In this paper, a non-myopic beam scheduling policy is proposed for multi-target tracking (MTT) in a phased-array radar network, seeking to minimize the discounted sum of tracking error of targets and improve the long-term tracking performance. The Whittle index policy based on the restless multiarmed bandit (RMAB) model can decompose the state space of the underlying optimization problem into independent spaces with reduced sizes. We consider the tracking error covariance (TEC) matrix as the state of each target (arm), which evolves based on the Kalman filter. However, for a real-world MTT, the exact calculation of the Whittle index in multiple dimensions is challenging. The neural network is established to achieve the feature extraction of TEC states and learn the corresponding Whittle index. The deep reinforcement learning (DRL) method is exploited to train the neural network by leveraging the threshold property of the Whittle index policy and engaging in interactions with a single target tracking environment. We propose the DRL-based Whittle index policy, namely DRLWI, aiming to solve the beam allocation problem for MTT with multi-dimensional TEC states. This approach effectively mitigates the exponential computational complexity of classical dynamic programming approaches and the low convergence rate caused by large joint state and action spaces in the simple application of DRL algorithms. Numerical results demonstrate the performance of the proposed DRLWI policy surpasses that of DRL algorithms and myopic policies.

Deep learning has been widely used in the field of radar image classification because of its powerful feature extraction capabilities. In the land-sea clutter classification of sky-wave over-the-horizon radar (OTHR), deep learning methods perform poorly due to the radar receiver noise and the ionosphere. Addressing this challenge, a dual attention aided residual neural networks (DAAResNet) is proposed for OTHR land-sea classification. Leveraging prior knowledge that landsea clutter features predominantly cluster around the 0 Hz frequency, two attention mechanisms are introduced. Firstly, a channel attention module (CAM) is proposed, which directs the network’s focus towards critical channels. Secondly, a frequency attention module (FAM) is proposed, which directs attention towards pivotal frequencies. The classification performance of DAAResNet is validated on the original dataset and the scarce dataset. Experimental results show that DAAResNet outperforms state-of-the-art methods.

This paper presents recursive two-filter smoothing (TFS) in the criterion of maximizing the correntropy (MC) instead of minimizing the mean square error, to pursue robustness for outlier rejections caused by non-Gaussian noises and obtain high-precision state estimate, which is motivated by non-cooperative target backtracking. Here, non-cooperative target tracking often needs to consider non-Gaussian noises. The MC-based recursive TFS (abbreviated as MRTFS) is put forward, where both the forward and backward filters are performed independently and recursively in the criterion of MC. Meanwhile, an MC-based fusion rule is further designed to obtain the final smoothed estimate by fusing the forward filtered estimate and backward predicted estimate step by step, in order to improve estimation accuracy. A target backtracking example with non-Gaussian noises is simulated to show the advantage of estimation accuracy of the proposed MRTFS over Kalman filter/smoothers, MC-based Kalman filter/Rauch-Tung-Striebel smoother, in terms of different kernel bandwidths and levels of process noises.

In clustering process, fuzzy partition performs better than hard partition when the boundaries between clusters are vague. Whereas, traditional fuzzy clustering algorithms produce less interpretable results, limiting their application in security, privacy, and ethics fields. To that end, this paper proposes an interpretable fuzzy clustering algorithm—fuzzy decision tree-based clustering which combines the flexibility of fuzzy partition with the interpretability of the decision tree. We constructed an unsupervised multi-way fuzzy decision tree to achieve the interpretability of clustering, in which each cluster is determined by one or several paths from the root to leaf nodes. The proposed algorithm comprises three main modules: feature and cutting point-selection, node fuzzy splitting, and cluster merging. The first two modules are repeated to generate an initial unsupervised decision tree, and the final module is designed to combine similar leaf nodes to form the final compact clustering model. Our algorithm optimizes an internal clustering validation metric to automatically determine the number of clusters without their initial positions. The synthetic and benchmark datasets were used to test the performance of the proposed algorithm. Furthermore, we provided two examples demonstrating its interest in solving practical problems.

This paper proposes a new virtual ionospheric height model for over-the-horizon radar (OTHR) target tracking. Considering the spatial correlation of different ionosphere site, the virtual ionospheric heights are modeled by a Gaussian Markov random field (GMRF). The priors of the GMRF model can be learned from the historical measurements from ionosondes. Given the acquired measurements of the ionosphere subregions, the virtual ionospheric heights of the unmeasured subregions are inferred based on the GMRF model. Then we present the multipath probabilistic data association for uncertain coordinate registration (MPCR) with the new virtual ionospheric height model. Numerical simulation shows that the accuracy of OTHR target tracking is improved.

