Doppler Based Relative Positioning for Aircraft-to-aircraft and Drone-to-drone Communication Systems
Michael Walter, Martin Schmidhammer, and Dmitriy Shutin, German Aerospace Center (DLR), Germany
Location: Galleria I/II
Alternate Number 3
A relative positioning algorithm is helpful in close formation flying, i.e., Blue Angels or Thunderbirds, or for the deployment of closely operating drones exploring a spatially limited environment. The objective of this paper is to estimate the velocity and relative position of an aerial vehicle with respect to another aerial vehicle. The estimate is based on the time-variant spreading function, which the receiver evaluates. The proposed algorithm is an extension of the vehicle-to-vehicle Doppler navigation presented in the previous paper in . The proposed approach can be applied to both aircraft-to-aircraft and drone-to-drone communication systems to add navigational capabilities.
In order to formulate the corresponding objective function, we investigate three different channel components that were already introduced by Bello in his seminal work on aeronautical channels: the line-of-sight component, the specular reflection component, and the scattering components. For each component, we derive the time-variant Doppler frequency coming from the ground scattering plane. If the airspeed of one aerial vehicle is known, the three components of the velocity vector of the other aerial vehicle can be determined by the three Doppler frequency equations. Furthermore, the velocity vectors projected on the scattering plane are needed. For a flat ground these projections can be obtained by the difference of airspeed and vertical speed.
In order to obtain the required delay-dependent description, the Doppler frequency is transformed into a prolate spheroidal coordinate system as was shown in . After the transformation, the delay dependency of the Doppler frequency is expressed exclusively by one of the coordinates. The Doppler frequency equation, however, is valid for the whole 3D space. For our purposes, we constrain the Doppler frequency at the receiver to contributions that are induced by scattering from the ground. Thus, the Doppler frequency becomes dependent on the scattering plane parameters. Finally, we obtain a time-variant, delay-dependent description of the Doppler in dependence on the scattering plane. This relationship is quite involved, but simplifies for the above mentioned components, i.e., for the line-of sight, the specular reflection and the scattered components.
The simplest relationship between Doppler and velocity vector is obtained for the line-of-sight component, which only depends on the z-component of the velocity vectors as defined in . The specular reflection component depends, in general, on all velocity vector components. The limiting frequencies of the scattering components for large delays depend only on the sum of the velocity vectors of transmitter and receiver, which are projected onto the scattering plane. In this way a completely analytical solution can be derived for the velocity vectors of the aerial vehicles.
After the three velocity vector components have been determined, the relationship between the velocity components determines the orientation of the prolate spheroidal coordinate system, since it is always defined by the location of the transmitter and receiver. Once the orientation is fixed, the relative position of the receiver in relation to the transmitter and vice versa can be infered.
Our preliminary analysis is based on aircraft-to-aircraft channel measurements presented in  and the theoretical works in . The measured Doppler-variant impulse response in Figs. 2 and 3 in  clearly show the line-of-sight, specular, and scattering components. The delay-dependent Doppler frequency for the three cases is then found in expressions (33), (37), and (38) in . With an algorithm similar to the one presented in , the velocity components can be calculated and afterwards the relative position can be estimated.
 Walter, Michael, Dammann, Armin, "Relative Positioning and Velocity Estimation Using V2V Delay and Doppler Information," Proceedings of the 31st International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2018), Miami, Florida, September 2018, pp. 3010-3017.
 M. Walter, D. Shutin, D. W. Matolak, N. Schneckenburger, T. Wiedemann and A. Dammann, "Analysis of Non-Stationary 3D Air-to-Air Channels Using the Theory of Algebraic Curves," in IEEE Transactions on Wireless Communications, vol. 18, no. 8, pp. 3767-3780, Aug. 2019.
 M. Walter and M. Schnell, "The Doppler-Delay Characteristic of the Aeronautical Scatter Channel," 2011 IEEE Vehicular Technology Conference (VTC Fall), San Francisco, CA, 2011, pp. 1-5.