Session B2a: Advancements in Navigation Algorithms

Ambiguity-Resolved Positioning Performance in Interferometric Measurement Systems: Can Constraining Phase Biases Play a Decisive Role?
Amir Khodabandeh, Dept. of Infrastructure Engineering, The University of Melbourne; Songfeng Yang, Dept. of Infrastructure Engineering, The University of Melbourne; Peter J.G. Teunissen, Dept. of Geoscience and Remote Sensing, Delft University of Technology
Location: Beacon B

Background: High-precision interferometric positioning systems such as Global Navigation Satellite Systems (GNSS), interferometric wireless networks (Maroti et al. 2005; Wang et al. 2015), and opportunistic navigation with non-conventional sensors (Shamaei and Kassas 2019) rely on the provision of carrier phase measurements. To exploit these ultra-precise measurements, the corresponding unknown ambiguities must be successfully resolved during the estimation process. However, due to the linear dependency between the integer ambiguities and the phase biases, only certain combinations of the ambiguities satisfy the integer-estimability conditions (Teunissen 2019), the conditions that dictate whether the solution of such combinations can serve as an admissible input to Integer Ambiguity Resolution (IAR) methods like LAMBDA (Teunissen 1993). As a consequence, a subset of the ambiguities cannot be resolved as they are absorbed by the corresponding estimable phase biases. Depending on the strength of the underlying measurement model, solutions of the remaining integer-estimable ambiguities may then be successfully mapped to their correct integers, thus essentially constructing ambiguity-resolved carrier phase data to enable high-precision model parameter solutions. The decision whether or not such integer-mapping is deemed successful is determined by the probability of correct integer estimation, the so-called ambiguity success-rate. When the ambiguity success-rate is not sufficiently large, it is likely that the output of the IAR method does not represent the sought-for integer-estimable ambiguities, seriously deteriorating the precision of the remaining parameter solutions.
Motivation and Methodology: In the literature, the estimable phase biases are either estimated along with the other model parameters or eliminated from the model through, e.g., forming double-differences of the carrier phase measurements. It has not yet been addressed whether the IAR performance can benefit from the information about the extreme values that such phase biases can take on. Therefore, the present contribution aims to address how constraining the stated biases can increase the ambiguity success-rate, improving the IAR performance, thereby delivering precise positioning solutions. In doing so, we employ the recently developed integer-search method of BEAT (Khodabandeh 2022) so as to incorporate the phase-bias constraint into the IAR process. To have the results generally applicable to the measurement systems with frequency-varying carrier phase signals like GLONASS or Low-Earth-Orbiting (LEO) communication satellites, we make use of the integer-estimable formulation (Khodabandeh and Teunissen 2023). Accordingly, we study the IAR performance of the integer-estimable parametrized observation equations with their ‘bias-bounded’ versions.
Results and conclusions: We discuss how the ‘bias-constrained integer least-squares estimation’ and its search method of BEAT leverage the bias constraint, significantly improving the ambiguity success-rate for different values of the phase-bias bound, and for certain frequencies of the carrier phase measurements. Provided that the phase-bias constraints are correctly specified, it is illustrated that more accurate ambiguity-resolved positioning solutions can be obtained. Through a number of real-world GNSS and simulated non-GNSS frequency-varying carrier phase signals, we demonstrate how the underlying IAR performance responds to the phase-bias bound, highlighting the feasibility of successful ambiguity-fixing in various interferometric positioning systems.
References:
- Khodabandeh A. (2022). Bias-bounded Estimation of Ambiguity: a method for radio interferometric positioning. IEEE Transactions on Signal Processing 70:3042–3057
- Khodabandeh A., Teunissen P.J.G. (2023). Ambiguity-fixing in frequency-varying carrier phase measurements: Global navigation satellite system and terrestrial examples. NAVIGATION 70(2)
- Maroti M., Volgyesi P., Dora S., Kusy B., Nadas A., Ledeczi A., Balogh G., Molnar K. (2005). Radio Interferometric Geolocation. In: Proceedings of the 3rd international conference on Embedded networked sensor systems, pp 1-12
- Shamaei K., and Kassas Z.M. (2019). Sub-Meter Accurate UAV Navigation and Cycle Slip Detection with LTE Carrier Phase Measurements. ION GNSS+ Conference Miami, FL, September 16–20, 2019.
- Teunissen P.J.G. (1993). Least-Squares Estimation of the Integer GPS ambiguities. In: Invited Lecture, Section IV Theory and Methodology, IAG General Meeting, Beijing, China, August
- Teunissen P.J.G. (2019). A new GLONASS FDMA model. GPS Solutions, https://doi.org/10.1007/s10291-019-0889-0
- Teunissen P.J.G., Montenbruck O. (eds) (2017). Handbook of global navigation satellite systems. Springer, Berlin
- Wang Y., Ma X., Chen C., Guan X. (2015). Designing Dual-Tone Radio Interferometric Positioning Systems. IEEE Trans Signal Process 63(6):1351–1365