The tutorial is an overview of tracking and data fusion for surveillance systems with applications both to defense and civilian systems. It is divided into four parts: Part 1 - Filtering: Covers the topics related to state estimation for stochastic dynamic systems: optimal Bayesian estimator, Kalman filter, nonlinear filters (extended and unscented Kalman filter, Gaussian sum filter, particle filter); filters for maneuvering motion (Interactive multiple-model filter); Crame-Rao lower bounds for filtering. Part 2 - Data association: Due to the imperfections of a detector, the input to a tracking system may lack the target originated detections and often contains false detections (due to clutter). The data association component of a tracking system determines the origin of each input detection. The tutorial will cover techniques such as: gating, (global) nearest neighbor algorithm, (joint) probabilistic data association, multiple hypotheses tracking. In addition, the idea of using random sets for multi-target tracking will be introduced with a review of the PHD filter. Part 3 - Distributed multi-sensor tracking: Modern surveillance systems typically consist of multiple sensors connected by a communication network for a data exchange. While the network surveillance offers potentially more accurate and reliable performance, there are many practical issues that need to be resolved beforehand. The tutorial will provide answers to problems: how to choose the multi-sensor architecture, how to avoid a repeated use of the same information, how to perform distributed track association and track fusion, how to ensure proper multi-sensor alignment in time and space. Part 4 - Selected applications: The last part of the tutorial will cover several practical applications: ballistic missile tracking, GMTI radar tracking, tracking with hard constraints, angle-only tracking, tracking using TDoA measurements, track-before-detect, video tracking, tracking using an acoustic sensor network, etc.
We consider the problem of estimator performance prediction in stochastic systems with Markov switching dynamical models. Following Hernandez et al, a new best-fitting Gaussian performance measure (BFG-PM) for jump Markov systems is proposed. The new BFG-PM matches the moments of the state transition density of the Markov switching system and the approximate uni-modal system. The new BFG-PM has a state-dependent process noise covariance matrix, hence its recursive computation is carried out via a new formulation of the Cramer-Rao bound for nonlinear filtering with state dependent noise statistics. The paper presents two numerical examples where the existing BFG-PM and the new BFG-PM are compared against the error performance of a typical state estimator for jump Markov systems.
Large-scale sensor array management has applications in a number of target tracking problems. For example, in ground target tracking, hundreds or even thousands of unattended ground sensors (UGS) may be dropped over a large surveillance area. At any one time it may then only be possible to utilize a very small number of the available sensors at the fusion center because of bandwidth limitations. A similar situation may arise in tracking sea surface or underwater targets using a large number of sonobuoys. The general problem is then to select a subset of the available sensors in order to optimize tracking performance. The Posterior Cramer-Rao Lower Bound (PCRLB), which quantifies the obtainable accuracy of target state estimation, is used as the basis for network management. In a practical scenario with even hundreds of sensors, the number of possible sensor combinations would make it impossible to enumerate all possibilities in real-time. Efficient local (or greedy) search techniques must then be used to make the computational load manageable. In this paper we introduce an efficient search strategy for selecting a subset of the sensor array for use during each sensor change interval in multi-target tracking. Simulation results illustrating the performance of the sensor array manager are also presented.
We consider the problem of tracking ground-based vehicles with moving target indicator (MTI) sensors. MTI sensors can only detect a target if the magnitude of the range-rate exceeds the minimum detectable velocity, and as a result targets typically exhibit evasive move-stop-move (MSM) behavior in order to avoid detection. Further complexity is added by the fact that the environment is cluttered, resulting in both missed detections and spurious false measurements. A key problem is then to distinguish between a missed detection of a moving target and a lack of a detection due to the target stopping (or moving at low velocity). In this paper, we provide a novel framework for calculating performance measures (which are not necessarily bounds) for this problem. Our approach unifies state-of-the-art posterior Cramér-Rao lower bound (PCRLB) approaches for dealing with manoeuvring targets (namely, the best-fitting Gaussian approach) and cluttered environments (the measurement sequence conditioning approach). Our approach is also able to exploit the correlation between the number of measurements at each sampling time and the target motion model. Furthermore, we are able to show that established PCRLB methodologies are special cases of this unifying approach. We therefore provide a general technique for calculating performance bounds/measures for target tracking that can be applied to a broad range of problems. We also introduce a multiple hypothesis tracker (MHT) implementation for this problem. In simulations, the MHT is shown to accurately track the target, and provided that the probability of detection is close to unity, the new performance measure is an extremely accurate predictor of the localization performance of the MHT. If the probability of detection is lower, and except when employing a short scanback, the MHT performance is significantly better than the measure. In such cases the true limit of performance is the measure calculated by assuming the correct motion model, and data association hypotheses are known. The MHT filter is also shown to maintain track of the target in a high percentage of simulations, even with a scanback of just a few time steps. Therefore if track maintenance is the most important requirement, the employment of long scanbacks is not essential. We conclude that our PCRLB-like measure and MHT implementation provide effective approaches for performance prediction and target tracking, respectively, in the challenging MTI domain.
