The Poisson multi-Bernoulli mixture (PMBM) and the multi-Bernoulli mixture (MBM) are two multi-target distributions for which closed-form filtering recursions exist. The PMBM has a Poisson birth process, whereas the MBM has a multi-Bernoulli birth process. This paper considers a recently developed formulation of the multi-target tracking problem using a random finite set of trajectories, through which the track continuity is explicitly established. A multi-scan trajectory PMBM filter and a multi-scan trajectory MBM filter, with the ability to correct past data association decisions to improve current decisions, are presented. In addition, a multi-scan trajectory $\text{MBM}_{01}$ filter, in which the existence probabilities of all Bernoulli components are either 0 or 1, is presented. This paper proposes an efficient implementation that performs track-oriented $N$-scan pruning to limit computational complexity, and uses dual decomposition to solve the involved multi-frame assignment problem. The performance of the presented multi-target trackers, applied with an efficient fixed-lag smoothing method, are evaluated in a simulation study.
With a large number of sensors and control units in networked systems, distributed support vector machines (DSVMs) play a fundamental role in scalable and efficient multi-sensor classification and prediction tasks. However, DSVMs are vulnerable to adversaries who can modify and generate data to deceive the system to misclassification and misprediction. This work aims to design defense strategies for DSVM learner against a potential adversary. We establish a game-theoretic framework to capture the conflicting interests between the DSVM learner and the attacker. The Nash equilibrium of the game allows predicting the outcome of learning algorithms in adversarial environments, and enhancing the resilience of the machine learning through dynamic distributed learning algorithms. We show that the DSVM learner is less vulnerable when he uses a balanced network with fewer nodes and higher degree. We also show that adding more training samples is an efficient defense strategy against an attacker. We present secure and resilient DSVM algorithms with verification method and rejection method, and show their resiliency against adversary with numerical experiments.
With the growing congestion in the airspace, Air Traffic Management(ATM) requires advances in massive data processing, sophisticated avionics techniques, coordination with weather updates, and assessment of multiple types of uncertainty. The complex situation overwhelms pilots and ATM controllers. To provide dependable artificial decision-making support for ATM and Unmanned Aerial System Traffic Management (UTM) systems, ontologies are an attractive knowledge technology. This paper proposes an Avionics Analytics Ontology (AAO) to bring together different types of uncertainties including semantic from operators, sensing from navigation, and situation from weather modeling updates. The approach is aligned with the Uncertainty Representation and Reasoning Evaluation Framework (URREF), that develops an uncertainty ontology. The degree of uncertainty to improve effectiveness in ATM/UTM decision-making processes quantifies information veracity; in addition to accuracy, timeliness, and confidence. Application examples are presented that involves two ATM/UTM operation scenarios where Unmanned Aerial Vehicles (UAVs) fly nearby commercial aircraft and/or airports which requires situation awareness safety response. As compared to a baseline approach without Automatic Dependent Surveillance-Broadcast (ADS-B), results from recorded ADS-B data demonstrate a over 0.75 veracity improvement) from Newark Liberty International Airport.
X-band marine radar systems are flexible and low-cost tools for monitoring multiple targets in a surveillance area. They can provide high resolution measurements both in space and time. Such features offer the opportunity to get accurate information not only about the target kinematics, as other conventional sensors, but also about the target size. In this paper we exploit the random matrix framework to track extended targets. Proper measurement models to deal with the radar’s measurement noise and its conversion into Cartesian coordinates are presented here. Benefits of the proposed extended target tracking using converted measurements can be mainly related to the problem of the targets’ size estimation, while advantages on estimation of the targets’ kinematic features can be considered negligible. The validity of the proposed approach has been demonstrated by using both simulated and real data. Gains up to 70% for the targets’ width estimation accuracy and around 65% for the length are observed on real data. The integration of the proposed model into the gamma Gaussian inverse Wishart probability hypothesis density tracker is also provided and tested on real data.
