Particle filters are a widely used Monte Carlo based data assimilation technique that estimates the probability distribution of a system's state conditioned on observations through a collection of weights and particles. A known problem for particle filters is weight collapse, or degeneracy, where a single weight attains a value of one while all others are close to zero, thereby collapsing the estimated distribution. We address this issue by introducing a novel modification to the particle filter that is simple to implement and inspired by energy-based diversity measures. Our approach adjusts particle weights to minimize a two-body energy potential, promoting balanced weight distributions and mitigating collapse. We demonstrate the performance of this modified particle filter in a series of numerical experiments with linear and nonlinear dynamical models, where we compare with the classical particle filter and ensemble Kalman filters in the nonlinear case. We find that our new approach improves weight distributions compared to the classical particle filter and thereby improve state estimates.

翻译：粒子滤波器是一种广泛使用的基于蒙特卡洛的数据同化技术，它通过一组权重和粒子来估计系统状态在观测条件下的概率分布。粒子滤波器存在一个已知问题，即权重崩溃或退化现象，其中单个权重达到一而其他权重接近零，从而导致估计分布崩溃。我们通过引入一种新颖的粒子滤波器改进方法来解决这一问题，该方法易于实现，并受到基于能量的多样性度量的启发。我们的方法通过调整粒子权重以最小化二体能量势，促进平衡的权重分布并缓解崩溃。我们在一系列线性和非线性动力学模型的数值实验中展示了这种改进粒子滤波器的性能，并在非线性情况下与经典粒子滤波器及集合卡尔曼滤波器进行了比较。我们发现，与经典粒子滤波器相比，我们的新方法改善了权重分布，从而提升了状态估计的准确性。