Estimation of satellite orbits using ground based radar concept

Abstract: Today an abundance of objects are circulating in earth captured orbit. Monitoring these objects is of national security interest. One way to map any object in orbit is with their Keplerian elements. A method for estimating the Keplerian elements of a satellite orbit simulating a ground based radar station has been investigated. A frequency modulated continuous wave radar (FMCW) with a central transmitter antenna and a grid of receivers was modeled in MATLAB. The maximum likelihood estimator (MLE) was obtained to estimate the parameters from the received signal. The method takes advantage of the relations between the Cartesian position and velocity and the Keplerian elements to confine the search space. For a signal to noise ratio (SNR) of 10dB, the satellite was followed during a time period of 0.1s where the positions were found within average error of range: ±1.4m, azimuth: ±2.0·10−6 rad and elevation: ±8.4·10−7 rad. Using a linear approximation of the velocity the Keplerian elements were found within average error of i: ±0.0050 rad, Ω:±0.0050 rad, ω: ±0.0058 rad, a: ±2.60·105m, e:±0.0021 and ν: ±0.24 rad. A method to obtain more accurate estimates is proposed.