# Hardware Prototyping and Validation of a W-\(\Delta\)DOR Digital Signal Processor
## 1 Introduction  
This paper presents the hardware implementation and characterization of a novel Delta-Differential One-Way Ranging (\(\Delta\)DOR) technique based on spread-spectrum waveforms [1; 2]. The relative angular position of a spacecraft with respect to known radio sources (typically, quasars) is currently determined by means of differential phase measurements using Very Long Baseline Interferometry (VLBI) technique [3; 4] according to CCSDS 500.1-G-1 _Delta-DOR Technical Characteristics and Performance_. In practice, the difference in arrival times of spacecraft radio signals at two widely separated ground stations is accurately measured, along with similar differential phase measurements of a nearby quasar. The quasar, being one of the radio sources defining the International Celestial Reference Frame (ICRF), has known angular coordinates and can serve as a fiducial landmark to reference the spacecraft phase (Figure 1). The spacecraft location is measured with excellent accuracy relative to the ICRF frame [5]. The ESA \(\Delta\)DOR system attains consistently angular accuracies of a few nanoradians (corresponding to delays in the order of \(10^{-10}\) s). Precise angular measurements are extremely valuable for both spacecraft navigation and scientific investigations of Solar System dynamics. The knowledge of the angular position proves very important, especially in the planetary approach phase in order to prepare and execute the planetary orbit insertion. Although Doppler observables also provide angular information, \(\Delta\)DOR observations are intrinsically more accurate and less dependent on the dynamical model of the spacecraft [6; 7]. The targeting of the capture maneuver (for an orbiter) or the Entry, Descent, and Landing (EDL) phase greatly benefit from, and even rely on, previous \(\Delta\)DOR observations. Accurate Solar System bodies and satellite ephemerides are crucial for Solar System exploration. In addition, the generation of precise ephemerides requires an accurate formulation of Solar System dynamics in the context of a fully relativistic model. Conversely, tracking the motion of Solar System bodies is an excellent experimental tool to test the adopted laws of gravity. The Solar System constitutes indeed the cleanest environment to carry out determinations of the space-time metric in the weak field limit, and to assess the range of validity of general relativity. The observable of choice for Solar System dynamics investigations are range and \(\Delta\)DOR. The two set of measurements complement each other, with \(\Delta\)DOR providing unique information in the out-of-plane components of planets and satellites positions. The orbits are determined by first referencing the orbit of the spacecraft to the planetary body using Doppler measurements, and then linking the body's position to a Solar System barycentric frame by means of angular and range measurements. Other interesting applications of interferometric techniques are related to the relative positioning of two spacecraft, landers, or a lander and an orbiter. This technique, called Same Beam Interferometry (SBI) [8], was originally proposed in a configuration with two antennas tracking simultaneously two probes in one-way mode. However, SBI can be considered in a simpler configuration where a single ground antenna tracks, simultaneously in two-way mode, two probes separated by a small line-of-sight angle (0.5 degrees or less). This powerful method allows a considerable improvement in the positioning of a probe when the orbit (or the position) of the second one is well determined. The coherent downlink signals coming from each probe are combined to form the differential phase, proportional to the relative distance between each probe of the pair. In the case of two (or more) landers, SBI would provide very accurate measurements of tides and rotational state of a planetary body, which are used in geophysical models to constrain the interior structure and evolution.