Directional data emerge in many scientific disciplines due to the nature of the observed phenomena or the working principles of a sensor. The problem of tracking with direction- only sensors is challenging since the motion of the target typically resides either in 3D or 2D Euclidean space, while the corresponding measurements reside either on the unit sphere or the unit circle, respectively. Furthermore, in multitarget tracking there is the need to deal with the problem of pairing sensors measurements with targets in the presence of clutter (the data association problem). In this paper we propose to approach multitarget tracking in clutter with direction-only data by setting it on the unit hypersphere, thus tracking the objects with a Bayesian estimator based on the von Mises-Fisher distribution and probabilistic data association. To achieve this goal we derive the probabilistic data association (PDA) filter and the joint probabilistic data association (JPDA) filter for the Bayesian von Mises-Fisher estimation on the unit hypersphere. The final PDA and JPDA filter equations are derived with respect to the Kullback-Leibler divergence by preserving the first moment of the hyperspherical distribution. Although the fundamental equations are given for the hyperspherical case, we focus on the filters on the unit 1- sphere (circle in R^2) and the unit 2-sphere (surface of the unit ball in R^3). The proposed approach is validated through synthetic data experiments on 100 Monte Carlo runs simulating multitarget tracking with noisy directional measurements and clutter.
Nonlinear Kalman filters are algorithms that approximately solve the Bayesian filtering problem by employing the measurement update of the linear Kalman filter (KF). Numerous variants have been dev ...
In this paper, we prove that specific widely used models in Content-based Image Retrieval for information fusion are interchangeable. In addition, we show that even advanced, non-standard fusion strategies can be represented in dual forms. These models are often classified as representing early or late fusion strategies. We also prove that the standard query modification method with specific similarity measurements can be represented in a late fusion form.
Integration of space based sensors into a Ballistic Missile Defense System (BMDS) allows for detection and tracking of threats over a larger area than ground based sensors [1]. This paper examines the effect of sensor bias error on the tracking quality of a Space Tracking and Surveillance System (STSS) for the highly non-linear problem of tracking a ballistic missile. The STSS constellation consists of two or more satellites (on known trajectories) for tracking ballistic targets. Each satellite is equipped with an IR sensor that provides azimuth and elevation to the target. The tracking problem is made more difficult due to a constant or slowly varying bias error present in each sensor's line of sight measurements. It is important to correct for these bias errors so that the multiple sensor measurements and/or tracks can be referenced as accurately as possible to a common tracking coordinate system. The measurements provided by these sensors are assumed time-coincident (synchronous) and perfectly associated. The line of sight (LOS) measurements from the sensors can be fused into measurements which are the Cartesian target position, i.e., linear in the target state. We evaluate the Cramer-Rao Lower Bound (CRLB) on the covariance of the bias estimates, which serves as a quantification of the available information about the biases. Statistical tests on the results of simulations show that this method is statistically efficient, even for small sample sizes (as few as two sensors and six points on the (unknown) trajectory of a single target of opportunity). We also show that the RMS position error is significantly improved with bias estimation compared with the target position estimation using the original biased measurements.
