We consider the problem of estimating the performance of a system that tracks moving objects on the ground using
airborne sensors. Expected Track Life (ETL) is a measure of performance that indicates the ability of a tracker to
maintain track for extended periods of time. The most desirable method for computing ETL would involve the use of
large sets of real data with accompanying truth. This accurately accounts for sensor artifacts and data characteristics,
which are difficult to simulate. However, datasets with these characteristics are difficult to collect because the coverage
area of the sensors is limited, the collection time is limited, and the number of objects that can realistically be truthed is
also limited. Thus when using real datasets, many tracks are terminated because the objects leave the field of view or the
end of the dataset is reached. This induces a bias in the estimation when the ETL is computed directly from the tracks.
An alternative to direct ETL computation is the use of Markov-Chain models that use track break statistics to estimate
ETL. This method provides unbiased ETL estimates from datasets much shorter than what would be required for direct
computation. In this paper we extend previous work in this area and derive an explicit expression of the ETL as a
function of track break statistics. An example illustrates the properties and advantages of the method.
The subject of traffic flow modeling began over fifty years ago when Lighthill and Whitham used flow continuity
equation from fluid dynamics to describe traffic behavior. Since then, a multitude of models, broadly classified into
macroscopic, mesoscopic, and microscopic models, has been developed. Macroscopic models describe the space-time
evolution of aggregate quantities such as traffic flow density whereas microscopic models describe behavior of
individual drivers/vehicles in the presence of other vehicles. In this paper, we consider tracking of vehicles using a
specific microscopic model known as the intelligent driver model (IDM). As in other microscopic models, the IDM
equations of motion of a vehicle are nonlinearly coupled to those of neighboring vehicles, with the magnitudes of
coupling terms becoming larger as vehicles get closer and smaller as vehicles get farther apart. In our approach, the state
of weakly coupled groups of vehicles is represented by separated probability distributions. When the vehicles move
closer to each other, the state is represented by a joint probability distribution that takes into account the interaction
among vehicles. We use a sum of Gaussians approach to represent the underlying interaction structure for state
estimation and reduce computational complexity. In this paper we describe our approach and illustrate the approach with
Structured pedigree is a way to compress pedigree information. When applied to distributed fusion systems, the
approach avoids the well known problem of information double counting resulting from ignoring the cross-correlation
among fused estimates. Other schemes that attempt to compute optimal fused estimates require the transmission of full
pedigree information or raw data. This usually can not be implemented in practical systems because of the enormous
requirements in communications bandwidth. The Structured Pedigree approach achieves data compression by
maintaining multiple covariance matrices, one for each uncorrelated source in the network. These covariance matrices
are transmitted by each node along with the state estimate. This represents a significant compression when compared to
full pedigree schemes. The transmission of these covariance matrices (or a subset of these covariance matrices) allows
for an efficient fusion of the estimates, while avoiding information double counting and guaranteeing consistency on the
estimates. This is achieved by exploiting the additional partial knowledge on the correlation of the estimates. The
approach uses a generalized version of the Split Covariance Intersection algorithm that applies to multiple estimates and
multiple uncorrelated sources. In this paper we study the performance of the proposed distributed fusion system by
analyzing a simple but instructive example.
One of the most critical challenges in distributed data fusion is the avoidance of information double counting (also called
"data incest" or "rumor propagation"). This occurs when a node in a network incorporates information into an
estimate - e.g. the position of an object - and the estimate is injected into the network. Other nodes fuse this estimate
with their own estimates, and continue to propagate estimates through the network. When the first node receives a fused
estimate from the network, it does not know if it already contains its own contributions or not. Since the correlation
between its own estimate and the estimate received from the network is not known, the node can not fuse the estimates
in an optimal way. If it assumes that both estimates are independent from each other, it unknowingly double counts the
information that has already being used to obtain the two estimates. This leads to overoptimistic error covariance
matrices. If the double-counting is not kept under control, it may lead to serious performance degradation. Double
counting can be avoided by propagating uniquely tagged raw measurements; however, that forces each node to process
all the measurements and precludes the propagation of derived information. Another approach is to fuse the information
using the Covariance Intersection (CI) equations, which maintain consistent estimates irrespective of the cross-correlation
among estimates. However, CI does not exploit pedigree information of any kind. In this paper we present an
approach that propagates multiple covariance matrices, one for each uncorrelated source in the network. This is a way to
compress the pedigree information and avoids the need to propagate raw measurements. The approach uses a generalized
version of the Split CI to fuse different estimates with appropriate weights to guarantee the consistency of the estimates.
