In the presence of outliers or non-Gaussian noise in linear estimator design, lightweight Kalman filters (KFs) suffer from severe vulnerability, whereas robust Gaussian mixture filters (GMFs) incur much higher computational costs. To reconcile the robustness of the estimation with resource constraints, this letter investigates a distributed heterogeneous fusion architecture integrating GMFs with KFs. For this multimodal KF-GMF fusion case, we prove the robustness superiority of the arithmetic average (AA) fusion in comparison to the geometric average (GA) fusion. Furthermore, to resolve the mode conflict caused by anomalous outliers in the KF nodes, a graph-centrality-based anomaly isolation mechanism is proposed. By mapping the statistical consensus of fused Gaussian components into a weighted topological graph, this mechanism utilizes a node strength criterion to identify and eliminate disturbance-induced, topologically isolated modes/components with theoretical guarantees. Simulations demonstrate that the proposed KF-GMF AA fusion approach significantly outperforms the GA fusion in terms of tracking accuracy and convergence.

This paper addresses the intractable track matching problem involved in multi-sensor multi-target tracking using the labeled multi-Bernoulli filters. Unlike the unlabeled density defined in the common state space, the labeled multi-target density is defined in the joint state and label space, where the label contains time-series/history information of the underlying track. To measure the similarity between labeled densities (individual tracks) that is required for inter-sensor track matching and fusion, one has to account for the divergences in both state and label spaces. The challenge, however, arises from the lack of a proper metric to measure the label difference. It requires considering the entire trajectory of the track, encompassing the whole-life information from the birth of the track to the present. In this paper, we provide a solution of comparing and matching labels based on the whole-life time-series state distributions of the labels/tracks, by extending the common divergences like the Cauchy-Schwarz and Kullback-Leibler from distributions at a single time-instant to those over time-series. Representative scenarios are considered for illustration.

We address the multisensor multitarget tracking problem based on a hierarchical sensor network. In this setup, there is a fusion center, several cluster heads, and many sensors. Each sensor runs a Gaussian mixture probability hypothesis density (PHD) filter. The sensors send their locally calculated Gaussian components to the local cluster head in the presence of false data injection (FDI) and denial-of-service (DoS) attackers. We propose a hybrid PHD averaging fusion framework that consists of two parts: one uses the arithmetic average (AA) fusion to compensate for information shortage due to DoS and the other uses the geometric average (GA) fusion to suppress false information due to FDI. By integrating the respective zero forcing and avoiding behaviors of the two average fusion approaches, our proposed hybrid fusion scheme is proven resilient to both FDI and DoS attacks. Experimental results illustrate that our proposed algorithm can provide reliable tracking performance against FDI and DoS attacks.

In pattern classification, we may have a few labeled data points in the target domain, but a number of labeled samples are available in another related domain (called the source domain). Transfer learning can solve such classification problems via the knowledge transfer from source to target domains. The source and target domains can be represented by heterogeneous features. There may exist uncertainty in domain transformation, and such uncertainty is not good for classification. The effective management of uncertainty is important for improving classification accuracy. So, a new belief-based bidirectional transfer classification (BDTC) method is proposed. In BDTC, the intraclass transformation matrix is estimated at first for mapping the patterns from source to target domains, and this matrix can be learned using the labeled patterns of the same class represented by heterogeneous domains (features). The labeled patterns in the source domain are transferred to the target domain by the corresponding transformation matrix. Then, we learn a classifier using all the labeled patterns in the target domain to classify the objects. In order to take full advantage of the complementary knowledge of different domains, we transfer the query patterns from target to source domains using the K-NN technique and do the classification task in the source domain. Thus, two pieces of classification results can be obtained for each query pattern in the source and target domains, but the classification results may have different reliabilities/weights. A weighted combination rule is developed to combine the two classification results based on the belief functions theory, which is an expert at dealing with uncertain information. We can efficiently reduce the uncertainty of transfer classification via the combination strategy. Experiments on some domain adaptation benchmarks show that our method can effectively improve classification accuracy compared with other related methods.

In this study, we provide an overview of recent advances in multisensor multitarget tracking based on the random finite set (RFS) approach. The fusion that plays a fundamental role in multisensor filtering is classified into data-level multitarget measurement fusion and estimate-level multitarget density fusion, which share and fuse local measurements and posterior densities between sensors, respectively. Important properties of each fusion rule including the optimality and sub-optimality are presented. In particular, two robust multitarget density-averaging approaches, arithmetic- and geometric-average fusion, are addressed in detail for various RFSs. Relevant research topics and remaining challenges are highlighted.

