Exploring the efficacy of neural networks for trajectory compression and the inverse problem

TL;DR

This paper demonstrates that neural networks can effectively predict initial conditions of complex nonlinear trajectories with high accuracy, enabling efficient trajectory compression and inverse problem solving in a simulated environment.

Contribution

It introduces a neural network approach for trajectory compression and inverse problem solving, capable of predicting initial conditions with sub-meter accuracy for complex nonlinear trajectories.

Findings

Neural network accurately predicts initial conditions within sub-meter deviation.

Model performs well for target points within a 2 km radius.

Simulation-based training enables handling trajectories of arbitrary dimensions.

Abstract

In this document, a neural network is employed in order to estimate the solution of the initial value problem in the context of non linear trajectories. Such trajectories can be subject to gravity, thrust, drag, centrifugal force, temperature, ambient air density and pressure. First, we generate a grid of trajectory points given a specified uniform density as a design parameter and then we investigate the performance of a neural network in a compression and inverse problem task: the network is trained to predict the initial conditions of the dynamics model we used in the simulation, given a target point in space. We investigate this as a regression task, with error propagation in consideration. For target points, up to a radius of 2 kilometers, the model is able to accurately predict the initial conditions of the trajectories, with sub-meter deviation. This simulation-based training process and novel real-world evaluation method is capable of computing trajectories of arbitrary dimensions.