This paper focuses on the multi-target tracking using the Stone Soup framework. In particular, we aim at evaluation of two multi-target tracking scenarios based on the simulated class-B dataset and ADS-B class-A dataset provided by OpenSky Network. The scenarios are evaluated w.r.t. selection of a local state estimator using a range of the Stone Soup metrics. Source code with scenario definitions and Stone Soup set-up are provided along with the paper.

This paper focuses on state prediction for stochastic dynamic models with linear dynamics, emphasizing a recently proposed efficient and robust Lagrangian approach for solving the Chapman–Kolmogorov equation. In contrast to the standard Eulerian perspective, the Lagrangian method separates the solution into two sequential steps: advection and diffusion. Advection is handled by moving a carefully designed grid, while diffusion is addressed using the convolution theorem. This approach significantly reduces computational complexity while preserving the same accuracy. In this paper, we propose formulating diffusion as a continuous-time process, leading to a partial differential equation (PDE). Various methods for solving this PDE are presented and compared within a unified framework, along with evaluations of their properties and example implementations. We demonstrate that the continuous formulation can yield substantial reductions in computational complexity with only marginal loss in accuracy.

This paper deals with state estimation of nonlinear stochastic dynamic models. In particular, the stochastic integration rule, which provides asymptotically unbiased estimates of the moments of nonlinearly transformed Gaussian random variables, is reviewed together with the recently introduced stochastic integration filter (SIF). Using SIF, the respective multi-step prediction and smoothing algorithms are developed in full and efficient square-root form. The stochastic-integration-rule-based algorithms are implemented in Python (within the Stone Soup framework) and in MATLAB® and are numerically evaluated and compared with the well-known unscented and extended Kalman filters using the Stone Soup defined tracking scenario.

This paper deals with the state estimation of stochastic models with continuous dynamics. The aim is to incorporate spectral differentiation methods into the solution to the Fokker-Planck equation in grid-based state estimation routine, while taking into account the specifics of the field, such as probability density function (PDF) features, moving grid, zero boundary conditions, etc. The spectral methods, in general, achieve very fast convergence rate of $\mathcal{O}\left(c^{N}\right)(O{\lt}$ $c{\lt}1$) for analytical functions such as the probability density function, where N is the number of grid points. This is significantly better than the standard finite difference method (or midpoint rule used in discrete estimation) typically used in grid-based filter design with convergence rate $\mathcal{O}\left(\frac{1}{N^{2}}\right)$. As consequence, the proposed spectral method based filter provides better state estimation accuracy with lower number of grid points, and thus, with lower computational complexity.

This paper deals with state estimation of stochastic models with linear state dynamics, continuous or discrete in time. The emphasis is laid on a numerical solution to the state prediction by the time-update step of the grid-point-based point-mass filter (PMF), which is the most computationally demanding part of the PMF algorithm. A novel efficient PMF (ePMF) estimator, unifying continuous and discrete, approaches is proposed, designed, and discussed. By numerical illustrations, it is shown, that the proposed ePMF can lead to a time complexity reduction that exceeds 99.9% without compromising accuracy. The MATLAB® code of the ePMF is released with this paper.

This paper is devoted to the Bayesian state estimation of the nonlinear stochastic dynamic systems. The stress is laid on the numerical solution to the Bayesian recursive relations by the point-mass filter for a class of state-space models with linear dynamics and nonlinear measurement. In particular, a novel reliable technique for convolution computation is proposed. The technique combines the standard point-mass-based convolution with a density-weighted integration to provide accurate results even for systems with small state noise. Several implementations of the technique are developed, theoretically analysed, and evaluated in a numerical study.