Passive Bistatic Radar (PBR), also known as Passive Coherent Location (PCL), uses illuminators of opportunity. Passive radar using signals in a single frequency network modulated according to the Digital Audio/Video Broadcasting (DAB/DVB) standards using orthogonal frequency division multiplexing (OFDM) has recently been of increasing interest. There has been considerable research to develop tracking systems addressing its inherent difficulties [3]—[7], [10]—[13]; the poor quality–or absence–of angular information, and the lack of label of the transmitter on top of the usual target/measurement association concerns. First, there are algorithms using the Multi-Hypothesis Tracker (MHT) [12], [13] addressing the complexity problem from association ambiguities between measurement, targets and illuminators by initially forming two dimensional (measurement-target) hypotheses in the two-dimensional range/Doppler domain. Tracking is thence performed directly on target parameters by the MHT without considering the association between measurements and illuminators: the range/Doppler MHT extracts measurements and removes false alarms. Then, de-ghosting is performed by evaluating likelihood probabilities of possible data associations. When a Cartesian track is confirmed, the remaining tracks from other possible associations are declared false and tracking starts in the Cartesian domain. This MHT approach is good but but is not without issues. One is the appropriate motion model in range and Doppler space: probably the target dynamics in the Cartesian domain are known, the trajectories are not easily described in a space of target parameters, because the trajectories are related to illuminator/receiver/target geometry and there is association ambiguity among measurements, illuminators, and targets. And that is another concern: the illuminator association is never explicitly addressed. Now, track maintenance algorithms that operate directly in Cartesian coordinates have been explored [4], [5], one using modified Joint Probabilistic Data Association (JPDA) and another a particle filter. For the former, in order to address the large number of threelist hypotheses, a “super-target” idea was proposed; and the particle filters work under the PMHT measurement model that each measurement’s assignments are independent of others’. These methods have also been examined downstream from an initiation approach (the PMHTI method, suggested in [6]) that initiates tracks in Cartesian coordinates. In fact the PMHT seems to be an effective and natural way to accommodate the data association with the extra list (transmitters). So in this paper, we present it: it is really very simple. This tracker, combined with the initiation algorithm (the modified PMHTI method in [6]), shows excellent performance in comparison with the JPDA filter and particle filter.
We propose an algorithm to combine both depth and position measurements when estimating a continuous surface. Position measurements originate from a fixed point on the surface, whereas depth measurements are determined by the intersection of the surface with a line originating from the depth sensor. Through fusion of both types of measurements, it is possible to benefit from the advantages of different sensors. The surface is obtained through interpolation of control points with splines, which allows a compact representation of the surface. In order to simplify the problem of intersecting the surface with lines originating from the depth sensor, we propose the use of polar or spherical coordinates in surface parameterization. The presented algorithm can be applied in both 2D and 3D settings and is independent of the particular choice of sensors. Our method can recursively include new information as it is obtained by using nonlinear filtering and it considers uncertainties associated with the measurements.
Data association is a crucial task in many surveillance systems and is a prerequisite for data fusion. In general data association solves the correspondence problem in either a “hard” or “soft” manner [2]. A typical step in tracking problems is the measurementto-track association where it decides which measurement to update which track. There are several state-ofthe-art methods in solving the type of association, for example, Joint Probabilistic Data Association (JPDA) and Multiple Hypothesis Tracking (MHT) [2]. In this paper, we consider another type of association called measurement-to-measurement association in a multisensor mutlitarget scenario, where each sensor generates a set of line of sight (LOS) or direction of arrival (DOA), i.e., incomplete position measurements of the targets and the goal is to decide which of the measurements in each sensor correspond to the same target. The measurements are grouped together by an association algorithm and are used to generate a composite (full position) measurement of a common target. In tracking applications, the composite measurements can be used in the subsequent measurement-to-track association to update existing tracks (this is fusion configuration III [2]). This measurement-to-measurement association is considered as “static” where the measurements are assumed to be synchronized, i.e., observed at the same time. The fusion of asynchronous measurements is discussed in [13]. Measurement-to-measurement association becomes especially challenging if the sensors are passive and measure LOS angles only for the targets. Measurements from multiple sensors have to be associated to determine the full positions of the targets. The brute force approach, i.e., enumerating all possible combinations and choosing the most likely one, is computationally prohibitive even for a moderate size problem. For example, the total number of combinations for a scenario of 20 targets and 2 sensors (assuming no missed detections or false alarms) is 20! = 2:4£ 1018. A practical approach is to formulate the multisensor data association as a multiple dimensional assignment (MDA) problem [2] and then employ (constrained) optimization techniques to obtain the optimal assignment. When the number of sensors is greater than or equal to three (i.e., S ̧ 3), the MDA is known to be NP hard. While a number of suboptimal techniques have been proposed, the Lagrangian relaxation based approaches [14], [16] have been shown to be superior to others (e.g., branch and bound, row-column heuristic) for their excellent balance between the accuracy and the efficiency. The relaxation technique in [9] is termed as the S-D (assignment) algorithm. In [18] an extended approach of determining the top m assignments (as opposed to only the best one) has been obtained by using Murty’s ranking algorithm [10]. Prior to the optimization step in the S-D algorithm, the first step is to calculate the candidate association
