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In this paper, a novel Takagi-Sugeno (T-S) fuzzy model particle filtering algorithm (TSF-PF) based on fuzzy C-regression clustering is proposed for uncertainty modeling of the target dynamic model with non-Gaussian noise. In the proposed algorithm, a generic semantic framework of the T-S fuzzy model is constructed to incorporate spatial feature information of a target into the particle filter, in which the spatial feature information is characterized by several semantic fuzzy sets. Meanwhile, a fuzzy C-regression clustering method based on correntropy is proposed to adaptively identify the premise parameters of the T-S fuzzy model, which is used to adjust the weight of models, and a Kalman filter is used to identify the consequent parameters. And then an efficient importance density function is constructed by using the proposed T-S fuzzy model, which can efficiently improve the robust and diversity of the sampling particles. Furthermore, in order to improve the real-time performance of the proposed algorithm, two improved T-S fuzzy model particle filtering algorithms are presented. The simulation results show that the tracking performance of the proposed algorithms are better than that of the traditional interacting multiple model (IMM), interacting multiple model unscented Kalman filter (IMMUKF), interacting multiple model particle filter (IMMPF) and interacting multiple model Rao-Blackwellized particle filter (IMMRBPF). Particularly, the proposed algorithms can accurately track the maneuvering target when the moving direction abruptly changes or the prior information of the target dynamic model is inaccuracy.

This paper presents an effective constrained multiple model particle filtering (CMMPF) for bearings-only maneuvering target tracking. In the proposed algorithm, the process of target tracking is factorized into two sub-problems: 1) motion model estimation and model-conditioned state filtering according to the Rao–Blackwellised theorem and 2) the target dynamic system is modeled by multiple switching dynamic models in a jump Markov system framework. To estimate the model set, a modified sequential importance resampling method is used to draw the model particles, which can be restricted into the feasible area coincide with the constrained bound. To the model-conditioned state nonlinear filtering, a truncated prior probability density function is constructed by utilizing the latest observations and auxiliary variables (target spatio–temporal features), which can guarantee the diversity and accuracy of the sampled particles. The tracking performance is compared and analyzed with other conventional filters in two scenarios: 1) uniform and time-invariant sampling scenario and 2) non-uniform and sparse sampling scenario. A conservative Cramer–Rao lower bound is also introduced and compared with the root mean square error performance of the suboptimal filters. Simulation results confirm the superiority of CMMPF algorithm over the other existing ones in comparison with respect to accuracy, efficiency, and robustness for the bearings-only target tracking system, especially for the aperiodic and sparse sampling environment.

This paper proposes a marginal multi-object Bayesian filter with multiple hypotheses to track multiple objects in the presence of object appearing and object disappearing, missed detection and clutter. This filter delivers the probability of existence and probability density function of each object. A mathematical model for searching K-best hypotheses is set up by the maximization of the generalized joint likelihood ratios of hypotheses, which results in a 2-dimensional assignment problem. The K-best hypotheses can be acquired by using the Murty algorithm to solve the 2-dimensional assignment problem. According to the K-best hypotheses, the existence probabilities and probability density functions of objects are formed. Furthermore, an implementation of this filter for a linear Gaussian system is developed and is extended to nonlinear observations. Experimental result demonstrates that the proposed filter outperforms other available filters at various numbers of clutter and different detecting probabilities.

In this paper, we propose a novel fuzzy expectation maximization (FEM) based Takagi-Sugeno (T-S) fuzzy particle filtering (FEMTS-PF) algorithm for a passive sensor system. In order to incorporate target spatial-temporal information into particle filtering, we introduce a T-S fuzzy modeling algorithm, in which an improved FEM approach is proposed to adaptively identify the premise parameters, and the model probability is adjusted by the premise membership functions. In the proposed FEM, the fuzzy parameter is derived by the fuzzy C-regressive model clustering method based on entropy and spatial-temporal characteristics, which can avoid the subjective influence caused by the artificial setting of the initial value when compared to the traditional FEM. Furthermore, using the proposed T-S fuzzy model, the algorithm samples particles, which can effectively reduce the particle degradation phenomenon and the parallel filtering, can realize the real-time performance of the algorithm. Finally, the results of the proposed algorithm are evaluated and compared to several existing filtering algorithms through a series of Monte Carlo simulations. The simulation results demonstrate that the proposed algorithm is more precise, robust and that it even has a faster convergence rate than the interacting multiple model unscented Kalman filter (IMMUKF), interacting multiple model extended Kalman filter (IMMEKF) and interacting multiple model Rao-Blackwellized particle filter (IMMRBPF).

