This paper considers tracking of a non-cooperative emitter based on a single sensor. To this end, the direct target motion analysis (DTMA) approach, where the target state is straightforwardly achieved from the received signal, is exploited. In order to achieve observability, the sensor has to perform a maneuver relative to the emitter. By suitably building an approximated likelihood function, the unscented Kalman filter (UKF), which is able to work under high nonlinearity of the measurement model, is adopted to recursively estimate the target state. Besides, the posterior Cramér-Rao bound (PCRB) of DTMA, which can be used as performance benchmark, is also achieved. The effectiveness of proposed method is verified via simulation experiments.

Recently, fuzzy set theory has been widely employed in building portfolio selection models where uncertainty plays a role. In these models, future security returns are generally taken for fuzzy variables and mathematical models are then built to maximize the investment profit according to a given risk level or to minimize a risk level based on a fixed profit level. Based on existing works, this paper proposes a portfolio selection model based on fuzzy birandom variables. Two original contributions are provided by the study: First, the concept of technical analysis is combined with fuzzy set theory to use the security returns as fuzzy birandom variables. Second, the fuzzy birandom Value-at-Risk (VaR) is used to build our model, which is called the fuzzy birandom VaR-based portfolio selection model (FBVaR-PSM). The VaR can directly reflect the largest loss of a selected case at a given confidence level and it is more sensitive than other models and more acceptable for general investors than conventional risk measurements. To solve the FBVaR-PSM, in some special cases when the security returns are taken for trapezoidal, triangular or Gaussian fuzzy birandom variables, several crisp equivalent models of the FBVaR-PSM are derived, which can be handled by any linear programming solver. In general, the fuzzy birandom simulation-based particle swarm optimization algorithm (FBS-PSO) is designed to find the approximate optimal solution. To illustrate the proposed model and the behavior of the FBS-PSO, two numerical examples are introduced based on investors' different risk attitudes. Finally, we analyze the experimental results and provide a discussion of some existing approaches.

The development of the electricity market enables us to provide electricity of varied quality and price in order to fulfill power consumers' needs. Such customers choices should influence the process of adjusting power generation and spinning reserve, and, as a result, change the structure of a unit commitment optimization problem (UCP). To build a unit commitment model that considers customer choices, we employ fuzzy variables in this study to better characterize customer requirements and forecasted future power loads. To measure system reliability and determine the schedule of real power generation and spinning reserve, fuzzy Value-at-Risk (VaR) is utilized in building the model, which evaluates the peak values of power demands under given confidence levels. Based on the information obtained using fuzzy VaR, we proposed a heuristic algorithm called local convergence-averse binary particle swarm optimization (LCA-PSO) to solve the UCP. The proposed model and algorithm are used to analyze several test systems. Comparisons between the proposed algorithm and the conventional approaches show that the LCA-PSO performs better in finding the optimal solutions.