like to thank all organisations and research centres providing the data used.

References (28)

A. El-Mowafy et al.
Limited sensitivity analysis of ARAIM availability for LPV-200 over Australia using real data
Adv. Space Res.
(2016)
Blanch, J., Walter, T., Enge, P., et al., 2012. Advanced RAIM user algorithm description: integrity support message...
J. Blanch et al.
Critical elements for a multi-constellation advanced RAIM
Navigation
(2013)
J. Blanch et al.
Optimal positioning for advanced RAIM
Navigation
(2014)
J. Blanch et al.
Baseline advanced RAIM user algorithm and possible improvements
IEEE Trans. AeroSpace Electron. Syst.
(2015)
M. Choi et al.
Evaluation of multi-constellation advanced RAIM for vertical guidance using GPS and GLONASS signals with multiple faults
J.M. Dow et al.
The international GNSS service in a changing landscape of Global Navigation Satellite Systems
J. Geod.
(2009)
Duong, V., Harima, K., Choy, S., et al., 2016. Performance of precise point positioning using current triple-frequency...
A. El-Mowafy
RAIM for vertical guidance using GPS and Beidou
J. Glob. Position. Syst.
(2013)
A. El-Mowafy
GNSS multi-frequency receiver single-satellite measurement validation method
GPS Solut.
(2014)

A. El-Mowafy et al.

Validation of BeiDou observations

J. Appl. Geod.

(2014)

A. El-Mowafy et al.

On biases in precise point positioning with multi-constellation and multi-frequency GNSS data

Meas. Sci. Technol.

(2016)

A. El-Mowafy

Pilot evaluation of integrating GLONASS, Galileo and BeiDou with GPS in ARAIM

Artif. Satellites

(2016)

M. Elsobeiey

Precise point positioning using triple-frequency GPS measurements

J. Navigat.

(2015)

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Advanced receiver autonomous integrity monitoring using triple frequency data with a focus on treatment of biases

Abstract

Introduction

Section snippets

The triple-frequency observation model

Receiver DCBs due to the use of a third frequency

Between-satellite single difference (BSSD) of triple observations model in ARAIM

Testing

Conclusion

Acknowledgments

Adv. Space Res.

Critical elements for a multi-constellation advanced RAIM

Navigation

Optimal positioning for advanced RAIM

Navigation

Baseline advanced RAIM user algorithm and possible improvements

IEEE Trans. AeroSpace Electron. Syst.

Evaluation of multi-constellation advanced RAIM for vertical guidance using GPS and GLONASS signals with multiple faults

The international GNSS service in a changing landscape of Global Navigation Satellite Systems

J. Geod.

RAIM for vertical guidance using GPS and Beidou

J. Glob. Position. Syst.

GNSS multi-frequency receiver single-satellite measurement validation method

GPS Solut.