In this paper, a rule learning method based on interval-constrained clustering is proposed to efficiently design a compact belief rule-based classifier. The main idea of this method is to learn a compact belief rule base based on a set of prototypes generated from the original training set. First, an interval-constrained clustering algorithm is used to divide the training data for each class into several clusters, with which the number of data belonging to each cluster can be constrained within a given interval. Then, we define a belief rule based on the centroid of each cluster. Finally, a two-objective optimization procedure is designed to get a compact belief rule base with a better trade-off between accuracy and interpretability. Two experiments based on synthetic and benchmark data sets have been carried out to evaluate the performance of the proposed classifier.

It is a challenging problem for pattern classification with few labeled instances. Transfer learning provides an efficient solution to improve the classification accuracy using some training knowledge in the related domain (called source domain). Nevertheless, the single transformation in one direction may be uncertain in some cases, and this is harmful for classification. So we propose a new classification method based on the fusion of data transformations in different directions between source domain and target domain. At first, the mapping of target in the source domain is estimated by K-nearest neighbor technique using some one-to-one instance pairs, and the estimated mapping instance (pattern) can be classified in the source domain according to the available training data. Then, the credibility of classification result is evaluated. If the credibility achieves the expected threshold, the classification result is directly output. Otherwise, it indicates that the transformation may be not very reliable, and the labeled instances in source domain will be transferred to target domain for the classification of target. The two versions of classification results will be fused with different weights based on evidential reasoning, and the weighting factors are optimized using the available training instances. By doing this, we can efficiently reduce the uncertainty of transformation and improve the classification accuracy. Some real data sets from UCI have been employed to validate the effectiveness of the proposed by comparing with other related methods.

This paper considers the joint recursive estimation of the dynamic state and the time-varying process noise covariance for a linear state space model. The conjugate prior on the process noise covariance, the inverse Wishart distribution, provides a latent variable. A variational Bayesian inference framework is then adopted to iteratively estimate the posterior density functions of the dynamic state, process noise covariance and the introduced latent variable. The performance of the algorithm is demonstrated with simulated data in a target tracking application.

In this paper, a novel nonlinear filter method named linear Gaussian regression filter (LG RF) is proposed. The LG RF utilizes the Variational Bayes (VB) to indirectly approximate the posterior probability density function (PDF) for state estimation. The core of the LG RF is to use a linear Gaussian distribution with a set of compensating parameters (CPs) to characterize the likelihood probability (LP) for maximizing the lower bound. Through iteratively and alternatively achieving the state estimation and CPs identification, the estimation accuracy can be improved gradually. In addition, compared with point-based filters, there is no decomposition of the covariance matrix in the LG RF so that the inborn defect of numerical instability is avoided. The superior performance of the LGRF is demonstrated in the simulation of maneuvering target tracking.

This paper considers the state smoothing problem for Markovian jump linear systems with non-Gaussian noises which obey Gaussian mixture distributions. On the basis of decomposing the total probability at the point of two adjacent Markov jumping parameters at the current and the next epochs, the posterior probability density of the state for smoothing is derived recursively. Then, through transforming the quotient of two Gaussian mixtures into the corresponding multiplication under the possible two adjacent Markov modes, a recursive Gaussian mixture smoother is designed with the conditional posterior probability density under each hypothesis being approximated by the Gaussian mixture. A maneuvering target tracking example with non-Gaussian noises validates the proposed method.

This paper considers the parameter estimation problem of linear system by constructing the iterative and stochastic measurement schedule (ISMS) rule for efficiently implementing the maximum likelihood (ML). When the unknown parameter varies or even mutates with the time proceeding, in the existing measurement schedule rule, estimator can not keep both accuracy and speed of parameter estimation due to the fact that the rule is established before communication. That is, the convergency of the parameter estimation is not fast and accurate enough, especially for the mutational parameter. So we propose a novel ISMS rule to solve this problem. Our ISMS rule can smartly choose these important measurements which are close to the current sampling time and correspondingly drop those useless and unimportant measurements far away from the current time. The accuracy of estimator is improved obviously, because these chosen measurements are able to well reflect the parameter variation. Correspondingly, those dropped measurements further contribute to increase the computation complexity and decrease the speed of tracking the mutational parameter. Based on the constructed ISMS rule, we derive the analytical maximum likelihood parameter estimation (MLPE) and prove its unbiasedness. Moreover, a new concept of average windows length (AWL) is defined as the evaluation index of estimator, and its computation expression is derived. Finally, a numerical example is given to demonstrate the superiority of the new ISMS rule and MLPE in quickly and efficiently estimating the constant or time-varying parameter compared with the existing methods.

