  State estimation is crucial for the performance and safety of numerous
robotic applications. Among the suite of estimation techniques, particle
filters have been identified as a powerful solution due to their non-parametric
nature. Yet, in high-dimensional state spaces, these filters face challenges
such as 'particle deprivation' which hinders accurate representation of the
true posterior distribution. This paper introduces a novel resampling-free
particle filter designed to mitigate particle deprivation by forgoing the
traditional resampling step. This ensures a broader and more diverse particle
set, especially vital in high-dimensional scenarios. Theoretically, our
proposed filter is shown to offer a near-accurate representation of the desired
posterior distribution in high-dimensional contexts. Empirically, the
effectiveness of our approach is underscored through a high-dimensional
synthetic state estimation task and a 6D pose estimation derived from videos.
We posit that as robotic systems evolve with greater degrees of freedom,
particle filters tailored for high-dimensional state spaces will be
indispensable.
