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In stochastic estimation problems, we aim to estimate an unknown state of interest given a set of measurements received from noisy sensory devices, such as radar, light detection and ranging, etc. A common model of the measurements’ random error is white Gaussian noise. This noise model is usually used to derive an estimator of the unknown state; accordingly, the state is described as a random variable with a Gaussian density. In some applications, the unknown state is known to take only positive values, e.g., estimating size or dimension. In such a case, the classical approaches based on Gaussian densities might fail, i.e., produce a negative value. In this article, a recursive Bayesian filter is proposed based on modeling the unknown state as Wishart distributed random matrix. This model ensures that the probability densities of the random variables are restricted to positive real values, even though the measurement’s noise is still modeled as white Gaussian noise. The feasibility of the proposed Bayesian–Wishart filter is demonstrated within the framework of extended target tracking. A target contour measurement model of a symmetric star-convex shape is presented and integrated in the proposed filter to track the target’s extent. [ABSTRACT FROM AUTHOR]

Extended objects generate a variable number of multiple measurements. In contrast with point targets, extended objects are characterized with their size or volume, and orientation. Multiple object tracking is a notoriously challenging problem due to complexities caused by data association. This paper develops a box particle filter (box PF) method for multiple extended object tracking, and for the first time, it is shown how interval-based approaches can deal efficiently with data association problems and reduce the computational complexity of the data association. The box PF relies on the concept of a box particle. A box particle represents a random sample and occupies a controllable rectangular region of nonzero volume in the object state space. A theoretical proof of the generalized likelihood of the box PF for multiple extended objects is given based on a binomial expansion. Next, the performance of the box PF is evaluated using a challenging experiment with the appearance and disappearance of objects within the area of interest, with real laser rangefinder data. The box PF is compared with a state-of-the-art particle filter with point particles. Accurate and robust estimates are obtained with the box PF, both for the kinematic states and extent parameters, with significant reductions in computational complexity. The box PF reduction of computational time is atleast 32% compared with the particle filter working with point particles for the experiment presented. Another advantage of the box PF is its robustness to initialization uncertainty. [ABSTRACT FROM AUTHOR]

The discrimination of closely spaced targets is a major challenge in the ground target-tracking domain based on measurements of airborne ground moving target indication radar. Being a standard output of modern radar systems, the measured signal strength of a radar detection can be used to estimate the characteristic mean radar cross section (RCS) of a ground target, which is then used as additional target attribute information to improve the tracking performance in situations with closely spaced targets. For this method to work, the fluctuations of the target RCS are assumed to follow the analytically tractable Swerling-I and Swerling-III cases. In this work, the RCS estimation scheme originally developed for air targets [1, 2] is generalized to ground-moving objects and then implemented into the Gaussian mixture cardinalized probability hypothesis density filter. The performance of the resulting algorithm is analyzed based on single and multiple-target simulation scenarios. In the latter case, a modified version of the optimal subpattern assignment metric that also accounts for labeling errors is used. [ABSTRACT FROM AUTHOR]

Detection of cars has a high variety of civil and military applications, e.g., transportation control, traffic monitoring, and surveillance. It forms an important aspect in the deployment of autonomous unmanned aerial systems in rescue or surveillance missions. In this paper, we present a two-stage algorithm for detecting automobiles in aerial digital images. In the first stage, a feature-based detection is performed, based on local histogram of oriented gradients and support vector machine classification. Next, a generative statistical model is used to generate a ranking for each patch. The ranking can be used as a measure of confidence or a threshold to eliminate those patches that are least likely to be an automobile. We analyze the results obtained from three different types of data sets. In various experiments, we present the performance improvement of this approach compared to a discriminative-only approach; the false alarm rate is reduced by a factor of 7 with only a 10% drop in the recall rate. [ABSTRACT FROM AUTHOR]

The increasing trend toward multisensor systems is driving an interest for distributed tracking algorithms. In such systems, data transmissions with imperfect communication links often lead to varying time delays. The challenge of online processing of delayed data is generally known as the out-of-sequence (OoS) problem. An exact solution to this problem is given by the accumulated state density (ASD) filter. However, the Rauch-Tung-Striebel (RTS) retrodiction1 is inherently integrated to the ASD approach, so a certain number of states must be updated at each filtering step. In this paper, a generalized form of the ASD filter is presented. In particular, the exact update formula for states that refer to time instants that are older and newer than a given measurement is calculated. As a consequence, OoS data can be processed without applying retrodiction. A novel smoothing scheme is presented that uses the exact cross-covariances of a measurement and a past state without recursion. A numerical evaluation shows that this smoothing scheme is about 25% faster than the RTS equations yet is still exact. [ABSTRACT FROM AUTHOR]

This paper develops a novel approach for multitarget tracking, called box-particle probability hypothesis density filter (box-PHD filter). The approach is able to track multiple targets and estimates the unknown number of targets. Furthermore, it is capable of dealing with three sources of uncertainty: stochastic, set-theoretic, and data association uncertainty. The box-PHD filter reduces the number of particles significantly, which improves the runtime considerably. The small number of box-particles makes this approach attractive for distributed inference, especially when particles have to be shared over networks. A box-particle is a random sample that occupies a small and controllable rectangular region of non-zero volume. Manipulation of boxes utilizes methods from the field of interval analysis. The theoretical derivation of the box-PHD filter is presented followed by a comparative analysis with a standard sequential Monte Carlo (SMC) version of the PHD filter. To measure the performance objectively three measures are used: inclusion, volume, and the optimum subpattern assignment (OSPA) metric. Our studies suggest that the box-PHD filter reaches similar accuracy results, like an SMC-PHD filter but with considerably less computational costs. Furthermore, we can show that in the presence of strongly biased measurement the box-PHD filter even outperforms the classical SMC-PHD filter. [ABSTRACT FROM AUTHOR]

