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The finite-set statistics (FISST) foundational approach to multitarget tracking and information fusion has inspired work by dozens of research groups in at least 20 nations; and FISST publications have been cited tens of thousands of times. This review paper addresses a recent and cutting-edge aspect of this research: exact closed-form—and, therefore, provably Bayes-optimal—approximations of the multitarget Bayes filter. The five proposed such filters—generalized labeled multi-Bernoulli (GLMB), labeled multi-Bernoulli mixture (LMBM), and three Poisson multi-Bernoulli mixture (PMBM) filter variants—are assessed in depth. This assessment includes a theoretically rigorous, but intuitive, statistical theory of “undetected targets”, and concrete formulas for the posterior undetected-target densities for the “standard” multitarget measurement model.

The finite-set statistics (FISST) foundational approach to multitarget tracking and information fusion was introduced in the mid-1990s and extended in 2001. FISST was devised to be as “engineering-friendly” as possible by avoiding avoidable mathematical abstraction and complexity—and, especially, by avoiding measure theory and measure-theoretic point process (p.p.) theory. Recently, however, an allegedly more general theoretical foundation for multitarget tracking has been proposed. In it, the constituent components of FISST have been systematically replaced by mathematically more complicated concepts—and, especially, by the very measure theory and measure-theoretic p.p.’s that FISST eschews. It is shown that this proposed alternative is actually a mathematical paraphrase of part of FISST that does not correctly address the technical idiosyncrasies of the multitarget tracking application.

Compared with the standard finite-set model-based predictive current control (FS-MPCC), the finite-set ultra-local model-based predictive current control (FS-ULMPCC) removes the use of actual system parameters and thus has some advantages like good robustness and easy implementation. However, the steady-state performance of FS-ULMPCC is relatively weak. In this paper, a novel FS-ULMPCC method is proposed and applied to the AC/DC converter of a direct-driven wind power generation system. The proposed method is designed based on a linear-extended state observer (LESO). In particular, a new control set reconstruction strategy is proposed to improve the steady-state performance. Only three options are included in the reconstructed control set, and each one is associated with two independent, active voltage vectors and their durations. The proposed FS-ULMPCC method is compared with the traditional one through experiments. The proposed method includes enhanced steady-state performance and reduced computational burden.

Conventional multitarget tracking systems presume that each target can produce at most one measurement per scan. Due to the multiple ionospheric propagation paths in over-the-horizon radar (OTHR), this assumption is not valid. To solve this problem, this paper proposes a novel tracking algorithm based on the theory of finite set statistics (FISST) called the multipath probability hypothesis density (MP-PHD) filter in cluttered environments. First, the FISST is used to derive the update equation, and then Gaussian mixture (GM) is introduced to derive the closed-form solution of the MP-PHD filter. Moreover, the extended Kalman filter (EKF) is presented to deal with the nonlinear problem of the measurement model in OTHR. Eventually, the simulation results are provided to demonstrate the effectiveness of the proposed filter.

We focus on the biological problem of tracking organelles as they move through cells. In the past, most intracellular movements were recorded manually, however, the results are too incomplete to capture the full complexity of organelle motions. An automated tracking algorithm promises to provide a complete analysis of noisy microscopy data. In this paper, we adopt statistical techniques from a Bayesian random set point of view. Instead of considering each individual organelle, we examine a random set whose members are the organelle states and we establish a Bayesian filtering algorithm involving such set states. The propagated multi-object densities are approximated using a Gaussian mixture scheme. Our algorithm is applied to synthetic and experimental data.

For exploring the meaning of the power set in evidence theory, a possible explanation of power set is proposed from the view of Pascal’s triangle and combinatorial number. Here comes the question: what would happen if the combinatorial number is replaced by permutation number? To address this issue, a new kind of set, named as random permutation set (RPS), is proposed in this paper, which consists of permutation event space (PES) and permutation mass function (PMF). The PES of a certain set considers all the permutation of that set. The elements of PES are called the permutation events. PMF describes the chance of a certain permutation event that would happen. Based on PES and PMF, RPS can be viewed as a permutation-based generalization of random finite set. Besides, the right intersection (RI) and left intersection (LI) of permutation events are presented. Based on RI and LI, the right orthogonal sum (ROS) and left orthogonal sum (LOS) of PMFs are proposed. In addition, numerical examples are shown to illustrate the proposed conceptions. The comparisons of probability theory, evidence theory, and RPS are discussed and summarized. Moreover, an RPS-based data fusion algorithm is proposed and applied in threat assessment. The experimental results show that the proposed RPS-based algorithm can reasonably and efficiently deal with uncertainty in threat assessment with respect to threat ranking and reliability ranking.

In the paper a comparative study of the two control structures based on MPC (Model Predictive Control) for an electrical drive system with an induction motor are presented. As opposed to the classical approach, in which DFOC (Direct Field Oriented Control) with four controllers is considered, in the current study only one MPC controller is utilized. The proposed control structures have a cascade free structure that consists of a vector of electromagnetic (torque, flux) and mechanical (speed) states of the system. The first investigated framework is based on the finite-set MPC. A short horizon predictive window is selected. The continuous set MPC is used in the second framework. In this case the predictive horizon contains several samples. The computational complexity of the algorithm is reduced by applying its explicit version. Different implementation aspects of both MPC structures, for instance the model used in prediction, complexity of the control algorithms, and their properties together with the noise level are analyzed. The effectiveness of the proposed approach is validated by some experimental tests.

Consider the family Ξ of all possible partitions of a given finite set into disjoint parts. Suppose we have A ∈ Ξ, and there is reason to consider this partition basic from a certain point of view. The greatest value d *(A) of the special cluster metric d(A, B) is found, which is reached when its second argument runs through all B ∈ Ξ. The value of d *(A) turns out to depend on the structure of the basic partition A. Using the found value of d *(A), we propose a numerical coefficient whose value allows us to estimate the degree of difference between the basic partition and the newly built one. Such an assessment can help us to make a decision about the possibility of using the new partition instead of the basic one.

We present an iterative formula for calculating the number of different R0-topologies on a finite set.

The magnet-less switched reluctance motor (SRM) speed-torque characteristics are ideally suited for traction motor drive characteristics and its advantage to minimize the overall cost of on-road EVs. The main drawbacks are torque and flux ripple, which have produced high in low-speed operation. However, the emerging direct torque control (DTC) operated magnitude flux and torque estimation with voltage vectors (VVs) gives high torque ripples due to the selection of effective switching states and sector partition accuracy. On the other hand, the existing model predictive control (MPC) with multiple objective and optimization weighting factors produces high torque ripples due to the system dynamics and constraints. Therefore, existing DTC and MPC can result in high torque ripples. This paper proposed a finite set (FS)-MPC with a single cost function objective without weighting factor: the predicted torque considered to evaluate VVs to minimize the ripples further. The selected optimal VV minimizes the SRM drive torque and flux ripples in steady and dynamic state behaviour. The classical DTC and proposed model were developed, and simulation results were verified using MATLAB/Simulink. The proposed model operated in SRM drives experimental results to prove the effective minimization of torque and flux ripples compared to the existing DTC.