# Passive Radar-Based Parameter Estimation of Low Earth Orbit Debris Targets
###### Abstract  
Major space agencies such as NASA and the ESA have long reported the growing dangers caused by resident space objects orbiting our planet. These objects continue to grow in number as satellites are imploded and space debris impacts each other, causing fragmentation. As a result, significant efforts by both the public and private sectors are geared towards enhancing space domain awareness capabilities to protect future satellites and astronauts from impact by these orbiting debris. Current approaches and standards implement very large radar arrays, telescopes, and laser ranging systems to detect and track such objects. These systems are very expensive, may take significant amounts of time to develop, and are still only sparingly able to efficiently track debris targets less than 10 cm in diameter. This work proposes a theoretical passive-radar-based method using illuminators of opportunity for detecting space debris while estimating motion direction and Doppler. We show that by using a signal processing chain based on the self-mixing technique and digital filters, Doppler information can be extracted and continuously tracked by a uniform linear receiver array. This can be achieved by a passive sensor system, which has the advantage of lower cost without the need to emit signals that constrain the spectrum sharing issues. (USSPACECOM) and the US Space Force (USSF) were established in 2019 following the acknowledgment of space as a domain of warfare similar to air, land, and sea [4]. Since space was now seen as a domain of warfare, the SSA term was retired in favor of Space Domain Awareness (SDA). Both terms are still used interchangeably, but it is generally understood that surveillance techniques and technologies are significant to economic, cyber, and physical safety as a planet. The importance of SSA is also recognized on a global scale. The Inter-Agency Space Debris Coordination Committee (IADC) was the name adopted for the unification of several space debris working groups in 1993 [5]. Currently, there are more than 13 agencies spread across 12 member nations [6] tasked with facilitating worldwide coordination with respect to space debris issues. A few years after the committee formation, the United Nations published the Technical Report on Space Debris [7], which highlighted debris measurement techniques, radar modalities, the space operational environment influence of the debris, environment modeling, and mitigation measures. The IADC has several working groups addressing these areas. The IADC Mitigation Guidelines [8] highlight the need for collision avoidance. The document highlights that public orbital states provided by the SSN are inadequate for maneuver determinations. The methods described in this paper are intended to support such efforts. Modern efforts towards tracking space debris objects rely on billion-dollar radar arrays and optical telescopes. The United States Space Surveillance Network (SSN) is composed of over 30 ground-based systems spread across five continents, working in conjunction with six satellites [9]. Even with this extent of technological footprint, the catalog consists of less than 30,000 objects greater than 10 cm in diameter. The European counterpart to the SSN is the European Union Space Surveillance and Tracking (EU SST) framework established in 2014 [10] tasked with the objectives of collision avoidance, re-entry analysis, and fragmentation analysis. This network assimilates data across 51 sensors consisting of radars, such as the Bistatic Radar for LEO Survey (BIRALES) [11] and the Tracking and Imaging Radar (TIRA) [12], telescopes, such as the Joan Oro Telescope (TJO) [13], and light detection and ranging systems (LIDAR's), such as the Matera Laser Ranging Observatory (MLRO) station [14]. The BIRALES system, in particular, employs a single 410-415 MHz transmitter and a 2800 m\({}^{2}\) receiver array [11].