This paper shows that functional derivatives of the probability generating functional (PGFL) of a finite point process can be calculated using ordinary derivatives. The result is new, and it is potentially useful to the class of Bayesian multitarget tracking problems that is based on finite point process models for targets and measurements. In this class, the distribution of the Bayes posterior multitarget process is a ratio of functional derivatives of the joint measurement-target PGFL. In some problems evaluating the functional derivatives is only a tedious task, but in other problems the number of terms in the derivatives is prohibitively large and limits practical applications of the method. The proof is straightforward–we reduce the PGFL to an ordinary function that is conceptually straightforward to differentiate. This function is called a secular function to emphasize that it is an “ordinary” function and not a functional. Existing symbolic software packages can be used to differentiate the secular function, a fact that is potentially of practical importance since software for functional differentiation of the PGFL does not seem to be available. The methods of this paper use the established theory of PGFLs and their functional derivatives. The proposed methods are compatible with particle, or sequential Monte Carlo (SMC), filter implementations. The basic strategy is to embed symbolic differentiation software in the production code and evaluate the symbolic derivatives of the secular functions at the points of the particle filter. One of the purposes of this paper is to show that this is a theoretically feasible strategy. Its practical utility is outside the scope of the paper. Two tracking applications where functional differentiation causes serious difficulties are discussed. One is multisensor target tracking [9]. The other is extendedtarget tracking problems in which targets can produce more than one measurement [8, 11]. The secular functions for both problems are derived. Functional differentiation of the PGFL is the result of a double limit. A theoretical question naturally arises, “Can these limits be interchanged?” The answer is, “Yes, for the problems of interest here.” This result seems to be new. It gives a better understanding of PGFLs and their relationship to classical probability generating functions (PGFs). Section II speaks of the PGFL as an encoding of the multitarget tracking problem and functional differentiation of the PGFL as the decoding algorithm. Section III gives a simple example of the method we use to reduce PGFLs to secular functions. Section IV proves that for the class of PGFLs of interest in this paper, ordinary derivatives of secular functions are identical to functional derivatives of PGFLs. Section V gives several examples of secular functions, including those for multisensor and extended-target tracking problems. Section VI discusses finite differences and series expansion
Due to their low cost and ease of deployment, the use of passive acoustic sensors for target tracking has seen increasing popularity. Such systems might consist of individual microphones or hydrophones that selfassemble into arrays [24], or, perhaps, sensors consisting of clusters of microphones or hydrophones, each producing measurements consisting of arrival angles and features/attributes for use in data association [19].1 The clusters of microphones or hydrophones form individual sensors, which can also be referred to as “nodes” in the system. This paper focusses on the latter scenario, localizing sensors with measurements taken with respect to a common, unknown coordinate axis. Determining which detection on one sensor corresponds to the same target on another sensor (measurement association) might be accomplished, for example, by utilizing acoustic patterns for classification, as has previously been done to aid acoustic tracking [19]. Target tracking is not considered here. The scenarios considered focus on angular noise levels up to 2± (root-mean squared error), which is the accuracy of the sensors in [19], though acoustic sensors can often have significantly worse angular accuracies. When considering the construction of land-based sensor networks, it cannot be assumed that satellitebased localization systems, such as GPS (USA) or GLONASS (Russia), will be available, and such signals cannot penetrate far underwater. However, many nonsatellite-based location estimation algorithms, which have been primarily designed for use in underwater and wireless networks may be used. A number of methods applied to sonar channels are described in [4]. These approaches typically utilize the communication characteristics between sensors and are divided into two categories: range-based and range-free. Range-based methods utilize range (distance) measurements. Range-free schemes do not utilize range information. Both techniques might take advantage of moving anchor nodes that broadcast their position [6, 9, 13, 22]. Our focus is on algorithms for node localization based on the angle-only observations of the nodes, though we do consider the case where range measurements are also available. Estimates based on angle-only measurements are particularly useful when the sensors have a limited broadcast range. Underwater, this might be the case when the sensor network is built using data MULEs (Mobile Ubiquitous LAN2 Extensions) [21]. A data MULE is a mobile device that approaches the sensors to collect data. In such a network, traditional methods of sensor localization, which rely on communication channels between sensors, are not applicable.
