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This paper develops three-dimensional (3D) Cartesian tracking algorithms for a high-resolution wide field of view (FOV) camera surveillance system. This system consists of a network linking multiple narrow FOV cameras side-by-side looking at adjacent areas. In such a multi-camera system, a target usually appears in the FOV of one camera first, and then shifts to an adjacent one. The tracking algorithms estimate target 3D positions and velocities dynamically using the angular information (azimuth and elevation) provided by multiple cameras. The target state (consisting of position and velocity) is not fully observable when it is detected by the first camera only. Once it moves into the FOV of the next camera, the state can then be fully estimated. The main challenge is how to transfer the state information from the first camera to the next one when the target moves across cameras. In this paper, we develop an approach, designated as Cartesian state estimation with full maximum likelihood information transfer (fMLIT), to cope with this challenge. Since the fMLIT consists of an implicit state relationship, the conventional Kalman-like filters (for explicit constraints) are not suitable. We then develop three Gauss-Helmert filters, and test them with simulation data. [ABSTRACT FROM AUTHOR]

In passive sensor target tracking, there are applications that require converting the angle-only measurements into Cartesian space. Multisensor methods can be used to convert the raw measurements into Cartesian measurements by finding the intersection of lines of sight. This method contains significant nonlinearity in its conversion; therefore, it is subject to corresponding errors such as a conversion bias and an improper covariance. The proposedmethod uses a secondorder Taylor series expansion to accurately account for the conversion nonlinearities. This results in an explicit (noniterative) expression of the Cartesian position based on two line-of-sight measurements in three dimensions. This paper investigates the severity of the conversion biases from nonlinearity and the efficiency of the unbiased conversion with regard to compensating for them. [ABSTRACT FROM AUTHOR]

This paper develops an Object Extraction (OE) algorithm from a remote sensor in the presence of multipath propagation between the sensor and the object. The OE is carried out by estimating the object's motion parameter by fusing the multipath measurements. The signals from the object are assumed to have a low signal-to-noise ratio i.e., the OE has to be done in the presence of numerous spurious detections. This paper also discusses a method to reduce the size of the motion parameter space by considering the object's motion in a non-inertial frame. The object is observed using a measurement model that produces range, azimuth, and range-rate using a multipath refraction model for the signal propagation through the medium. The OE accounts for the multipath environment as the model allows for multiple returns from a single object. Finally, the paper shows the effectiveness of the OE by evaluating the accuracy of the estimation with Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

The maximum-likelihood probabilistic multi-hypothesis tracker (ML-PMHT) is a tracking method whose flexibility and scalability derive from relinquishing the assumption that each target emits at most one "hit" per scan of the sensor. This is an ML method that essentially reduces to an optimization problem--recursively maximizing a likelihood function that is simple to evaluate given a batch of observations. Unlike maximum a posteriori or minimum mean squared error (MMSE) trackers, this likelihood maximization tracker requires neither prior knowledge about target motion nor measurement association, making it conceptually easy to work with. Here, this method is used to track targets in a three-dimensional "global" space with observations provided by multiple two-dimensional sensors placed throughout the global space. Since the observation model is non-linear, the likelihood maximization is done via hill climbing. For this purpose, we also address the issue of "hill finding." Due to the presence of clutter in the measurement model, the likelihood is a multi-modal function of the parameter space. That is, there are multiple hills in the likelihood function, and it is of great advantage to the tracker to initialize the hill climber close to the right hill--the one whose peak is the global maximum. In this work, we present a data-driven method of initializing the hill climber based on the received observations. [ABSTRACT FROM AUTHOR]

The sensor bias estimation problem is crucial in autonomous driving systems for perception and target tracking. This work considers the bias estimation for two collocated synchronized sensors with slowly varying additive biases. The differences between the two sensors' observations are used to eliminate the target state. Consequently, the bias estimation is independent of the target-state estimation. The biases' observability condition is met when the two sensors' biases are Ornstein--Uhlenbeck stochastic processes with different time constants. The bias models, including the time constants and measurement noises, can be identified based on a sample autocorrelation or using the maximum-likelihood estimation technique. A maximumlikelihood measurement fusion technique is introduced for the biascompensated observations. Simulation results, for several scenarios with various bias model parameters, prove the consistency of the estimator. It is shown that the uncertainties of biases are significantly reduced by the estimation algorithm presented. The sensitivity of the proposed algorithm is also tested with mismatched filters as well as the estimated bias models. Finally, the benefits of bias estimation in measurement fusion are evaluated. [ABSTRACT FROM AUTHOR]

