# Optimal Initialization Strategies for Range-Only Trajectory Estimation

arXiv: https://arxiv.org/abs/2309.09011 · HTML: https://mlsanity.com/paper/2309.09011/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Sep 2023.

## Built on by (most cited first, 1 of 1)

- [Multi-Robot Relative Pose Estimation in SE(2) with Observability Analysis: A Comparison of Extended Kalman Filtering and Robust Pose Graph Optimization](https://mlsanity.com/paper/2401.15313/) (2024)

## Abstract (arXiv)

Range-only (RO) pose estimation involves determining a robot's pose over time by measuring the distance between multiple devices on the robot, known as tags, and devices installed in the environment, known as anchors. The nonconvex nature of the range measurement model results in a cost function with possible local minima. In the absence of a good initialization, commonly used iterative solvers can get stuck in these local minima resulting in poor trajectory estimation accuracy. In this work, we propose convex relaxations to the original nonconvex problem based on semidefinite programs (SDPs). Specifically, we formulate computationally tractable SDP relaxations to obtain accurate initial pose and trajectory estimates for RO trajectory estimation under static and dynamic (i.e., constant-velocity motion) conditions. Through simulation and real experiments, we demonstrate that our proposed initialization strategies estimate the initial state accurately compared to iterative local solvers. Additionally, the proposed relaxations recover global minima under moderate range measurement noise levels.