For the problem of inaccurate or difficult to obtain statistical characteristics of non-Gaussian noise, an interacting T-S fuzzy modeling algorithm is proposed to incorporate spatial-temporal information into particle filtering. In the proposed method, feature information is characterized by multiple semantic fuzzy sets, and the model transition probabilities are estimated by using the fuzzy set transition probabilities, which can be derived by the closeness degrees between the fuzzy sets. Furthermore, the correntropy can capture the statistical information to solve the non-Gaussian noise, thus a kernel fuzzy C-regression means (FCRM) based on correntropy and spatial-temporal information is proposed to adaptively identify the premise parameters of T-S fuzzy model, and a modified strong tracking method is used to estimate the consequence parameters. By using the proposed interacting T-S fuzzy model, an efficient importance density function is constructed for the particle filtering algorithm. Finally, the simulation results show that the tracking performance of the proposed algorithm is effective in processing non-Gaussian noise.

In the paper, a novel auxiliary truncated particle filtering for bearings-only maneuvering target tracking (ATPF-BOT) is proposed. In the proposed algorithm, a modified prior probability density function (PDF) is derived to solve the modeling uncertainty problem, which can simultaneously incorporate current measurement information and target characteristic information. Meanwhile, the proposal distribution is jointly designed by using the prior PDF and the modified prior PDF. Moreover, the proposal distribution is approximately calculated based on adaptive least square method so as to apply the ATPF algorithm for bearings-only maneuvering target tracking, and a practical algorithm is also developed. The experiment results show that the proposed algorithm is computationally efficient and successfully implemented in bearings-only target tracking systems.

Catalytic asymmetric formal synthesis of (−)-Triptophenolide and (+)-Triptolide have been achieved. Key reaction involves Palladium catalyzed asymmetric conjugate addition of aryl boronic acid to 3-methyl cyclohexe-1-none to form quaternary carbon. Claisen rearrangement and subsequent aldol reaction furnished trans-decaline key intermediate, which assured a formal total synthesis of (−)-Triptophenolide and (+)-Triptolide. Graphical Abstract Electronic supplementary material The online version of this article (doi:10.1007/s13659-016-0100-z) contains supplementary material, which is available to authorized users.

Multiple object tracking (MOT) is one of the most important research areas in visual surveillance. However, some practical challenges remain to be overcome for implementing this technology, such as occlusion, missed detection, false detection, and abrupt camera motion. In this paper, to the visual multi-object tracking, a novel fuzzy data association algorithm is proposed. In order to incorporate expert experience into the proposed algorithm, a fuzzy inference system based on knowledge is designed, and the fuzzy membership degrees are used to substitute the association probabilities between the objects and observations. The experiment results on several public data sets show that the proposed algorithm has advantages over other state-of-the-art tracking algorithms in terms of efficiency.

For the conventional truncated unscented Kalman filtering (TUKF) algorithm requires the measurement to be a bijective function, a novel improved truncated unscented Kalman filtering is proposed. In the proposed algorithm, we linearize the bijective measurements function based on the statistical linear regression (SLR) in order to obtain the only inverse function of the measurement function. It is a modified algorithm which extends the range of practical application of the filtering problems. Finally, the experiments show that the performance of the proposed algorithm is better than the unscented Kalman filter (UKF) and the quadrature Kalman filter (QKF). This approach can efficiently deal with this problem that measurement functions are not bijective.

Bayesian filter is an efficient approach for multi-target tracking in the presence of clutter. Recently, considerable attention has been focused on probability hypothesis density (PHD) filter, which is an intensity approximation of the multi-target Bayesian filter. However, PHD filter is inapplicable to cases in which target detection probability is low. The use of this filter may result in a delay in data processing because it handles received measurements periodically, once every sampling period. To track multiple targets in the case of low detection probability and to handle received measurements in real time, we propose a sequential measurement-driven Bayesian filter. The proposed filter jointly propagates the marginal distributions and existence probabilities of each target in the filter recursion. We also present an implementation of the proposed filter for linear Gaussian models. Simulation results demonstrate that the proposed filter can more accurately track multiple targets than the Gaussian mixture PHD filter or cardinalized PHD filter.

Tracking the target that maneuvers at a variable turn rate is a challenging problem. The traditional solution for this problem is the use of the switching multiple models technique, which includes several dynamic models with different turn rates for matching the motion mode of the target at each point in time. However, the actual motion mode of a target at any time may be different from all of the dynamic models, because these models are usually limited. To address this problem, we establish a formula for estimating the turn rate of a maneuvering target. By applying the estimation method of the turn rate to the multi-target Bayes (MB) filter, we develop a MB filter with an adaptive estimation of the turn rate, in order to track multiple maneuvering targets. Simulation results indicate that the MB filter with an adaptive estimation of the turn rate, is better than the existing filter at tracking the target that maneuvers at a variable turn rate.

Multi-target tracking is a key problem in the field of multi-sensor data fusion. A novel algorithm of multip-target tracking based on multiple FCMs data association is proposed for the multi-sensor multi-target (MSMT) tracking system. The algorithm can make full use of the information embedded in the measurements of sensors, make the minimization of the variance of the measurement fusion value through a linear weighting, and with a great reduction of the tracking errors caused by the association errors. Then the flow diagram is presented. In a scenario having five sensors, and five targets, the simulation results show that the proposed algorithm has the advantages over the existing ones of simplicity and efficiency.