A novel approach to the track-to-track fusion (T2TF) of state estimates from interacting multiple-model (IMM) estimators using inside information [mode-conditioned estimates (MCEs) and mode probabilities] is described in this paper. Fusion is performed on-demand, i.e., without conditioning on past track data. The local trackers run IMM estimators to track a maneuvering target with switching process noise and they transmitMCEs andmode probabilities to a fusion center. The fused state posterior probability density is a Gaussian mixture, where the parameters of the required likelihood functions can be computed recursively. Mode probabilities are fused by transforming them to logratios and using them as statistical information in the likelihood function of themode. This results in consistent data fusion based on known target and local tracker (IMM) parameters. Simulations show that this method outperforms the fusion of the local IMM estimator Gaussianapproximated outputs both in terms of error during target maneuvers and in terms of the consistency of the mean-squared error (MSE). It is a generalization of Gaussian T2TF with crosscovariance, and its performance is close to that of centralized measurement fusion (CMF)--by accounting for the error and log-ratio crosscovariances, the fused covariance consistency matches the ideal consistency of CMF without requiring memory of past fused tracks. The method is also shown to be more accurate, informative, consistent in MSE, and of lower computational and communication cost than Chernoff fusion, a recently published method for Gaussian mixture fusion. [ABSTRACT FROM AUTHOR]

The Information Matrix Fusion (IMF) algorithm for nonlinear, asynchronous (with arbitrary local tracker sampling times for full rate as well as reduced-rate communication) and heterogeneous systems is presented. The heterogeneous estimates from local trackers are in different state spaces with different dimensions and are related by a nonlinear and noninvertible transformation. The main application of these results is the fusion of tracks from radar and infrared/electrooptical sensors. Different from Track-to-Track Fusion, the IMF does not require the cross-covariance between the local estimation errors. The performance of the proposed algorithm is shown via simulation based on Monte Carlo runs and is compared with the optimal solution--fullrate centralized fusion for both full-rate fusion and reduced-rate fusion for heterogeneous and asynchronous sensors. [ABSTRACT FROM AUTHOR]

In target tracking applications, it is necessary to account for measurement biases present within the sensors. For passive sensors, these biases are commonly represented as unknown rotations of the sensor measurements and must be estimated. As targets may move in unpredictable ways, it is advantageous to decouple target state and sensor bias estimation to simplify the estimation problem. To do this, a bias pseudo-measurement method must be used in which the measurements are converted and differenced to eliminate the presence of the true target state. For passive angle-only sensors, it is important to appropriately convert lines of sight into Cartesian space. By using the closest point of approach method, it is possible to apply the bias pseudo-measurement method to these sensors. The Cramér--Rao lower bound can be obtained for this method, and, furthermore, it can be attained by using a maximum likelihood estimation method. [ABSTRACT FROM AUTHOR]

The article focuses on the track-to-track fusion has been studied extensively for both homogeneous and heterogeneous cases. It mentions that in a heterogeneous system, the state models used by local sensors are in different state spaces with different dimensions. It also mentions the cross-covariance of the estimation errors from two local tracks (LTs) is derived in a recursive form by taking into account the relationship between the local state model process noises.

The article focuses on a target tracking problem in a non-cooperative multistatic system, where several transmitters are moving and their positions are unknown. It mentions that passive detection and tracking is desirable in surveillance systems. It also mentions that additional information needs to be provided to estimate the transmitter positions.

