# Population-Aware Physics-Informed Neural Particle Flow for Robust Spacecraft Bayesian Navigation

arXiv: https://arxiv.org/abs/2606.10959 · HTML: https://mlsanity.com/paper/2606.10959/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 22 references that are in the map.
- First posted on arXiv 9 Jun 2026.

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

- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [On Deep Set Learning and the Choice of Aggregations](https://mlsanity.com/paper/1903.07348/) (2019)
- [A survey on Bayesian inference for Gaussian mixture model](https://mlsanity.com/paper/2108.11753/) (2021)
- [Particle Filtering with Invertible Particle Flow](https://mlsanity.com/paper/1607.08799/) (2016)
- [Sampling via Gaussian Mixture Approximations](https://mlsanity.com/paper/2509.25232/) (2025)
- [Physics-informed neural particle flow for the Bayesian update step](https://mlsanity.com/paper/2602.23089/) (2026)
- [Advances in Particle Flow Filters with Taylor Expansion Series](https://mlsanity.com/paper/2505.01597/) (2025)
- [Dynamical Update Maps for Particle Flow with Differential Algebra](https://mlsanity.com/paper/2505.01598/) (2025)

## Abstract (arXiv)

Spacecraft navigation often requires Bayesian inference from sparse nonlinear measurements that produce curved, multimodal, or geometrically constrained posterior distributions. Physics-informed neural particle flow (PINPF) addresses such problems by learning a deterministic prior-to-posterior transport field from the governing probability evolution equation, but its particle-wise architecture does not explicitly account for the empirical particle population. This paper introduces population-aware PINPF (PA-PINPF), which conditions each particle velocity on a permutation-invariant Deep Sets representation of the complete particle set. PA-PINPF-State summarizes particle positions, whereas PA-PINPF-Feature summarizes the local physics-informed features, including likelihood and score information. Both retain the unsupervised PINPF residual and require neither posterior samples nor labeled transport trajectories. The methods are evaluated over 100 randomized time-difference-of-arrival tasks representative of RF cross-link and ground-station localization and 100 range-measurement tasks with an onboard sensor field-of-view constraint. Results demonstrate that population-level Bayesian features provide useful global information for learned particle transport in nonlinear spacecraft-navigation problems.