This paper presents a novel approach to path planning for multi-platform bearings-only tracking of a target in the presence of epistemic detection uncertainty. Instead of using the traditional probabilistic framework, we propose a solution with a coordinated intelligent sensor platform motion control strategy in the possibilistic framework, offering a viable and robust alternative for improved tracking performance. We use track fusion of possibilistic Bernoulli filter implemented with Gaussian-max models to integrate information gathered by multiple platforms. The reward function for intelligent platform motion control is constructed using the concept of possibilistic entropy. The tracking performance of the proposed solution is evaluated using selected metrics via simulations.

This paper investigates the benefit of using game theoretic sensor control for the tracking of a reactive intelligent target. Game theory is adopted as a robust strategy which facilitates the study of interactions between intelligent players, in contrast to the alternative control strategies which only consider non-reactive targets. A general multi-step ahead optimisation strategy is designed and studied in the context of a passive tracking operation. Numerical results demonstrate the advantages of employing game-theoretic control for optimal tracking of evasive targets.

The paper develops a valuation network for sequential assessment of threat under epistemic uncertainty based on theoretical foundations and semantics of imprecise probability theory. The valuations are expressed as credal sets defined by coherent probability intervals on singletons. The combination rule is the generalized Bayes rule introduced by Walley. The model of a single-target threat is based on the classical “capability-intent” paradigm in an air surveillance context. Numerical results illustrate the performance of developed credal valuation network (with imprecise probabilities) against the valuation network with precise probabilistic models.

Consider the problem of maritime surveillance using a high-resolution airborne radar for the detection and tracking of small surface targets. This is a challenging problem as the sea clutter is spiky with a non-Gaussian amplitude distribution and contains both temporally and spatially varying characteristics. As a possible solution, we have recently proposed a Bayesian track-before-detect algorithm, which assumes a compound K-distributed clutter model with Swerling 1 target fluctuations. This paper considers a suitable modification of this algorithm to work in the range-Doppler domain and evaluates its performance on real datasets collected by the Defence Science and Technology Group’s (DSTG) Ingara X-band radar.

The paper formulates the solution to area search for targets in the framework of possibility theory. The rationale is that the required measurement model parameters, such as the probability of detection and/or the probability of false alarm, are rarely known as precise values. Possibility theory was developed for quantitative modelling of and reasoning with epistemic uncertainty. It provides an elegant Bayesian like solution to target area search. A reward function is proposed as an uncertainty measure which takes into account the epistemic uncertainty. The robustness of the proposed search algorithm is demonstrated by numerical results.

An extended object in target tracking refers to the object which produces a time-varying number of noisy detections (measurements) from its scattering or feature points. The optimal sequential Bayesian state estimator for an appearing/disappearing extended object in the presence of false and missed detections is known as the Bernoulli Filter Ext (BF-X) [1]. Bayesian estimation methods rely on probabilistic models. When probabilistic models are known only partially or imprecisely, quantitative modeling of uncertainty can be carried out using possibility functions. This paper formulates the analog of the BF-X in the framework of possibility theory, where uncertainty is represented using possibility functions, rather than probability distributions. Possibility functions have the capacity to model with integrity the partial or imprecise probabilistic specifications and thus the proposed possibilistic BF-X is characterised by an enhanced robustness in the absence of precise measurement or dynamic models.

Realistic reasoning applications typically involve many interrelated variables and require the interpretation of data that is both heterogeneous in nature and affected by various types of uncertainty. Accordingly, in this paper we investigate the performance of valuation based algebra networks for reasoning in uncertain multivariate systems. Specifically, we consider networks built from two different approaches to modelling uncertainty: possibility theory and Dempster-Shafer evidence theory. To compare these differing networks, we propose a new possibilistic counterpart to the uncertain implication rule that exists in evidential networks. Using the Captain's decision problem, we analyse the performance of these networks when estimating the number of days a ship will be delayed based on a mixture of uncertain knowledge. We demonstrate that the evidential network is more cautious to changes in uncertainty whereas the possibilistic network is more sensitive. This characteristic could allow the possibilistic network to be used to perform sensitivity analysis on a system.