In order to carry out data fusion, it is crucial to account for the imprecision of sensor measurements due to systematic errors. This requires estimation of the sensor measurement biases. In this paper, we consider a three-dimensional multisensor-multitarget maximum likelihood bias estimation approach for both additive and multiplicative biases in the measurements. Multiplicative biases can more accurately represent real biases in many sensors; however, they increase the complexity of the estimation problem. By converting biased measurements into pseudo-measurements of the biases, it is possible to estimate biases separately from target state estimation. The conversion of the spherical measurements to Cartesian measurements, which has to be done using the unbiased conversion, is the key that allows estimation of the sensor biases without having to estimate the states of the targets of opportunity. The measurements provided by these sensors are assumed time-coincident (synchronous) and perfectly associated. We evaluate the Cramér-Rao lower bound on the covariance of the bias estimates, which serves as a quantification of the available information about the biases. Through the use of the iterated least squares, it is proved that it is possible to achieve statistically efficient estimates. [ABSTRACT FROM AUTHOR]

The problem of localizing an unknown number of stationary transient emitters using passive sensors in the presence of missed detections and false alarms is investigated. Each measurement is based on one detection by a passive sensor and consists of a time of arrival and a bearing. It is assumed that measurements within a short time interval have to be associated before estimation. Both a Bernoulli measurement model and a Poisson measurement model are considered for each target. These two measurement models lead to two different proposed problem formulations: one is an S-dimensional (S-D) assignment problem and the other is a cardinality selection problem. The former can be solved by the Lagrangian relaxation algorithm reliably when the number of sensors is small. The sequential m-best 2-D (SEQ[m(2-D)]) assignment algorithm, which is resistant to the ghosting problem due to the estimation of the emitter signal's emission time, is developed to solve the problem when the number of sensors becomes large. Simulation results show that the SEQ[m(2-D)] assignment algorithm is efficient for real-time processing with reliable associations and estimates. In the cardinality selection formulation, a list of measurements is modeled as either realizations of a random variable with a uniform-Gaussian mixture (UGM) density or a Poisson point process (PPP).Because of an efficient way of incorporating false alarm rate, the UGM formulation is shown to be a useful alternative to the PPP formulation. Simulation studies show that both UGM and PPP formulations, which are based on the expectation-maximization algorithm, require the right initial estimates to yield reliable localization results. [ABSTRACT FROM AUTHOR]

In this paper we provide a new methodology using an exoatmospheric target of opportunity seen in a satellites borne sensor's field of view to estimate the sensor's biases simultaneously with the state of the target. Each satellite is equipped with an Infra Red (IR) sensor that provides the Line Of Sight (LOS) measurements azimuth and elevation to the target. The measurements provided by these sensors are assumed to be noisy but perfectly associated, i.e., it is known perfectly that they belong to the same target. The evaluation of the Cramér-Rao Lower Bound (CRLB) on the covariance of the bias estimates and the statistical tests on the results of simulations show that both the target trajectory and the biases are observable and this method is statistically efficient. [ABSTRACT FROM AUTHOR]

Acoustic propagation delay has not been investigated for a continuous wave multistatic sonar tracking system except for the recent study conducted by Jauffret et al. [6], which estimates the trajectory of a constant velocity target. The results showed that the estimate bias caused by the propagation delay is not negligible, especially for a bistatic system. This paper develops an interacting multiple model unscented Gauss-Helmert filter with numerical Jacobian (IMM-UGHF-NJ) to track a maneuvering target with propagation delay using a bistatic sonar system. The IMM-UGHF-NJ can overcome the two tracking challenges introduced by the delay, namely, implicit state transition model and lack of analytical expression of the Doppler shifted frequency in the measurement model. Simulation tests have been conducted, and the results show that the IMMUGHF- NJ can reduce the estimation error significantly, especially for long range or fast moving targets. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of deploying a network of passive sensors to estimate the positions of an unknown number of stationary transient emitters. Since a completely connected network, which has a link between every pair of nodes, is not feasible because of the power and bandwidth constraints, we developed a distributed algorithm that relies only on local communications between neighboring sensors. This distributed algorithm requires information diffusion within the network with the goal that every node achieves all target location estimates as accurate as a fusion center with centralized access to all information. The locations of the emitters are not completely observable by any single sensor since bearings and times of arrival with origin uncertainty are the only available measurements. These measurements are modeled as a realization of a Poisson point process at each sensor. The problem is formulated as a constrained optimization problem, which is solved via an alternating direction method of multipliers in a distributed manner based on the expectation maximization and averaging consensus algorithms. Consensus on the number of candidate targets as well as the inter-node estimate association are addressed so that the distributed algorithm converges to the maximum likelihood estimate. A likelihood function based approach using the estimated probability of detection is presented to determine the number of targets. Simulation results show that the distributed algorithm converges very fast and the root mean square error of target locations is almost as small as that obtained using the centralized algorithm. It is also shown that one can accurately determine the number of targets using the estimated probability of detection. [ABSTRACT FROM AUTHOR]

