Preliminary orbits with line-of-sight correction for LEO satellites observed with radar

Abstract

We propose a method to account for the Earth oblateness effect in preliminary orbit determination of satellites in low orbits with radar observations. This method is an improvement of the one described in [9], which uses a pure Keplerian dynamical model. Since the effect of the Earth oblateness is strong at low altitudes, its inclusion in the model can sensibly improve the initial orbit, giving a better starting guess for differential corrections and increasing the chances to obtain their convergence. The input set consists of two tracks of radar observations, each one composed of at least 4 observations taken during the same pass of the satellite. A single observation gives the topocentric position of the satellite, where the range is very accurate, while the line of sight direction is poorly determined. From these data we can compute by a polynomial fit the values of the range and range rate at the mean epochs of the two tracks. In order to obtain a preliminary orbit we wish to compute the angular velocities, that is the rate of change of the line of sight. In the same spirit of [9], we also wish to correct the values of the angular measurements, so that they fit the selected dynamical model if the same holds for the radial distance and velocity. The selected model is a perturbed Keplerian dynamics, where the only perturbation included is the secular effect of the J2 term of the geopotential. The proposed algorithm models this problem with 8 equations in 8 unknowns.

Orbit determination for standard-like maps: asymptotic expansion of the confidence region in regular zones

“…These algorithms crucially depend on the choice of the initial conditions. See [7], [12] for some recent results on this topic for the asteroid and space debris cases. In the following we will always suppose that the least squares solution (x 0 , y 0 ) exists and we will refer to it as the nominal solution.…”

Asymptotic behaviour of orbit determination for hyperbolic maps

“…These algorithms crucially depend on the choice of the initial conditions. See Gronchi et al (2015), Ma et al (2018) for some recent results on this topic for the asteroid and space debris cases. For the case of chaotic maps that we study in this paper, the problem is considered in Serra et al (2018), Spoto and Milani (2016) where computational problems that occur for large N are treated with advanced techniques.…”

Applying Lambert problem to association of radar-measured orbit tracks of space objects

“…Gronchi et al used algebraic integrals of the two-body problem to calculate the initial orbital elements (Gronchi et al 2015a). Ma et al selected a perturbated Keplerian dynamics model to correct the angular measurements and to determine the initial orbital elements of LEO satellite (Ma et al 2018). Feng proposed a novel quasi linearization-local variational iteration method to solve the perturbed Lambert problem (Feng et al 2021).…”