Despite imprecision and possible ambiguity expressed by spatially referring natural language statements, they are potentially useful “measurements” (also known as soft data) for target localisation and tracking. The likelihood functions of such measurements typically include the parameters that model the inherent uncertainty in soft data. Adopting a binary model for spatially referring statements involving the word “near”, the paper derives the theoretical posterior Cramér-Rao bound for the estimation (learning) of the parameter which features in the likelihood function. A numerical analysis of the bound is presented with an example demonstrating estimation/learning in practice.

Sonobuoy fields, comprising a network of sonar transmitters and receivers, are used to find and track underwater targets. For a given environment and sonobuoy field layout, the performance of such a field depends on the scheduling, that is, deciding which source should transmit, and which waveform should be transmitted at any given time. In this paper, we explore the choice of cost function used in myopic scheduling and its effect on tracking performance. Specifically, we consider 5 different cost functions derived from the predicted error covariance matrix of the track. Importantly, our cost functions combine both positional and velocity covariance information to allow the scheduler to choose the optimum source-waveform action. Using realistic multistatic sonobuoy simulations, we demonstrate that each cost function results in a different choice of source-waveform actions, which in turn affects the performance of the scheduler. In particular, we show there is a trade-off between position and velocity error performance such that no one cost function is superior in both.

Sonobuoy fields, comprising a network of transmitters and receivers, are commonly deployed to find and track underwater targets. For a given environment and sonobuoy field layout, the performance of such a field depends on the scheduling, that is, deciding which source should transmit, and which from a library of available waveforms should be transmitted at any given time. In this paper, we propose a novel scheduling framework based on multi-objective optimization. Specifically, we pose the two tasks of the sonobuoy field-tracking and searching-as separate, competing, objective functions. Using this framework, we propose a characterization of scheduling based on Pareto optimality. This characterization describes the trade-off between the search-track objectives and is demonstrated on realistic multistatic sonobuoy simulations.

Particle filters using Gmapping proposal distribution has demonstrated their effectiveness in target tracking and robot self-localization. Due to the number of particles required in this approach, the computational demand is an issue associated with the Gmapping proposal distribution. The traditional approach is often ad hoc by setting a threshold for acceptance/rejection sampling to reduce the number of particles. However, the number of particles required in this approach is fixed and needs to be selected in advance which can be subjective and inefficient in representing a posterior distribution of various complexity. In parallel, the KLD-MCL algorithm has the capability to adaptively change the sample size of particles with an arbitrarily chosen proposal distribution. This paper combines the Gmapping proposal distribution with the KLD-MCL algorithm, resulting in an efficient particle filter which systematically adapts the number of particles. Simulation results demonstrate that the proposed approach has higher self-localization accuracy and requires a lower number of particles than the standard KLD-MCL algorithm.

Doppler radars are low cost and light weight sensors that have a potential to find wide applications in building a large team of mobile vehicle platforms. Because of the nonlinearity associated with the measurement from Doppler radars, it is both interesting and challenging to extract meaningful information from the low cost sensors. Building upon the authors' previous work on self localization with a feature-based map with known landmark associations using Doppler radars and an Extended Kalman Filter (EKF), this paper investigates the effects of positioning and the number of landmarks in a feature-based map on the accuracy of the position estimation of a robot. The computations of Cramer-Rao Lower Bound (CRLB) at the terminating sample show that the CRLB has a drastic reduction when the number of landmarks is increased from 1 to 2 while the root mean square errors (RMSE) of EKF indicate a gradual error reduction for the first 4 landmarks. The results presented in this paper will provide an essential guideline on the experiment design for feature-based robot self-localization.

This paper describes the implementation of a miniature open-source and cost-effective SLAM-robot, utilizing a novel occupancy-grid SLAM algorithm based on the concept of random-finite-sets (RFS). This robotic platform is remotely controlled to move and scan unknown environments using a differential drive system algorithm, sending instantaneous position feedback to the remote operator. The mobile robot utilizes a LIDAR-Lite 2 laser range finder to map the environment while simultaneously estimating its position and orientation within the map. Even though there are many mobile robots that implement this behavior, the main advantage in this proposed robotic platform is modeling of LIDAR measurements at each scan as a RFS. This model provides robustness against the random count of received returns, due to false and missed detections, allowing the use of an inexpensive LIDAR sensor and commercial off the shelf hardware.

