# Generalizing Trilateration: Approximate Maximum Likelihood Estimator for Initial Orbit Determination in Low-Earth Orbit

arXiv: https://arxiv.org/abs/2407.15180 · HTML: https://mlsanity.com/paper/2407.15180/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 67 references that are in the map.
- First posted on arXiv 21 Jul 2024.

## Builds on (most cited first, 9 of 9)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [A Primer on Coordinate Descent Algorithms](https://mlsanity.com/paper/1610.00040/) (2016)
- [Machine Learning in Orbit Estimation: a Survey](https://mlsanity.com/paper/2207.08993/) (2022)
- [Coordinate Friendly Structures, Algorithms and Applications](https://mlsanity.com/paper/1601.00863/) (2016)
- [Simple and fast convex relaxation method for cooperative localization in sensor networks using range measurements](https://mlsanity.com/paper/1408.4728/) (2014)
- [Range and Bearing Data Fusion for Precise Convex Network Localization](https://mlsanity.com/paper/2110.03523/) (2021)
- [Parameter-free Maximum Likelihood Localization of a Network of Moving Agents from Ranges, Bearings and Velocity measurements](https://mlsanity.com/paper/2304.05988/) (2023)
- [One-Shot Initial Orbit Determination in Low-Earth Orbit](https://mlsanity.com/paper/2312.13318/) (2023)

## Abstract (arXiv)

With the increase in the number of active satellites and space debris in orbit, the problem of initial orbit determination (IOD) becomes increasingly important, demanding a high accuracy. Over the years, different approaches have been presented such as filtering methods (for example, Extended Kalman Filter), differential algebra or solving Lambert's problem. In this work, we consider a setting of three monostatic radars, where all available measurements are taken approximately at the same instant. This follows a similar setting as trilateration, a state-of-the-art approach, where each radar is able to obtain a single measurement of range and range-rate. Differently, and due to advances in Multiple-Input Multiple-Output (MIMO) radars, we assume that each location is able to obtain a larger set of range, angle and Doppler shift measurements. Thus, our method can be understood as an extension of trilateration leveraging more recent technology and incorporating additional data. We formulate the problem as a Maximum Likelihood Estimator (MLE), which for some number of observations is asymptotically unbiased and asymptotically efficient. Through numerical experiments, we demonstrate that our method attains the same accuracy as the trilateration method for the same number of measurements and offers an alternative and generalization, returning a more accurate estimation of the satellite's state vector, as the number of available measurements increases.