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Nonlinear Output Frequency Response Functions (NOFRFs), which are a one-dimensional extension of the linear Frequency Response Function (FRF) to nonlinear cases, have been introduced for nonlinear system characterization and compensation. The evaluation of NOFRFs is accomplished by solving a series of linear difference or differential equations, known as Generalized Associated Linear Equations (GALEs). However, the derivation of GALEs often includes numerous recursive and symbolic calculations, posing significant challenges in both practical applications and computer programming. In the present study, a fast-computing algorithm, based on combinatorial calculations as opposed to recursive and symbolic calculations, is proposed for fast evaluation of GALEs. This allows for the evaluation of NOFRFs in a more streamlined and straightforward manner. The applications of the proposed fast-computing algorithm for nonlinear system characterization and compensation are demonstrated through several case studies including a High Power Amplifier (HPA) and a Duffing system. The results of the case studies show the effectiveness of applying the GALEs and NOFRFs for system design and safety control across a wide range of engineering applications. [ABSTRACT FROM AUTHOR]

For target tracking systems, the probability of detecting a target is difficult to determine, and the process noise often has non-Gaussian heavy-tailed characteristics owing to interference from outliers. To address the issues associated with single target tracking within clutters in scenarios with an unknown detection probability and heavy-tailed process noise, this paper presents a variational Bayesian-based adaptive probabilistic data association filter (VB-APDAF). The beta distribution, Pearson type VII distribution and multinomial distribution are used to model the detection probability, the process noise, and the association events, respectively. To guarantee the conjugation, a novel parameter estimation strategy is employed. In this strategy, the previous state is introduced in the state update process to construct the joint probability density function of parameters to be estimated and data set. The VB framework is used to estimate the target state, detection probability, and associated events. An experiment was performed under simulated conditions to demonstrate the effectiveness of the proposed filter. [ABSTRACT FROM AUTHOR]