Bearing-only and ground moving target indicator (GMTI) filtering are important practical nonlinear filtering problems that have been widely studied. The bearing-only filtering problem is regarded as a challenging nonlinear filtering problem. The degree of nonlinearity (DoN) of these problems were previously studied using differential geometry based parameter-effects and intrinsic curvatures. In this paper we analyze these two problems using a recently proposed measure of nonlinearity (MoN) for state estimation. We compute the conditional MoN (unnormalized and normalized) using an unscented Kalman filter (UKF) and a particle filter (PF). Numerical results from Monte Carlo simulations show that the normalized MoN values for these two problems are quite small, ~ 10-4and the normalized MoN values for the GMTI filtering are slightly higher than those for the bearing-only filtering. For each problem, we also compute the root mean square (RMS) position and velocity errors and posterior Cramer-Rao lower bound (PCRLB) to asses the state estimation accuracy.

The problem is target motion analysis (TMA) in situations where the variance (standard deviation) of additive white Gaussian measurement noise is unknown and time-varying. In particular, the paper examines a somewhat surprising result from the theoretical analysis based on the Cramer-Rao bound, which suggests that the best-achievable (second-order) error in target state estimation is unaffected by the lack of knowledge of the measurement noise variance. In order to examine this result, the paper develops three recursive Bayesian filters for TMA, which jointly estimate the target state and the measurement variance. The basis of all filters is the Cubature Kalman filter for bearings-only tracking, combined with (i) the variational Bayesian approach, (ii) the Rao-Blackwellised particle filter, and (iii) the interactive multiple-model (IMM), to deal with the unknown time-varying measurement variance. The paper presents extensive numerical simulation results and comparisons, which confirm that the lack of knowledge of the measurement noise variance is by no means a handicap for TMA.

In this paper, we investigate cooperative passive sensor trajectory planning for tracking a target where the tracking error is sensor trajectory dependent. We consider the problem under a scenario of tracking a moving target using two unmanned bearings-only sensors. The basic idea is to maximise the target information acquired from the processing measurements of the two sensors by cooperatively scheduling their future trajectories at which sensor measurements will be taken. In the literature this problem is modeled by a partially observed Markov decision process and optimal action which maximises an expected reward function is sought. Three reward functions, namely, the Expected Reward, the Determinant, and Trace of the associated Fisher Information Matrix (FIM) for the underlying problem are analysed and discussed. These rewards may only be evaluated practically through various approximations. We show that the correlation between two sensor states is weakened significantly for the Expected Reward due to linearisation and thus the closed-form Expected Reward as well as the Trace of FIM are inappropriate for this sensor trajectory scheduling problem. Finally, we present simulation results which are based on the example of a non-cooperative target chasing via two cooperative bearing-only sensors.

Sonobuoy fields, consisting of many distributed emitter and receiver sonar sensors on buoys, are used to seek and track underwater targets in a defined search area. A sensor scheduling algorithm is required in order to optimise tracking performance by selecting which emitter sonobuoy should transmit in each time interval, and which waveform it should use. In this paper we describe a new long term sensor scheduling algorithm for sonobuoy fields, called the continuous probability states algorithm. This algorithm reduces the scheduling search space by keeping track of the probability that a target is undetected, rather than modelling all possible detection outcomes, which reduces the computation complexity of the algorithm. It is shown that this approach results in high quality tracking for multiple targets in a simulated sonobuoy field.

The paper is devoted to the implementation of the Sequential Monte Carlo Probability Hypothesis Density (SMC-PHD) filter. A measurement driven proposal for persistent target particles requires the predicted persistent target particles to be partitioned in a probabilistic manner using the received measurement set. Each partition is subsequently updated using a conveniently designed efficient proposal distribution (in this paper we apply the progressive correction). The performance of the described algorithm is demonstrated in the context of autonomous tracking of multiple moving targets using bearings-only measurements.