Recent interest in the development of wireless sensor networks for surveillance introduces new problems that will need to be addressed when developing target tracking algorithms for use in such networks. Specifically the power and stealth requirements when combined with the wireless communications architecture will lead to potentially significant delays in the measurement collection process. The recent development of out-of-sequence tracking algorithms and posterior Cramer-Rao lower bounds for tracking with measurement origin uncertainty makes it possible to investigate how robust these new tracking algorithms are to a wide range of communications delays and a range of false alarm densities. This paper brings together these various components and presents the performance analysis for a simulated wireless network. Results show that position estimate accuracy close to the lower bound should be possible for communications intervals up to 4 s for challenging false alarm densities.
In this paper, we present notable recent developments in the management of multi-sensor systems, established by the Pattern and Information Processing (PIP) group at QinetiQ Ltd. We describe a generic methodology for the management of multi-sensor systems in target tracking and present advances in associated implementation within four key application domains. These are: sonobuoy deployment in anti-submarine warfare, fast-jet flight-path optimisation, ground moving target indicator (GMTI) tracking of road-based vehicles, and electronic support measures (ESM) search and track.
Recently, a general framework for sensor resource deployment (Hernandez, et. al. 2004) has been shown to allow efficient and effective utilization of a multisensor system. The basis of this technique is to use the posterior Cramer-Rao lower bound (PCRLB) to quantify and control the optimal achievable accuracy of target state estimation. In the original formulation (Hernandez, et. al. 2004) it was assumed that the sensor locations were known without error. In the current paper, the authors extend this framework by addressing the issues of imperfect sensor placement and uncertain sensor movement (e.g., sensor drift). The crucial consideration is then how these two forms of uncertainty are factored into the sensor management strategy. If unaccounted for, these uncertainties will render the output of the resource manager inaccurate and overoptimistic. The authors adjust the PCRLB to account for sensor location uncertainty, and we also allow for measurement origin uncertainty due to missed detections and false alarms. The work is motivated by the problem of tracking a submarine by adaptively deploying sonobuoys from a helicopter. Simulation results are presented to show the advantages of accounting for sensor location uncertainty within this focal domain of antisubmarine warfare. The authors note that the generic nature of the technique allows it to be utilized within other problem domains, including tracking ground-based targets using unattended ground sensors (UGSs) or unmanned aerial vehicles (UAVs)
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
The Multiple Airborne Sensor Targeting and Evaluation Rig (MASTER) is a high fidelity simulation environment in which data fusion, tracking and sensor management algorithms developed within QinetiQ Ltd. can be demonstrated and evaluated. In this paper we report an observer trajectory planning tool that adds considerable functionality to MASTER. This planning tool can coordinate multiple sensor platforms in tracking highly manoeuvring targets. It does this by applying instantaneous thrusts to each platform, the magnitude of which is chosen to gain maximum observability of the target. We use an efficient search technique to determine the thrust that should be applied to each platform at each time step, and the planning horizon can either be one-step (greedy) or two-step. The measure of performance used in evaluating each potential sensor manoeuvre (thrust) is the posterior Cramer-Rao lower bound (PCRLB), which gives the best possible (lowest mean square error) tracking performance. We exploit a recent novel approach to approximating the PCRLB for manoeuvring target tracking (the "best-fitting Gaussian" (BFG) approach: Hernandez et al., 2005). A closed-form expression gives the BFG approximation at each sampling time. Hence, the PCRLB can be approximated with a very low computational overhead. As a result, the planning tool can be implemented as an aid to decision-making in real-time, even in this time-critical airborne domain. The functionality of MASTER enables one to access the performance of the planning tool in a range of sensor-target scenarios, enabling one to determine the minimal sensor requirement in order to satisfy mission requirements.
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