This letter addresses the constrained target tracking problem based on the approach of the trajectory function of time (T-FoT). Both state equality and inequality constraints such as the trajectory geometry and width are considered, respectively. The penalty function is used in the T-FoT framework to account for the constraint. Specifically, the logarithmic barrier function is used to solve the challenging inequality constraint. Different from existing works which are mostly based on constrained Bayesian filters, our approaches make full use of constraints with little approximation. Three representative scenarios have been considered in the simulation for demonstrating the performance of our proposed approaches in comparison with existing constrained approaches based on Bayes filters.

We present a distributed probability hypothesis density (PHD) filter for multitarget tracking in decentralized sensor networks with severely constrained communication. The proposed “cardinality consensus” (CC) scheme uses communication only to estimate the number of targets (or, the cardinality of the target set) in a distributed way. The CC scheme allows for different implementations-e.g., using Gaussian mixtures or particles-of the local PHD filters. Although the CC scheme requires only a small amount of communication and of fusion computation, our simulation results demonstrate large performance gains compared with noncooperative local PHD filters.

We present a distributed Bernoulli filter for tracking a target that may be present or absent in the cluttered surveillance area in unknown time intervals by using a decentralized sensor network. As a key feature of the Bernoulli filter, a parameter referring to the target existence probability is online updated jointly with the target state probability density function. We propose to fuse them in parallel, both in an arithmetic average fusion manner via the standard consensus or flooding scheme. Alternatively, one may communicate and fuse merely target existence probabilities, leading to a communication-inexpensive protocol. We experimentally compare the proposed approaches, based on the Gaussian mixture implementation of the Bernoulli filter, with the cutting-edge geometric average fusion approach based on a Doppler shift sensor network. Advantages are observed in computing efficiency and in dealing with local missed detection.

This paper presents a joint trajectory smoothing and tracking framework for a specific class of targets with smooth motion. We model the target trajectory by a continuous function of time (FoT), which leads to a curve fitting approach that finds a trajectory FoT fitting the sensor data in a sliding time-window. A simulation study is conducted to demonstrate the effectiveness of our approach in tracking a maneuvering target, in comparison with the conventional filters and smoothers. Note to Practitioners-Estimation, such as automatically tracking and predicting the movement of an aircraft, a train, or a bus, plays a key role in our daily life. In this paper, we provide a new approach for the online estimation of the target trajectory function by means of fitting the time-series observation, which accommodates the lack of quantifiable knowledge about the target motion and of the statistical property of the sensor observation noise. The resulting trajectory function can be used to infer either the past or the present state of the target. Engineering-friendly strategies are provided for computationally efficient implementation. The proposed approach is particularly appealing to a broad range of real-world targets that move in smooth courses, such as passenger aircraft and ships.

We propose a straightforward but efficient networking approach to distributed multi-target tracking, which is free of ingenious target model design. We confront two challenges: One is from the lack of statistical knowledge about the target appearance/disappearance and movement, and about the sensors, e.g., the rates of clutter and misdetection; The other is from the severely limited computing and communication capability of the low-powered sensors, which may prevent them from running a full-fledged tracker/filter. To overcome these challenges, a flooding-then-clustering (FTC) approach is proposed which comprises two components: a distributed flooding scheme for iteratively sharing the measurements between sensors and a clustering-for-filtering approach for target detection and position estimation from the local aggregated measurements. We compare the FTC approach with cutting edge distributed probability hypothesis density (PHD) filters that are modeled with appropriate statistical knowledge about the target motion and the sensors. A series of simulation studies using either linear or nonlinear sensors, have been presented to verify the effectiveness of the FTC approach.

Environment monitoring remains a major challenge for mobile robots, especially in densely cluttered or highly populated dynamic environments, where uncertainties originated from environment and sensor significantly challenge the robot's perception. This paper proposes an effective occupancy filtering method called the dual probability hypothesis density (DPHD) filter, which models uncertain phenomena, such as births, deaths, occlusions, false alarms, and miss detections, by using random finite sets. The key insight of our method lies in the connection of the idea of dynamic occupancy with the concepts of the phase space density in gas kinetic and the PHD in multiple target tracking. By modeling the environment as a mixture of static and dynamic parts, the DPHD filter separates the dynamic part from the static one with a unified filtering process, but has a higher computational efficiency than existing Bayesian Occupancy Filters (BOFs). Moreover, an adaptive newborn function and a detection model considering occlusions are proposed to improve the filtering efficiency further. Finally, a hybrid particle implementation of the DPHD filter is proposed, which uses a box particle filter with constant discrete states and an ordinary particle filter with a time-varying number of particles in a continuous state space to process the static part and the dynamic part, respectively. This filter has a linear complexity with respect to the number of grid cells occupied by dynamic obstacles. Real-world experiments on data collected by a lidar at a busy roundabout demonstrate that our approach can handle monitoring of a highly dynamic environment in real time.