In active sonar and radar target tracking, measurements consist of position and often also include range rate. Tracking algorithms use these measurements over time to estimate target state comprising position, velocity and, where applicable, turn rate. In most cases there is an underlying assumption in the tracking algorithm that the target is a "point target" (i.e. the target has no physical extent). Another common assumption is that at most one measurement per scan originates from the target. For certain combinations of transmitted waveform and target type, the resolution of the waveform is such that the target is "over-resolved" (i.e. the sensor resolution is high enough that closely spaced scatter centers can be resolved). For such cases the point target assumption must be replaced with an extended target assumption. This work provides a methodology to exploit the extended nature of the target for the case of a rigid target whose spatial characteristics are fixed with respect to the line of motion. By employing a combination of the expectation maximization (EM) algorithm and allowing more than one measurement per scan to originate from the target, a technique is developed that uses a single scan of raw measurements that include range, bearing and range rate to provide an estimate of target position, velocity, heading and turn rate. This single scan estimate is then used in a nearly constant turn rate extended Kalman filter to provide a multi-scan estimate of the target state. [ABSTRACT FROM AUTHOR]

In this paper, an approach to bias estimation in the presence of measurement association uncertainty using common targets of opportunity, is developed. Data association is carried out before the estimation of sensor angle measurement biases. Consequently, the quality of data association is critical to the overall tracking performance. Data association becomes especially challenging if the sensors are passive. Mathematically, the problem can be formulated as a multidimensional optimization problem, where the objective is to maximize the generalized likelihood that the associated measurements correspond to common targets, based on target locations and sensor bias estimates. Applying gating techniques significantly reduces the size of this problem. The association likelihoods are evaluated using an exhaustive search after which an acceptance test is applied to each solution in order to obtain the correct solution. We demonstrate the merits of this approach by applying it to a simulated tracking system, which consists of two or three satellites tracking a ballistic target. We assume the sensors are synchronized, their locations are known and we estimate their orientation biases together with the unknown target locations. [ABSTRACT FROM AUTHOR]

In this paper we provide a new methodology using an exoatmospheric target of opportunity seen in a satellites borne sensor's field of view to estimate the sensor's biases simultaneously with the state of the target. Each satellite is equipped with an Infra Red (IR) sensor that provides the Line Of Sight (LOS) measurements azimuth and elevation to the target. The measurements provided by these sensors are assumed to be noisy but perfectly associated, i.e., it is known perfectly that they belong to the same target. The evaluation of the Cramér-Rao Lower Bound (CRLB) on the covariance of the bias estimates and the statistical tests on the results of simulations show that both the target trajectory and the biases are observable and this method is statistically efficient. [ABSTRACT FROM AUTHOR]

The performance of the conventional bearings-only tracking (BOT) from a single passive sensor hinges on the sensor platform maneuvers. This paper presents a new BOT approach based on fusion from two heterogenous bearings-only sensors residing on the same moving or stationary platform. The two sensors are an ESM/EO with negligible propagation delay and an acoustic sensor with significant propagation delay. The time difference between the reception times of the two sensors (corresponding to the same emission time) is the acoustic propagation delay. Since target range information is contained in the acoustic propagation delay (which is not known but can be estimated), the target state is shown to be completely observable even when the platform is stationary. The observability is studied in this paper via the Fisher information matrix (FIM). Two estimators are developed. They are the maximum likelihood (ML) estimator for batch estimation and the out-of-sequence measurements fusion from acoustic and ESM/EO sensors (OOSMAE) for recursive estimation. It shows that the ML estimator for batch estimation attains the Cram'er-Rao lower bound (CRLB)-it is statistically efficient-except in cases with a small number of measurements and the target heading close to the bearing from the sensor platform. The OOSM-AE is developed to handle out-ofsequence measurements (OOSM) due to the acoustic propagation delay. It consists of an unscented Kalman filter (UKF) to handle the in-sequence ESM/EO measurements and an OOSM unscented Gauss-Helmert filter (OOSM-UGHF) to handle the out-of-sequence acoustic measurements. Simulation results are presented to demonstrate the performance of this new BOT approach. [ABSTRACT FROM AUTHOR]