Fusion of telescopic and Doppler radar data

The most usual ways of observation of satellites and space debris and measurement of their orbits are • telescopic images, • radar reflections, • laser measurements. We use two of these three modalities, we combine telescopic images with response of Doppler radars. We use single images from a terrestrial telescope. Our radar is passive, we receive the signal of a distant terrestrial transmitter. The receiver has a non-directional antenna and only Doppler shift is employed to gain information about an object’s movement. Due to sensitivity limitations, our approach is applicable to large objects (RCS ≥ 5m) at distances ≤ 2000 km. Our method requires simultaneous detections by a telescope and a radar during the same fly-over, not necessarily at exactly the same time. I. WHAT CAN AND WHAT CANNOT BE DETERMINED FROM TELESCOPIC IMAGES We have data from the telescope at Ondřejov observatory (N 49.9091◦, E 14.791966◦, 528 m altitude) of the Astronomical Institute of the Czech Academy of Sciences. The telescope has a mirror with diameter 60 cm and field of view 20′ and is equipped with a 1054×1027 CCD camera, thus having resolution 1.177”/pixel. The images are taken with or without sidereal tracking; this influences the methods and sensitivity of detection, but not much the principal information obtained. Our observation (a single image or a sequence of images taken during a single fly-over) allows us to determine up to 4 orbital parameters. This is sufficient for the estimation of a circular orbit. This is true under optimal conditions when the object is seen as a short line segment (streak) with both endpoints inside the image, so that they correspond to the beginning and end of the exposure time. Near GEO objects with almost circular orbits usually allow us to estimate all important orbital parameters. These violate the assumptions only with a low probability—if the object enters/leaves the FOV during the exposure or if it is not visible all the time due to reflections, background stars, etc. There is also another uncertainty—we cannot distinguish the beginning of the streak from its end, thus we have two possibilities which cannot be recognized from the image alone. LEO objects usually pass through the whole FOV during the exposure, thus we know only a line in the image which contains the projected trajectory. Due to an imprecise timing, we even do not know the plane in space containing the orbit. Knowing a line in a 2D image, we can reduce the number of degrees of freedom by 2. One possible solution is to use a camera with a wide FOV, so that the endpoints are inside the image. However, this leads to a very imprecise localisation. For HEO objects, the endpoints of a streak may or may not be visible in the image, but the assumption of circular orbits is inadequate and leads to erroneous results. In general, one observation does not bring enough information to detect all 6 parameters of an elliptic orbit; this requires repeated observations and the knowledge that they refer to the same object. For this, the estimates assuming circular orbits from single observations may be helpful [3]. We do not deal with this task here. Our approach is also not applicable to objects which are not subject to Keppler’s laws. We assume that the only important forces determining the trajectory are the inertia and the Earth’s gravity. This is violated when the engines of a satellite are switched on—at the time of launch or landing or during maneuvers. Deceleration due to the atmosphere is also ignored. For LEO objects, a telescopic image gives only 2 of 4 parameters of a circular orbit. We try to get the missing parameters from fusion with Doppler radar data. Reprint. Published as: Navara, M., Matoušek, M. and Drbohlav, O.: Fusion of telescopic and Doppler radar data. In Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, 2014. Receiver Transmitter Fig. 1: Bi-static radar setup. The GRAVES transmitter radiates some power via its side lobes towards the receiver, though its main power goes in the opposite direction. We are able to receive reflections in both cases. The distance receiver–transmitter is 712 km, so there is no direct reception of the carrier. II. DOPPLER RADAR DATA A. Bi-static Doppler radar setup We are using a passive bi-static Doppler radar setup for radio observations of LEO objects. We use the signal transmitted by a terrestrial transmitter, reflected by the satellite and received by one or more terrestrial stations distant from the transmitter, as illustrated in Figure 1. The signal from the transmitter of the French radar-based space surveillance system GRAVES (Grand Réseau Adapte à la Veille Spatialle; Large Network Adapted to Space Watch) is passively used. The transmitter located near Dijon, France, transmits a continuous wave signal on 143.050 MHz carrier. The signal beam (main lobe) irradiates the vertical angle interval of elevations between 15◦ and 40◦. In azimuthal direction, the beam has the radiation angle of 7.5◦ and sweeps a 45◦ wide sector in 6 steps, each for 3.2 s. Four antenna fields transmit simultaneously into four sectors, covering azimuthal range from 90◦ to 270◦, i.e., the transmitter radiates to the south. However, it is assumed that the antenna system has some side/rear lobes that radiate to the north. We proved in our experiments that we are able to receive reflected signal from both the main and side lobes. We use data provided to us by Czech Radio-Astronomers Amateur Network. The network consists of several amateur receivers located across the Czech Republic (the mutual distance of the receivers is about 100 km). The stations are operated either by public astronomical observatories or by private amateurs. Since the transmitter–receiver distance is 700 km or more, there is an advantage of no direct reception of GRAVES carrier. The primary aim of the network is meteors observation, when reflections of the carrier on a ionized track of a meteor upon entering the mesosphere are detected. A meteor trace causes a detectable reflection lasting several seconds, with the frequency of the carrier, possibly with small Doppler shift (10–30 Hz) caused by winds. In contrast to meteors, reflections from (LEO) satellites can be observed up to 2 minutes and possess a characteristic pattern of Doppler shift. Since the meteor detection does not need an accurate measurement of frequency of the reflection, currently a majority of stations cannot provide precise information about the received frequency. We are measuring the Doppler shift of the GRAVES carrier, reflected by a LEO object. Our requirements on precision of frequency measurement (5 Hz at 143.05 MHz, i.e., relative error 3.5 · 10−8) pose requirements on stability and accuracy of the local oscillator of a receiver mixer. Currently only one station can provide us with suitable data (its distance to GRAVES is 712 km). Our future work includes upgrading and using the other stations. The receiver is equipped with a ground-plane antenna type. Its sensitivity is independent of the azimuth, with a slight preference of smaller elevations, as sketched in Figure 1. The receiver is able to detect reflections from satellites at altitudes ≤ 1000 km with RCS about 5 m or more. Thus it can be used only for LEO objects. In our experiments, satellites are detected in total distance from the receiver up to 2000 km. B. Characterization and preprocessing of radio data The receiver produces a quadrature signal on intermediate frequency that is digitised in 2× 16 bit channels (I and Q channel) at 48 kHz sampling frequency. Thus the received frequency band around the carrier has sufficient width w.r.t. the assumed Doppler shifts of LEO objects (several kHz). As a preprocessing, 2D spectrograms are computed from the data, using the sliding window FFT of the complex quadrature signal, with non-overlapping 1/3 s long window. For a given time interval, the spectrogram is represented as a matrix, three rows per second, where each row contains magnitudes of FFT coefficients in the selected frequency range (typically ±7 kHz around the carrier). The phase of FT is not used. An example of a typical spectrogram of an ISS1 fly-over is shown in Figure 2. A single signal from the radar at a given time gives us one real variable, enabling us to reduce the number of degrees of freedom by 1. To determine the 2 degrees of freedom missing in the telescopic observation of a LEO object, we need more. We can use: 1We have problems with optical observation of large space objects (ISS, Iridium), whose magnitude can be up to −8 and this could damage the camera. As an alternative, we proposed a unique solution based on telescopic detection of large satellites illuminated by the Moon instead of the Sun.