State Estimation Algorithm for One-Dimensional Variables Using Combined Particle Filter and UKF Approach

This document presents a state estimation algorithm that integrates the strengths of particle filters and Unscented Kalman Filters (UKF) to achieve higher accuracy in estimating one-dimensional state variables. Both filter types possess distinct advantages and limitations: particle filters demonstrate excellent performance in nonlinear system estimation but require substantial computational resources, while UKF offers lower computational complexity but reduced effectiveness in handling strong nonlinearities.

To address these trade-offs, we developed a novel hybrid algorithm that combines the benefits of both approaches. The implementation typically involves using UKF for preliminary state prediction and covariance estimation, followed by particle filter refinement through importance sampling and resampling techniques. This combination enables more accurate one-dimensional state estimation with relatively lower computational overhead compared to standalone particle filters.

In practical applications, this algorithm can be deployed in various systems requiring one-dimensional state variable estimation, such as robotic navigation (for position/velocity tracking), object tracking systems, and sensor fusion applications. The code implementation generally involves initializing sigma points for UKF transformation, followed by particle propagation and weight updating steps, with systematic resampling to prevent particle degeneracy.