Rotational modulation collimation (RMC) is a technique commonly used for standoff imaging of radiological sources in the context of homeland security. The paper presents a novel method for gamma ray image reconstruction from modulation signals acquired by a RMC detector prototyped by DSTO. The image is represented in a parametric form as a weighted sum of Gaussian radial basis functions. The problem is thus formulated as a parameter estimation problem and solved in the Bayesian framework using a multi-stage Monte Carlo technique known as progressive correction. A comparison with EM and MAP image reconstruction algorithms is provided.

The paper formulates the problem of sequential Bayesian estimation of a compound state consisting of a multi-object dynamic state and a multi-sensor bias. The compound state is modelled by a doubly stochastic point process, where the multi-object bias is a parent, whereas the multi-object state is the offspring point process. The prediction and the update steps for the first-order moment of the posterior density of the doubly-stochastic point process can be expressed analytically. The implementation, however, in general has to be done numerically. The paper presents a particle filter implementation illustrated in the context of multi-target tracking using range-azimuth measuring sensors with unknown biases.

The problem is to establish the presence and subsequently to track a target using multi-static Doppler shift measurements. The assumption is that in the surveillance volume of interest a single transmitter of known frequency is active with multiple spatially distributed receivers collecting and reporting Doppler-shift frequencies. The measurements are affected by additive noise and also contaminated by false detections. The paper develops a Bernoulli particle filter for this application and analyzes its performance by simulations.

In many practical applications of statistical signal processing, the likelihood functions are only partially known. The measurement model in this case is affected by two sources of uncertainty: stochastic uncertainty and imprecision. Following the framework of random set theory , the paper presents the optimal Bayesian estimator for this problem. The resulting Bayes estimator in general has no analytic closed form solution, but can be approximated, for example, using the Monte Carlo method. A numerical example is included to illustrate the theory.

Accurately locating the geographical position of Internet hosts has many useful applications. Existing approaches for host geolocation use Internet latency measurements, IP-to-location mapping and also geographical and demographical hints. In this paper, we investigate the applicability of the Maximum Likelihood Estimation (MLE) technique for Internet host geolocation. Our approach is based on a probability model for latency measurements that we developed by analyzing a large set of data collected on the PlanetLab network test bed. This approach uses latency measurements from multiple hosts of known location to the host to be geolocated, to estimate the target location. Using both simulated and real data, we analyze the accuracy of our approach. Our results for geolocating Internet hosts in North America confirms the validity of using MLE with certainty as its accuracy is found to be better in comparison to existing techniques that are based on Internet latency.

The problem considered in this paper is parameter estimation of a multivariate Gaussian mixture distribution with a known number of components. The paper presents a new Bayesian method which sequentially processes the observed data points by forming candidate sequences of labels assigning data points to mixture components. Using conjugate priors, we derive analytically a recursive formula for the computation of the probability of each label sequence. The practical implementation of this algorithm keeps only a predefined number of the highest ranked label sequences with the ranking based on posterior probabilities. We show by numerical simulations that the proposed technique consistently outperforms both the k-means and the EM algorithm.

The problem is statistical prediction of the number of people that will be infected with a contagious illness in a closed population over time. The prediction is based on the Susceptible-Infectious-Recovered (SIR) model of epidemic dynamics with inhomogeneous population mixing. The paper presents a theoretical analysis of the predictive accuracy based on the Cramer-Rao lower bound (CRLB). The CRLB provides a tool that enables us to quantify the prediction accuracy of a scale of an epidemic as a function of the prior uncertainty of SIR model parameters, measurement accuracy of the number of infected people and the amount of data available for processing. A verification of the theoretical analysis is carried out by Monte Carlo simulations.

The paper develops an information fusion system that aims at supporting a commander's decision making by providing an assessment of threat, that is an estimate of the extent to which an enemy platform poses a threat based on evidence about its intent and capability. Threat is modelled in the framework of the valuation-based system (VBS), by a network of entities and relationships between them. The uncertainties in the relationships are represented by belief functions as defined in the theory of evidence. Hence the resulting network for reasoning is referred to as an evidential network. Local computations in the evidential network are carried out by inward propagation on the underlying joint binary tree. This allows the dynamic nature of the external evidence, which drives the evidential network, to be taken into account by recomputing only the affected paths in the joint binary tree.

