Abstract
<jats:p>Abstract. This paper proposes an improved method for the merging particle filter (MPF), which is employed as a data assimilation technique for nonlinear systems. While MPF achieves good root mean square error (RMSE) with a small number of particles relative to the basic particle filter, it suffers from a lack of systematic guidelines in setting merging coefficients, and estimation accuracy plateaus when the number of particles increases. Here, merging coefficients refer to the weight parameters used in the linear combination of multiple particles, with the constraints that their sum equals 1 and their sum of squares equals 1. However, these coefficients are chosen empirically, without theoretical understanding. In this study, we propose the randomized merging particle filter (RMPF) that randomly generates the merging coefficients and obtains estimates from the pre-merging distribution. Furthermore, a theoretical analysis clarifies how the merging dimension shapes the merged-particle distribution, casting its selection as a bias–variance trade-off that we resolve in practice by likelihood maximization. Numerical experimental results using Lorenz-63 and Lorenz-96 models demonstrated highly accurate estimation by RMPF.</jats:p>