KEYWORDS: Monte Carlo methods, Sensors, Data modeling, Surveillance, Detection and tracking algorithms, Statistical analysis, Stochastic processes, Target detection, Error analysis, Data analysis
The central problem in multitarget, multisensor surveillance is that of determining which reports from separate sensors arise
from common objects. Due to stochastic errors in the source reports, there may be multiple data association hypotheses
with similar likelihoods. Moreover, established methods for performing data association make fundamental modeling
assumptions that hold only approximately in practice. For these reasons, it is beneficial to include some measure of
uncertainty, or ambiguity, when reporting association decisions. In this paper, we perform an analysis of the benefits
versus runtime performance of three methods of producing ambiguity estimates for data association: enumeration of the
k-best data association hypotheses, importance sampling, and Markov Chain Monte Carlo estimation. In addition, we
briefly examine the sensitivity of ambiguity estimates to violations of the stochastic model used in the data association
procedure.
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.
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.
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.
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