Hierarchical multilevel optimization with multiple-leaders multiple-followers setting and nonseparable objectives

Hierarchical multilevel multi-leader multi-follower problems are non-cooperative decision problems in which multiple decision-makers of equal status in the upper-level and multiple decision-makers of equal status are involved at each of the lower-levels of the hierarchy. Much of solution methods proposed so far on the topic are either model specific which may work only for a particular sub-class of problems or are based on some strong assumptions and only for two level cases. In this paper, we have considered hierarchical multilevel multi-leader multi-follower problems in which the objective functions contain separable and non-separable terms (but the non-separable terms can be written as a factor of two functions, a function which depends on other level decision variables and a function which is common to all objectives across the same level) and shared constraint. We have proposed a solution algorithm to such problems by equivalent reformulation as a hierarchical multilevel problem involving single decision maker at all levels of the hierarchy. Then, we applied a multi-parametric algorithm to solve the resulting single leader single followers problem.

Single-Channel Multiple-Receiver Sound Source Localization System with Homomorphic Deconvolution and Linear Regression

The conventional sound source localization systems require the significant complexity because of multiple synchronized analog-to-digital conversion channels as well as the scalable algorithms. This paper proposes a single-channel sound localization system for transport with multiple receivers. The individual receivers are connected by the single analog microphone network which provides the superimposed signal over simple connectivity based on asynchronized analog circuit. The proposed system consists of two computational stages as homomorphic deconvolution and machine learning stage. A previous study has verified the performance of time-of-flight estimation by utilizing the non-parametric and parametric homomorphic deconvolution algorithms. This paper employs the linear regression with supervised learning for angle-of-arrival prediction. Among the circular configurations of receiver positions, the optimal location is selected for three-receiver structure based on the extensive simulations. The non-parametric method presents the consistent performance and Yule–Walker parametric algorithm indicates the least accuracy. The Steiglitz–McBride parametric algorithm delivers the best predictions with reduced model order as well as other parameter values. The experiments in the anechoic chamber demonstrate the accurate predictions in proper ensemble length and model order.

Detection Characteristics of the Parametric Method of Signal Processing in a Sparse Antenna Array of a Transportable Decameter Range Radar

Introduction. The possibility of application of modified parametric methods of spatial signal processing in a sparse antenna array (SEAA) of the receiving position of transportable over-the-horizon decameter range radar (DRR) intended for all-weather remote monitoring of the shelf zone is considered in this paper. With an operational deployment of DRR on unprepared coast, problems of the equidistant location of antenna elements (AEs) often arise. In the case of nonequidistant AEs location and matched spatial processing, antenna pattern has interference sidelobes, which level can significantly exceed the allowable or calculated one for an equidistant AA. A well-known alternative to matched processing are parametric methods of spectral analysis based on the using of models with a finite number of parameters, but their direct application requires an equidistant sampling of the spatial signal.Aim. The aim of the research is to develop and analyze the method of parametric processing of spatial signals of the SEAA which AEs are located on the line with a random step in the range from λ/2 to several λ, where λ is the DRR wavelength.Materials and methods. To construct the detection characteristics (DC) computer modeling in the MatLab environment, the reliability of which was confirmed by the construction of known and theoretically calculated DC, was used.Results. The developed method includes a procedure of restoring (synthesizing) of artificial signal of equidistant AA with subsequent application of Burg parametric algorithm to obtain an estimate of the angular spatial frequency spectrum. To prove the applicability of the parametric method of SEAA signals processing in the case of location signals detecting, DC were obtained and compared with optimal ones.Conclusions. The obtained results have proved the suboptimality of the parametric method of SEAA signal processing at the random AEs spacing step lying in the range from λ/2 to 3λ, what makes it possible to recommend it for using in transportable DRRs.