This paper considers the recursive estimation of emitter location using time difference of arrival measurements formed by the correlation of signals received by two unmanned aerial vehicles. The time difference of arrival measurement defines an hyperbola of possible emitter locations. This hyperbola is used as a measurement in a nonlinear filter. The performance of two such filters, an extended Kalman filter (EKF) and an unscented Kalman filter (UKF), is analysed for a stationary and moving emitter and compared with the Cramer-Rao lower bound. The UKF performs generally better than the EKF, but both algorithms suffer from diverged tracks.

Given an area where an unknown number of unaccounted radioactive sources potentially exist, and using gamma- radiation count measurements collected at known locations within this area, the problem is to estimate the number of sources as well as their locations and intensities. Two approaches are investigated. The first is based on the maximum likelihood estimation and the generalised maximum likelihood rule for multiple hypothesis testing. The second approach estimates the parameters and the number of sources in the Bayesian framework via Monte Carlo integration. Numerical analysis and the performance comparison of both approaches against the Cramer-Rao bound are carried out.

The problem is joint detection and tracking of possibly several objects moving through a region of interest. A wireless sensor network (WSN), deployed in the region, collects the acoustic energy measurements and sends them to the fusion center for processing. The problem is cast in the sequential Bayesian estimation framework and solved using a particle filter. The number of objects is unknown and can vary over time. The paper presents the algorithm and demonstrates its performance by computer simulations. The particle filter error performance is compared to the theoretical Cramer-Rao bound (CRB) for multiple target tracking with the described WSN.

The paper presents an algorithm for detection and a subsequent information gain driven search for an unaccounted point source of relatively low-level gamma radiation. Source detection and parameter estimation are carried out jointly in the Bayesian framework using a particle filter. The observer control vector consists of the next sensor location and the exposure time. During the pre-detection search, the control vectors take predefined values. After detection, the optimal control vector is selected via a multiple-step ahead maximisation of the Fisher information gain.

Research in Wireless Sensor Networks (WSN) is widespread and pervasive in many disciplines because of the potential to embed tiny, inexpensive,

Mobility tracking based on data from wireless cellular networks is a key challenge that has been recently investigated both from a theoretical and practical point of view. This paper proposes Monte Carlo techniques for mobility tracking in wireless communication networks by means of received signal strength indications. These techniques allow for accurate estimation of mobile station's (MS) position and speed. The command process of the MS is represented by a first-order Markov model which can take values from a finite set of acceleration levels. The wide range of acceleration changes is covered by a set of preliminary determined acceleration values. A particle filter and a Rao-Blackwellised particle filter are proposed and their performance is evaluated both over synthetic and real data. A comparison with an extended Kalman filter (EKF) is performed with respect to accuracy and computational complexity. With a small number of particles the RBPF gives more accurate results than the PF and the EKF. A posterior Cramer Rao lower bound (PCRLB) is calculated and it is compared with the filters' root- mean-square error performance.

We consider here the case where our knowledge is partial and based on a betting density function which is n-dimensional Gaussian. The explicit formulation of the least committed basic belief density (bbd) of the multivariate Gaussian pdf is provided. Beliefs are then assigned to hyperspheres and the bbd follows a chi2distribution. An application to model based classification in the joint speed-acceleration feature space is presented

Smoothing algorithms for maneuvering target tracking with nonlinear target dynamic and measurement equations are described and investigated. Target motion is represented using a multiple model approach. Techniques based on the interacting multiple model filter (IMMF), hypothesis pruning and maximum a posteriori (MAP) estimation of the maneuvering mode are described. All three techniques are based on the use of the unscented transformation with an augmented state model. A procedure for selecting the sigma points which exploits the partial lineairty of the augmented state model is used. The performances of the algorithms are analysed using a scenario involving a target which undergoes coordinated turn maneuvers. In this scenario, for a sufficiently large number of smoothing lags, the MAP approach and the pruning algorithm have almost equal performance and significantly superior performance to the augmented state IMMF. The MAP approach has the benefit of a reduced computational expense