Highly accurate predictions of tracking performance usually require high fidelity Monte Carlo simulations that entail
significant implementation time, run time, and complexity. In this paper we consider the use of Markov Chains as a
simpler alternative that models critical aspects of the tracking process and provides reasonable estimates of tracking
performance, while maintaining much lower cost and complexity. We describe a general procedure for Markov-Chain
based performance prediction, and illustrate the use of this procedure in the context of an airborne system that employs
a steerable EO/IR sensor to track single targets or multiple targets in non-overlapping fields of view. We discuss the
effects of key model parameters, including measurement sampling rates, track termination, target occlusions, and
missed detections. We also present plots of performance as a function of occlusion probability and target recognition
probability that exemplify the use of the model.
Tracking multiple surface targets with a single steerable airborne video sensor is accomplished by several interrelated functions: (i) image registration for camera motion compensation and accurate image-to-ground mapping, (ii) video processing for object detection and feature extraction, (iii) target tracking for detection association and track creation and maintenance, (iv) signature extraction and exploitation, and (v) sensor resource management for the generation of sensor steering commands. The first function is often overlooked, but has a significant impact in the performance of the overall system. A rudimentary registration can be achieved by using the platform location and attitude as well as the sensor orientation and field of view information, but the accuracy of this registration is typically poor due to inertial navigation system errors, particularly in small unmanned aerial vehicles with cost and hardware limitations. Successful registration of successive frames enables the use of multiple frame video processing for improved object detection and provides stable image-to-ground mapping for improved data association by the tracker. In systems with a steerable sensor that slews back and forth to track more than one target simultaneously, the image registration module creates and maintains multiple mosaics corresponding to the different tracking areas. In this paper we discuss primarily the image registration module and the system of coordinate frames that is maintained to improve data association and tracking.
The goal of the DARPA Video Verification of Identity (VIVID) program is to develop an automated video-based ground targeting system for unmanned aerial vehicles. The system comprises several modules that interact with each other to support tracking of multiple targets, confirmatory identification, and collateral damage avoidance. The Multiple Target Tracking (MTT) module automatically adjusts the camera pan, tilt, and zoom to support kinematic tracking, multi-target track association, and confirmatory identification. The MTT system comprises: (i) a video processor that performs moving object detection and feature extraction, including object position and velocity, (ii) a multiple hypothesis tracker that processes video processor reports to generate and maintain tracks, and (iii) a sensor resource manager that aims the sensor to improve tracking of multiple targets. This paper presents a performance assessment of the current implementation of the MTT under several operating conditions. The evaluation is done using pre-recorded airborne video to assess the ability of the video tracker to detect and track ground moving objects over extended periods of time. The tests comprise a number of different operational conditions such as multiple targets and confusers under various levels of occlusion and target maneuverability, as well as different background conditions. The paper also describes the challenges that still need to be overcome to extend track life over long periods of time.
The goal of the DARPA Video Verification of Identity (VIVID) program is to develop an automated video-based ground targeting system for unmanned aerial vehicles that significantly improves operator combat efficiency and effectiveness while minimizing collateral damage. One of the key components of VIVID is the Multiple Target Tracker (MTT), whose main function is to track many ground targets simultaneously by slewing the video sensor from target to target and zooming in and out as necessary. The MTT comprises three modules: (i) a video processor that performs moving object detection, feature extraction, and site modeling; (ii) a multiple hypothesis tracker that processes extracted video reports (e.g. positions, velocities, features) to generate tracks of currently and previously moving targets and confusers; and (iii) a sensor resource manager that schedules camera pan, tilt, and zoom to support kinematic tracking, multiple target track association, scene context modeling, confirmatory identification, and collateral damage avoidance. When complete, VIVID MTT will enable precision tracking of the maximum number of targets permitted by sensor capabilities and by target behavior. This paper describes many of the challenges faced by the developers of the VIVID MTT component, and the solutions that are currently being implemented.
The performance of tracking systems depends on numerous factors including the scenario, operating conditions, and choice of tracker algorithms. For tracker system design, mission planning, and sensor resource management, the availability of a tracker performance model (TPM) for the standard measures of performance (MOPs) would be of high practical value. Ideally, the TPM has high computational efficiency, and is insensitive to the particular low-level details of highly complex algorithms and unimportant operating conditions. These characteristics would eliminate the need for high fidelity Monte Carlo simulations that are expensive and time consuming. In this paper, we describe a performance prediction model that generates track life distributions and other MOPs. The model employs a simplified Monte Carlo simulation that accounts for sensor orbits, sensor coverage, target dynamics. A key feature is an analytical expression that approximates the probability of correct association (PCA) among reports and tracks. The expression for the PCA that we use was developed by Mori et. al. for simplified scenarios where there is a single class of targets, the noise is Gaussian, and the covariance matrices are identical for all targets. Based on heuristic considerations, we extend this result to the case of road-constrained tracking where both on-road and off-road targets are present. We investigate the validity of the proposed expression by means of Monte Carlo simulations, and present preliminary results of a validation study that compares the performance of an actual tracker with the performance predictions of our model.