Meaning
Variance reduction methods select new points from a weighted distribution by choosing a single random starting point and moving at fixed intervals. Applying systematic resampling to a particle filter ensures that the new set of samples is distributed according to the desired weights with minimal noise. This technique replaces a set of weights with a set of equally weighted points that represent the same distribution.
It is highly effective when the particles are already sorted or ordered.
Selection Efficiency
Algorithmic speed is a primary benefit of this approach compared to other methods. In systematic resampling, only one random number is generated for the entire set. This reduces the computational overhead significantly.
The process is deterministic once the initial offset is chosen.
Low Discrepancy
Geometric properties of the sample set remain consistent across the space. Because systematic resampling uses a fixed grid, it avoids the clustering of points that can happen with purely random selection. This uniformity leads to a precise representation of the underlying density.
It is a preferred choice for high-performance simulations.
Sample Uniformity
Consistency in the resulting weights simplifies the next stage of the calculation. After systematic resampling, every point has a weight of one over the total number of points. This reset prevents a few high-weight particles from dominating the entire filter.
It maintains the health of the particle population over many iterations.