This paper describes the integration of a particle filter and a continuous version of the transferable belief model. The output from the particle filter is used as input to the transferable belief model. The transferable belief model's continuous nature allows for the prior knowledge over the classification space to be incorporated within the system. Classification of objects is demonstrated within the paper and compared to the more classical Bayesian classification routine. This is the first time that such an approach has been taken to jointly classify and track targets. We show that there is a great deal of flexibility built into the continuous transferable belief model and in our comparison with a Bayesian classifier, we show that our novel approach offers a more robust classification output that is less influenced by noise

The paper presents an analysis of the phased array radar allocation demands, when tracking highly maneuverable anti-ship missiles (ASM) using a collocated radar/IRST sensor combination. The motion of the ASM is modeled using the quantized acceleration levels. The principal aim of this analysis is to determine an upper bound on the average radar update time. This bound follows from a Cramer-Rao type error bound for the estimation of linear jump Markov dynamic systems. Given a dynamic motion model of an ASM, the IRST/radar sensor characteristics and a tolerable level of target state estimation error, we can theoretically predict the maximum average update time required for the phased-array radar. The presented analysis allows us to quantify the IRST benefits in ASM defence, without a need for extensive Monte Carlo simulations

A new centroid formula for range-free sensor node location estimation using the proximity anchor positions is proposed. A detailed statistical analysis of the estimator is presented in one-dimension, taking into account the boundary conditions. The estimator is optimal in the minimum-mean square error sense for the one-dimensional case and outperforms the averaging centroid formula for N>2, where N is the number of proximity anchors

A method for performing unscented Kalman filtering with a reduced number of sigma points is proposed. The procedure is applicable when either the process or measurement equations are partially linear in the sense that only a subset of the elements of the state vector undergo a nonlinear transformation. It is shown that for such models second-order accuracy in the moments required for the unscented Kalman filter recursion can be obtained using a number of sigma points determined by the number of nonlinearly transformed elements rather than the dimension of the state vector. A procedure for computing the sigma points is developed. An application of the proposed method to smoothed target state estimation from bearings measurements is presented

Recent works have shown that the particle filter using color as observation feature is a powerful technique for tracking deformable objects in image sequences with complex backgrounds. This paper presents a hybrid valued sequential state estimation algorithm, and its particle filter-based solution, that extends the standard color particle filter in two ways. Firstly, track initialization is embedded in the particle filter without relying on an external target detection algorithm. Secondly, the algorithm is able to track multiple objects sharing the same color description. We evaluate the performance of the proposed filter on various real-world video sequences with appearing and disappearing targets.

This paper develops a novel concept of higher-order moment and cumulant functions in the compress/stretch domain, and their corresponding higher-order spectra in the scale domain. Then higher-order Q time-scale distributions are introduced and their properties are investigated. The importance of the paper is to link the concept of scale signal representations with well established and important methods of higher-order spectral analysis.

The paper establishes the relationship between the two methods of higher order time-frequency analysis: the polynomial Wigner-Ville distribution (WVD) and the higher order WVD. Using the projection-slice theorem, it is shown that the polynomial WVD represents a unique projection of the higher-order WVD from the time-multifrequency space to the time-frequency subspace. The implication of this relationship is investigated from the aspect of the analysis of multicomponent signals.

Time-varying higher-order spectra (TV-HOS), have recently been proposed for (poly)spectral analysis of non-stationary signals. Two new results are presented here. First, the cumulant TV-HOS (in particular, cumulant Wigner-Ville trispectrum (WVT)), is shown to preserve the essential properties of cumulant higher-order spectra (e.g. eliminate Gaussian additive noise) and at the same time characterise time-variations of the signal's frequency content. Second, when dealing with composite FM signals, a special kind of "non-oscillating cross-terms" is shown to appear in the moment TV-HOS time-frequency subspace. We show that these cross-terms cannot be eliminated by smoothing the WVT, but rather by an appropriate projection from the full time-multi-frequency space to a time-frequency subspace.>