One of the main challenges in the domain of ground target tracking based on measurements from airborne ground moving target indication (GMTI) radar is the masking of targets due to the Doppler blind zone of the sensor. This blind zone arises from the clutter cancellation by space-time adaptive processing (STAP) to separate moving target returns from the general clutter background. Low-Doppler targets can easily be masked by such a blind zone, leading to sequences of missed detections that strongly deteriorate the performance of a standard tracking filter. This work investigates the Doppler blind zone in the case of bistatic transmitter and receiver configurations and its impact on the tracking of ground targets. The knowledge on the Doppler blind zone is incorporated into a Bayesian unscented Kalman filter multiple hypothesis tracker (UKF-MHT) tracking filter that is also capable of using road-map information. Based on different simulation scenarios, it is demonstrated that in contrast to a monostatic configuration with sideways-looking radar, the blind zone width determined by the minimum detectable velocity is not constant in general. The obtained track results reveal the benefit of exploiting this additional knowledge, especially in combination complementary with road-map information if available. [ABSTRACT FROM PUBLISHER]

This article presents advances in determining the maximum estimation accuracy, as well as estimating the state for a piecewise maneuvering target with unknown maneuver change times, using passively obtained azimuth (bearings only), azimuth rate, and range measurements. We investigate two types of piecewise target motion and calculate the maximum estimation accuracy represented by the Cramer-Rao bound (CRB). Moreover, an estimation approach for estimating the target state, including the unknown maneuver change times, is developed on the basis of a maximum likelihood estimator. For two typical scenarios considering each motion model, we present and compare the results of the accuracy study, as well as the results for state estimation. Here, Monte Carlo simulations show that the estimator is able to attain the CRB. [ABSTRACT FROM PUBLISHER]

Target tracking with adaptive phased-array radars in the presence of standoff jamming presents both challenges and opportunities to the track filter designer. A measurement likelihood function is derived for this situation which accounts for the effect of both positive and negative contact information. This likelihood function is approximated as a weighted sum of Gaussian terms consisting of both positive and negative weights, accounting for the positive and negative contact information. Additionally, recent theoretical results have been reported which have derived an accurate measurement error covariance in the vicinity of the jammer when adaptive beamforming is used by the radar to null the effects of the jammer. We compare the impact of using a likelihood function that accounts for negative contact information and the corrected measurement error covariance by comparing five Kalman filter-based trackers in five different scenarios. We show that only those track filters which use both the negative contact information and the corrected measurement error covariance are effective in maintaining track on a maneuvering target as it passes through the jamming region. This approach can also be generalized to any target tracking problem where the sensor response is anisotropic. [ABSTRACT FROM AUTHOR]

Tracking ground targets with airborne GMTI (ground moving target indicator) sensor measurements proves to be a challenging task due to high target density, high clutter, and low visibility. The exploitation of nonstandard background information such as road maps and terrain information is therefore highly desirable for the enhancement of track quality and track continuity. The present paper presents a Bayesian approach to incorporate such information consistently. It is particularly suited to deal with winding roads and networks of roads. The target dynamics is modeled in quasi one-dimensional road coordinates and mapped onto ground coordinates using linear road segments taking road map errors into account. The case of several intersecting roads with different characteristics, such as mean curvature, slope, or visibility, is treated within an interacting multiple model (IMM) scheme. Targets can be masked both by the clutter notch of the sensor and by terrain obstacles. Both effects are modeled using a sensor-target state dependent detection probability. The iterative filter equations are formulated within a framework of Gaussian sum approximations on the one hand and a particle filter approach on the other hand. Simulation results for single targets taken from a realistic ground scenario show strongly reduced target location errors compared with the case of neglecting road-map information. By modeling the clutter notch of the GMTI sensor, early detection of stopping targets is demonstrated. [ABSTRACT FROM AUTHOR]

Presents a study that investigated Bayesian retrodiction for interacting multiple-model (IMM) to multiple hypothesis tracking (MHT) methods concerning air surveillance. Importance of IMM-MHT filtering in solving target-tracking problems; Application of statistical models in Bayesian filtering and retrodiction; Discussion on the IMM-MHT simulation results.

This correspondence shows that the expression for the marginal density of the kinematic state in [1], which is valid only if the kinematic state is fully observable by the sensor, can be generalized. Our second comment concerns the direct integration of a scaling factor for the extent estimate. Thirdly, we show an equivalent update step based on sequential processing of single measurements (instead of the indirect parameters "mean measurement" and "measurement spread" in [1]). [ABSTRACT FROM PUBLISHER]

In target tracking applications, the full information on the kinematic target states accumulated over a certain time window up to the present time is contained in the joint probability density function of these state vectors, given the time series of all sensor data. This joint density may also be called an accumulated state density (ASD) and provides a unified treatment of filtering and retrodiction insofar as by marginalizing the ASD, the standard filtering and retrodiction densities are obtained. In addition, ASDs fully describe the posterior correlations between the states at different instants of time. The notion of ASDs and closed formulae for calculating them are discussed. The practical usefulness of considering ASDs is illustrated by applications, where out-of-sequence (OoS) measurements are to be processed within the framework of a centralized measurement fusion architecture, i.e., when the sensor data do not arrive in the temporal order, in which they were produced. The approach can be applied to Kalman, multiple hypothesis tracking (MHT), and interacting multiple model (IMM) filtering. [ABSTRACT FROM AUTHOR]