Effective multi-sensor, multi-target, distributed composite tracking requires the management of limited network
bandwidth. In this paper we derive from first principles a value of information for measurements that
can be used to sort the measurements in order from most to least valuable. We show the information metric
must account for the models and filters used by the composite tracking system. We describe how this value
of information can be used to optimize bandwidth utilization and illustrate its effectiveness using simulations
that involve lossy and latent network models.
The goal of this paper is to demonstrate the coordination in real-time of the operation of multiple sensors in
such a way that those best-equipped for certain missions should perform those missions for the entire network,
while other sensors fill in the gaps with their capabilities. The networked system of sensors must search, detect,
track, classify, and engage targets of high value in a timely fashion. The information transmitted should be that
which contributes the most toward achieving the performance goals (e.g., track accuracy, track completeness,
and a consistent operational picture or single integrated air picture (SIAP)) subject to the network bandwidth
constraints and the capabilities of the sensors.
We present an overview of an assignment based sensor resource manager, a distributed algorithm for coordinating
the assignment problem, and simulation results that validate this approach. While the assignment
formulation and algorithms could include both sensor resource and bandwidth constraints with versions for single
and multiple time periods, i.e., myopic and non-myopic, the distributed prototype formulation and algorithms
developed for these experiments were restricted to the tasking of certain sensors to make measurements and
transmit them over the network based on the current air picture. The number of measurements put on the
network was controlled by limiting the number of sensors that could transmit measurements on each target.
The communication loading was then measured to demonstrate that indeed one can design a distributed sensor
resource manager capable of achieving the objectives of significantly reducing the communication loading and
maintaining SIAP.
Bias estimation using objects with unknown data association requires concurrent estimation of both biases and optimal
data association. This report derives maximum a posteriori (MAP) data association likelihood ratios for concurrent bias
estimation and data association based on sensor-level track state estimates and their joint error covariance. Our approach
is unique for two reasons. First, we include a bias prior that allows estimation of absolute sensor biases, rather than just
relative biases. Second, we allow concurrent bias estimation and association for an arbitrary number of sensors. The
two-sensor likelihood ratio is derived as a special case of the general M-sensor result.
Fusion of data from multiple sensors can be hindered by systematic bias errors. This may lead to severe degradation
in data association and track quality and may result in a large growth of redundant and spurious tracks.
Multi-sensor networks will generally attempt to estimate the relevant bias values (usually, during sensor registration),
and use the estimates to debias the sensor measurements and correct the reference frame transformations.
Unfortunately, the biases and navigation errors are stochastic, and the estimates of the means account only
for the "deterministic" part of the biases. The remaining stochastic errors are termed "residual" biases and
are typically modeled as a zero-mean random vector. Residual biases may cause inconsistent covariance estimates,
misassociation, multiple track swaps, and redundant/spurious track generation; we therefore require
some efficient mechanism for mitigating the effects of residual biases. We present here results based on the
Schmidt-Kalman filter for mitigating the effects of residual biases. A key advantage of this approach is that it
maintains the cross-correlation between the state and the bias errors, leading to a realistic covariance estimate.
The current work expands on the work previously performed by Numerica through an increase in the number
of bias terms used in a high fidelity simulator for air defense. The new biases considered revolve around the
transformation from the global earth-centered-earth-fixed (ECEF) coordinate frame to the local east-north-up
(ENU) coordinate frame. We examine not only the effect of bias mitigation for the full set of biases, but also
analyze the interplay between the various bias components.
KEYWORDS: Sensors, Error analysis, Detection and tracking algorithms, Monte Carlo methods, Data analysis, Matrices, Data fusion, Mathematical modeling, Electroluminescence, Computer simulations
Fusion of data from multiple sensors can be hindered by systematic errors known as biases. Specifically, the presence of biases can lead to data misassociation and redundant tracks. Fortunately, if an estimate of the unknown biases can be obtained, the measurements and transformations for each sensor can be debiased prior to fusion. In this paper, we present an algorithm that uses targets of opportunity in the sensor field-of-view for online estimation of time-variant biases. The algorithm uses the singular value decomposition (SVD) to automatically handle the issue of parameter observability during tracking, allowing for shorter estimation windows and more accurate bias estimation. Our approach extends the novel methods proposed in the companion paper by Herman and Poore that used the SVD within a nonlinear least-squares estimator to handle the issue of parameter
observability during offine estimation of time-invariant biases using truth data.
KEYWORDS: Sensors, Data analysis, Algorithm development, Monte Carlo methods, Computer simulations, Detection and tracking algorithms, Data modeling, Computer programming, Radar, Kinematics
The problem of joint maximum a posteriori (MAP) bias estimation and data association belongs to a class of
nonconvex mixed integer nonlinear programming problems. These problems are difficult to solve due to both the
combinatorial nature of the problem and the nonconvexity of the objective function or constraints. Algorithms for
this class of problems have been developed in a companion paper of the authors. This paper presents simulations
that compare the "all-pairs" heuristic, the k-best heuristic, and a partial A*-based branch and bound algorithm.
The combination of the latter two algorithms is an excellent candidate for use in a realtime system. For an
optimal algorithm that also computes the k-best solutions of the joint MAP bias estimation problem and data
association problem, we investigate a branch and bound framework that employs either a depth-first algorithm
or an A*-search procedure. In addition, we demonstrate the improvements due to a new gating procedure.
The problem of joint maximum a posteriori (MAP) bias estimation and data association belongs to a class of
nonconvex mixed integer nonlinear programming problems. These problems are difficult to solve due to both the
combinatorial nature of the problem and the nonconvexity of the objective function or constraints. A specific
problem that has received some attention in the tracking literature is that of the target object map problem in
which one tries match a set of tracks as observed by two different sensors in the presence of biases, which are
modeled here as a translation between the track states. The general framework also applies to problems in which
the costs are general nonlinear functions of the biases.
The goal of this paper is to present a class of algorithms based on the branch and bound framework and
the "all-pairs" and k-best heuristics that provide a good initial upper bound for a branch and bound algorithm.
These heuristics can be used as part of a real-time algorithm or as part of an "anytime algorithm" within the
branch and bound framework. In addition, we consider both the A*-search and depth-first search procedures
as well as several efficiency improvements such as gating. While this paper focuses on the algorithms, a second
paper will focus on simulations.
Access to the requested content is limited to institutions that have purchased or subscribe to SPIE eBooks.
You are receiving this notice because your organization may not have SPIE eBooks access.*
*Shibboleth/Open Athens users─please
sign in
to access your institution's subscriptions.
To obtain this item, you may purchase the complete book in print or electronic format on
SPIE.org.
INSTITUTIONAL Select your institution to access the SPIE Digital Library.
PERSONAL Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.