In the complex pattern classification problem, the reliability of classifier output for the patterns located at different regions of the data set may be different. In order to efficiently improve the classification accuracy, we propose a new method to correct the original classifier output using the local knowledge of the classifier performance in different regions. The training data set can be divided into some small clusters corresponding to different regions. The prior knowledge of the classifier performance on each cluster is characterized by a confusion matrix representing the conditional probability of the pattern belonging to one class but committed to another class by the classifier. The matrix associated with each cluster is learnt by minimizing an error criteria using training data, which is assigned different weights to achieve the highest possible accuracy. If the classification accuracy of the training data in one cluster can be improved according to the corrected classification results, the associated confusion matrix becomes valid. Otherwise, the confusion matrix is invalid and patterns in this cluster cannot be modified any more. For each object, if it lies in the cluster with valid confusion matrix, its classification result will be corrected by the matrix before making the class decision. The above correction process can be regarded as the fusion of local and global information. Several experiments are given to test the performance of the proposed method using real data sets, and it shows that the new method is able to efficiently improve the classification accuracy compared with other related methods.

This paper considers the state estimation of Markovian jump linear systems with random parameters and estimate feedback. The state estimate at the previous epoch is introduced into the dynamical model to depict some phenomena that the system evolvement may depend on the most recent estimate. Then, the linear minimum mean square error estimator is derived for the considered system. A filtering framework for state estimation and data association for multiple maneuvering targets tracking is presented via the considered system, by using the state estimate at previous epoch to model the false echo which is dropped into the (overlapped) validation regions and the random parameters to describe the uncertainty between targets and possible echoes. A simulation about tracking two closely maneuvering targets in clutter shows the effectiveness of the proposed method.

The theory of belief functions is an effective tool to deal with the multiple uncertain information. In recent years, many evidence combination rules have been proposed in this framework, such as the conjunctive rule, the cautious rule, the PCR (Proportional Conflict Redistribution) rules and so on. These rules can be adopted for different types of sources. However, most of these rules are not applicable when the number of sources is large. This is due to either the complexity or the existence of an absorbing element (such as the total conflict mass function for the conjunctive-based rules when applied on unreliable evidence). In this paper, based on the assumption that the majority of sources are reliable, a combination rule for a large number of sources, named LNS (stands for Large Number of Sources), is proposed on the basis of a simple idea: the more common ideas one source shares with others, the more reliable the source is. This rule is adaptable for aggregating a large number of sources among which some are unreliable. It will keep the spirit of the conjunctive rule to reinforce the belief on the focal elements with which the sources are in agreement. The mass on the empty set will be kept as an indicator of the conflict. Moreover, it can be used to elicit the major opinion among the experts. The experimental results on synthetic mass functions verify that the rule can be effectively used to combine a large number of mass functions and to elicit the major opinion.

Vacation rental websites such as Airbnb have become increasingly popular where rentals are typically short-term and travels or vacations related. Reasonable rental prices play a crucial role in improving user experiences and engagements in these websites. However, the unique properties of their rentals challenge traditional house rentals that are often long-term and study or work related. Therefore, in this paper we investigate the novel problem of price recommendation in vacation rental websites. We identify some important factors that affect the rental prices and propose a framework that consists of Multi-Scale Affinity Propagation (MSAP) to cluster houses, Nash Equilibrium filter to remove unreasonable price and Linear Regression model with Normal Noise (LRNN) to predict the reasonable prices. Experimental results demonstrate the effectiveness of the proposed framework. We conduct further experiments to understand the important factors in rental price recommendation.

The estimation of Markov jump systems (MJS) is widely used in target tracking, fault detection, signal processing and digital communications. However, the above researches all assume that state measurement and additional mode observation are synchronous which means both state measurement and mode observation at each sampling time arrive at the fusion centre at the same time. The problem of estimation of MJS that mode observation is one-step lagged to its corresponding state measurement is considered. Along state-augmentation approach and the derivation of image-enhanced interacting multiple model (IE-IMM), a new generic estimation algorithm is proposed. It is shown by simulation result that the proposed algorithm is effective.