A New Error Model for Terrestrial Multipath

Okuary Osechas, Gianluca Zampieri, Nicolas Schneckenburger

Abstract: One of the bigger challenges in providing ground-based navigation with integrity, to aviation users, is the ranging error due to multipath propagation. A particular flavor of the problem is sometimes referred to as “line-of-sight multipath”, which is a ranging error that appears when there is direct visual contact between the location and the ground station. To some this effect may seem counter-intuitive and the standard error model does not account for its existence. The conventional approach to modeling multipath in terrestrial ranging for aviation is the two-ray model. The current standard for Distance Measuring Equipment (DME) [DME_MOPS] accounts for a maximum of 100 m in ranging error due to multipath. The two-ray model does not explain line-of-sight multipath greater than 100 m, nor does it explain the numerous occurrences have been documented, where ranging errors far exceed this value. We understand this as evidence for the deficiency of the two-ray model. In our paper we will describe a modified approach to modeling terrestrial ranging errors due to multipath. The new approach differs from the standard method in that the underlying fault hypothesis is different. To understand the fault hypothesis it is useful to understand the four-component model proposed in [Schneckenburger]. This four-component model includes the following effects: a) Lateral multipath b) Ground multipath c) Occlusions d) Antenna misalignment In this approach lateral multipath refers to rays that are reflected without coherence, typically by virtue of having phase delays greater than the wavelength of the carrier. Ground multipath, on the other hand, refers to coherently reflected signals that cause electromagnetic interference and, therefore, erasure of the line-of-sight signal. In simplified terms the components b, c and d have the effect of reducing the power of the line of sight signal, thus making the receiver vulnerable to locking on to the strongest reflections from lateral multipath, which lead to faulted range measurements. Shortcomings in the Two-Ray Model Empirical evidence suggests that lateral multipath is impossible to prevent and is, in essence, always present in a ground-air channel [Schneckenburger,Osechas]. Thus the threat of ranging errors due to multipath stems from reductions in the power of the line of sight signal. A direct consequence of this observation is that the two-ray model is under-conservative, making it ineffective for integrity purposes. Our claim is substantiated by the existence of multipath-induced ranging errors greater than 100 m. Instances of such errors are known in France, Japan and Spain, but could well be more wide-spread than currently acknowledged. In our paper we will introduce a new approach to modeling multipath errors that accounts for lateral multipath in a new way. The conventional approach is to model the maximum ranging error for a given delay, assuming that the two-ray model is accurate. This does not account for situations where the line of sight power is reduced through destructive interference. A power drop in the line-of-sight signal, which can be caused caused by a single reflector, can open the floodgates for strong components of lateral multipath. For a given coherent reflector (i.e. ground multipath), the maximum possible power drop is usually large enough to attenuate the LoS signal below the reflections received from lateral multipath (non-coherent reflectors). Given that lateral multipath can occur anywhere, there is no reason why it would be bounded. In consequence, the ranging error due to multipath propagation is, for all practical purposes, unbounded. Again, this observation is consistent with the findings of our colleagues in France, Japan and Spain. A second consequence of the four-component model is that the worst-case ranging error due to multipath is not guaranteed to be detected by inspection of the received spectrum, at least not in a single snapshot. In the final paper we will substantiate this claim with a model-driven analysis of the worst-case ranging error. Monitoring the distortion over time, however, makes multipath errors observable. In the paper we will also present evidence to support this claim, based on equations, as well as measurement data from previous flight campaigns. It is important to note that some of the effects of Multipath on ranging errors are not specific to on technology. They may appear in DME signals as much as in other terrestrial ranging signals, such as the L-Band Digital Aeronautical Communications System (LDACS). In our approach we will focus on the changing transfer function of the multipath channel; as such we expect our results to work on a variety of terrestrial ranging systems. Outline of the Proposed Solution Distortion-based monitoring is effective against the aforementioned line-of-sight multipath, when observed over a batch of epochs. The fact that there errors exibit a particular phase relationships between the line-of-sight signal and the ground multipath form the basis of the proposed monitor.The basis of the monitor is that these errors occur under very particular phase relationships between the line-of-sight signal and the ground multipath. In this sense, the absence of distortion over a number of epochs gives a measure of certainty that multipath did not occur during those epochs. Similar to the approach in bounding multipath with a two-ray scenario we seek a bound on the worst-case situation. For that purpose we look at channel impulse responses and their respective transfer functions, to model the resulting ranging error. Using the changing of the channel over time we analyze the affected signals over time, assessing the likelihood that a particular batch of measurements is faulted by multipath propagation or not. This part of the work includes a theoretical model for the channel, both instantaneously and over time. Once we have established the worst-case error situation, we expect to transition from theory and simulation to real data. For that purpose we resort to several sets of channel-sounding data, collected in a variety of measurement flights, both in Germany [Schneckenburger] and in the USA [Osechas]. This data-driven analysis may not be critical in developing the fault model or understanding its implications. It will, however, give a feeling for the frequency with which pathological channel responses can be expected to occur in the environments that were tested. The sensitivity of the monitor depends on the nominal level of distortion, naturally encountered in situations that are free of multipath-induced errors. Currently ongoing work focuses on quantifying this sensitivity, both in terms of false positive detections and false negatives. References [DME-MOPS] EUROCAE: ED-57. Minimum Performance Specification for Distance Measuring Equipment (DME/N and DME/P) (Ground Equipment). October 1992. [Schneckenburger] Schneckenburger, Jost, Shutin, Walter, Thiasiriphet, Schnell, Fiebig: Measurement of the L-Band Ground-to-Air Channel for Positioning Applications. Transactions in Aerospace and Electronic Systems. [Osechas] Osechas, Schneckenburger, Pelgrum, Nossek, Meurer: Characterization of the Ground-to-Air Ranging Performance of the 960-1215 MHz ARNS Band Using OFDM Measurements in the 902-928 MHz ISM Band. Proceedings of ION ITM 2016, Monterey, CA.
Published in: Proceedings of the 33rd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2020)
September 21 - 25, 2020
Pages: 99 - 113
Cite this article: Osechas, Okuary, Zampieri, Gianluca, Schneckenburger, Nicolas, "A New Error Model for Terrestrial Multipath," Proceedings of the 33rd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2020), September 2020, pp. 99-113.
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