Under the common state space model for tracking a maneuvering target, the tracker needs to adapt its state transition model timely to match the target maneuver, which is usually carried out by finding the best one from a bank of candidate Markov models or employing all of them simultaneously but assigning different probabilities. Both methods suffer from time delay for confirming the target maneuver. To avoid these problems, we model the target motion by a continuous time trajectory function and the tracking problem is formulated as an optimization problem with the goal of finding the trajectory function that best fits the observation over a sliding time window. The trajectory function can be used for smoothing, filtering and even prediction. The approach is particularly applicable to a class of target motion patterns such as passenger aircraft, where little prior statistical information is available on the target dynamics or even the sensor observation except the linguistic information that “the target moves in a smooth trajectory” (as being called smoothly maneuvering target). Simulation is provided to demonstrate the supremacy of our approach with comparison to a number of classical Markov-Bayes approaches, based on Hartikainen et al.'s example.

Some concerns are raised on the prevailing generalized covariance intersection (GCI) based Gaussian mixture probability hypothesis density (GM-PHD) fusion for distributed multiple target tracking under cluttered environments, which is both communicative and computation expensive, and generates a large amount of Gaussian components (GCs) of little physical significance. The problems become more serious when targets are closely distributed and/or when clutter is heavy. To avoid these problems and to save communication and computation, we advocate to only share the sufficiently strong-weighted GCs between neighboring sensors. The shared significant GCs are simply merged based on their spatial proximity, which resembles a type of multisensor signal superposition and will enhance the signal-noise-ratio (SNR) since strong GCs are more likely to be a “target signal” than a weak one, thereby facilitating less likely false alarms and a more accurate estimation. In parallel to the conservative GC sharing and merging, a standard averaging consensus is also sought on the cardinality distribution (a.k.a. the probability distribution of the target number) among sensors. Simulations have been provided to demonstrate the superiority and reliability of our approach with comparison to the benchmark GCI approach.

Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity.

A preliminary framework for inferring continuous-time target trajectory (namely “track”) is given for a class of target tracking problems in which the target is subject to a rather smooth evolving process in time series, such as tracking passenger aircrafts or ships that have scheduled routes. As the core idea, the distant estimates given over time by a recursive estimator are `fitted' by using a function of continuous-time, which can be then used to infer the state for any time instants in the effective fitting period, either the past (like conventional smoothing, but curried out online) or the future (including long-term prediction). This regression analysis methodology, referred to as fitting for smoothing (F4S), also facilitates combating misdetection and outliers from which most existing tracking systems suffer. Simulations are provided to illustrate how it works and benefits in either cluttered or non-cluttered environments, with either a single target or multiple targets.

4:1! Google’s artificial intelligence (AI) program, AlphaGo, has won Go Master Lee Sedol in a best-of-five competition held in Korean March 9−15, 2016. Seen by many as a landmark moment for AI, the outcome did not come as a surprise, considering the excellent combination of 1920 CPUs with sophisticated AI algorithms, including neural networks and Monte Carlo tree search (Gibney, 2016; Silver et al ., 2016). Indeed, research on distributed computing and artificial intelligence (DCAI) has matured during the last decade and many effective applications are now deployed, performing an increasingly important role in modern computer science, including the two most hyped technologies: Internet of Things and Big Data. Indeed, it is fair to say that the application of artificial intelligence in distributed environments is becoming an essential element of high added value and economic potential.

Resampling is a critical procedure that is of both theoretical and practical significance for efficient implementation of the particle filter. To gain an insight of the resampling process and the filter, this paper contributes in three further respects as a sequel to the tutorial (Li et al., 2015). First, identical distribution (ID) is established as a general principle for the resampling design, which requires the distribution of particles before and after resampling to be statistically identical. Three consistent metrics including the (symmetrical) Kullback-Leibler divergence, Kolmogorov-Smirnov statistic, and the sampling variance are introduced for assessment of the ID attribute of resampling, and a corresponding, qualitative ID analysis of representative resampling methods is given. Second, a novel resampling scheme that obtains the optimal ID attribute in the sense of minimum sampling variance is proposed. Third, more than a dozen typical resampling methods are compared via simulations in terms of sample size variation, sampling variance, computing speed, and estimation accuracy. These form a more comprehensive understanding of the algorithm, providing solid guidelines for either selection of existing resampling methods or new implementations.