Pseudorange and Doppler-Based Positioning: Enabling Convergence of Least-Squares Estimation from MEO to LEO

The growing interest of the space industry in satellite systems within the low Earth orbit (LEO) region has prompted attention to their potential for positioning, navigation, and timing applications. This study addresses the convergence issue highlighted in the literature when the Gauss Newton (GN) method is applied to least squares (LS) position estimation algorithms in LEO scenarios, with analyses conducted independently for pseudorange and Doppler shift measurements. To address these limitations, this paper examines two line search techniques in combination with the GN method. A comprehensive analysis of the LS method is conducted through tests on satellite constellations at various orbital altitudes, from medium Earth orbits to LEOs. The results, evaluated in terms of the number of iterations required to achieve convergence, show that adjusting the GN step using a damping factor, namely the damped GN factor, effectively resolves convergence issues, even in LEO scenarios. In particular, the proposed algorithm consistently converges in the LEO region within an average of seven iterations.