Highly accurate small-arms gunfire detection systems on individual soldiers are vital requirement for added battlefield situational awareness and threat assessment. Today, several acoustic shooter localization systems are commercially available [2, 7, 29]; an overview of such systems can be found in [26]. A few examples of soldier-wearable shooter localization systems include the Shoulder-Worn Acoustic Targeting System (SWATS) by QinetiQ North America, Inc., Boomerang Warrior-X by BBN Technologies, and PinPoint by BioMimetic Systems. These Soldier-wearable Gunfire Detection Systems (SW-GDSs) can provide a good level of localization accuracy as long as the soldier is at an ideal location relative to the shooter and the bullet trajectory. However, due to the dissipative nature of acoustic signals, localization systems suffer severe performance degradation as the distance to the shooter and the bullet trajectory increases [22, 23, 28]. Moreover, when a relative solution, i.e., the shooter location relative to the sensor, is transformed into a georectified solution using a magnetometer and GPS, the solution often becomes unusable due to localization errors. Geo-rectified solutions are necessary when displaying hostile fire icons on a Command and Control Geographic Information System (C2 GIS) map display. SW-GDSs use acoustic phenomena analysis of small-arms fire to localize the source of incoming fire, usually with a bearing and range relative to the user [12]. Currently, the individual SW-GDSs operate separately and are not designed to exploit the sensor network layout of all the soldiers within a Small Combat Unit (SCU) to help increase accuracy. Researchers are exploring some novel solutions that utilize the team aspect of these SCUs by exploiting all SW-GDSs in a squad/platoon to increase detection rates and localization accuracy [9, 10, 32]. Apart from soldier-wearable systems, there exist several single-microphone as well as microphone array-based sensor network approaches to shooter localization [6, 15, 16, 19, 24]. Most of the existing sensor fusion schemes for shooter localization are centralized approaches where the individual sensor measurements, such as time of arrival or angle of arrival of the muzzle blast or the shockwave are combined to yield a single estimate of the shooter position [5, 16, 19, 20, 32]. Here we consider a hierarchical approach where the relative shooter position from the individual sensors are fused to obtain a more accurate geo-rectified shooter position. The proposed approach takes full advantage of the team aspect of a SCU to provide a fused solution that would be more accurate and suitable for a C2 GIS map display than the individual soldier’s solution. The objective here is to improve accuracy across an entire SCU so even soldiers in non-ideal settings (out of range, bad angle, etc.) can exploit the good solutions
Authors’ addresses: Joachim Biermann, Dept. for Sensor Data and Information Fusion, Fraunhofer FKIE, 53343 Wachtberg, Germany, E-mail: (joachim.biermann@fkie.fraunhofer.de); Pontus Hörling, Dept. for Information and Aeronautical Systems, Swedish Defence Research Agency (FOI), SE-164 90 Stockholm, Sweden, E-mail: (hoerling@foi.se); Lauro Snidaro, Dept. of Mathematics and Computer Science, University of Udine, Udine, Italy, E-mail: (lauro. snidaro@uniud.it).
Passive acoustic sensor arrays for tracking ground targets are becoming increasingly popular due to their low cost and ease of deployment. In this paper we present an algorithm for locating sensor arrays in two-dimensions in an acoustic network (or in any network where angle-only measurements are used) when external references, such as GPS or known-location targets, are unavailable. We consider sensor localization when angular measurements are taken from the sensor arrays to targets of opportunity when all sensors take measurements with respect to a common axis of unknown orientation and where the sensors can not “see” each other. The solutions provided consist of low-complexity (generally closed-form) methods of getting initial estimates with no prior information, followed by maximum likelihood (ML) optimization to refine the estimates. Simulation shows that the accuracy approaches the Cramér Rao Lower Bound (CRLB), something that similar algorithms from previous research have been unable to achieve.
