Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

https://www.alaakhamis.org/teaching/MCT200/reading/Information%20Fusion.pdf

Multisensor data fusion: A review of the state-of-the-art

Numerical Initial Value Problems in Ordinary Differential Equations

Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the “bible of computer algebra”, gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany oneor two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of the Fast Euclidean Algorithm chapter has been renovated.

Modern computer algebra

An analytic solution to the multi-target Bayes recursion known as the $\delta $ -Generalized Labeled Multi-Bernoulli ( $\delta $ -GLMB) filter has been recently proposed by Vo and Vo in [“Labeled Random Finite Sets and Multi-Object Conjugate Priors,” IEEE Trans. Signal Process., vol. 61, no. 13, pp. 3460–3475, 2014]. As a sequel to that paper, the present paper details efficient implementations of the $\delta $ -GLMB multi-target tracking filter. Each iteration of this filter involves an update operation and a prediction operation, both of which result in weighted sums of multi-target exponentials with intractably large number of terms. To truncate these sums, the ranked assignment and K-th shortest path algorithms are used in the update and prediction, respectively, to determine the most significant terms without exhaustively computing all of the terms. In addition, using tools derived from the same framework, such as probability hypothesis density filtering, we present inexpensive (relative to the $\delta $ -GLMB filter) look-ahead strategies to reduce the number of computations. Characterization of the $L_{1}$ -error in the multi-target density arising from the truncation is presented.

Labeled Random Finite Sets and the Bayes Multi-Target Tracking Filter

The task of tracking extended objects or (partly) unresolvable group targets raises new challenges for both data association and track maintenance. Due to limited sensor resolution capabilities, group targets (i.e., a number of closely spaced targets moving in a coordinated fashion) may show a similar detection pattern as extended objects, namely a varying number of detections whose spread is determined by both the statistical sensor errors as well as the physical extension of the group or extended object. In both cases, tracking and data association under the “one target-one detection” assumption are no longer applicable. This paper deals with the problem of maintaining a track for an extended object or group target with varying number of detections. Herein, object extension is represented by a symmetric positive definite random matrix. A recently published Bayesian approach to tackling this problem is analyzed and discussed. From there, a new approach is derived that is expected to overcome some of the weaknesses the mentioned Bayesian approach suffers from in certain applications.

Tracking of Extended Objects and Group Targets Using Random Matrices

Among the possible approaches to tackling the problem of data incest in distributed data fusion networks, covariance intersection is a candidate that yields consistent estimates independent of network structure and any possible cross-correlation between local estimates. The corresponding weighting coefficients are usually chosen with the aim for a minimum trace or determinant of the resulting error variance matrix. A fast non-iterative algorithm exists that, to a certain extent, approximately solves this nonlinear optimization problem with extremely reduced numerical implementation effort. Yet, the obtained weighting coefficients do not depend on the relative orientation of the estimation error variance matrices which may lead to a degraded performance in certain applications. Hence, an improved fast covariance intersection algorithm is developed that comes with a slightly increased implementation effort while yielding significantly better estimation results in some cases and comparable results in all other ones. Simulation results confirm the postulated performance improvement.

Improved fast covariance intersection for distributed data fusion

The cardinalized probability hypothesis density (CPHD) filter is a recursive Bayesian algorithm for estimating multiple target states with varying target number in clutter. In the present work, it is shown that a missed detection in one part of the field of view has a significant effect on the probability hypothesis density (PHD) arbitrarily far apart from the missed detection. In the case of zero false alarm rate, this effect is particularly pronounced and can be calculated by solving the CPHD filter equations analytically. While the CPHD filter update of the total cardinality distribution is exact, the local target number estimate close to the missed detection is artificially strongly reduced. A first ad-hoc approach towards a "locally" CPHD filter for reducing this deficiency is presented and discussed.

"Spooky Action at a Distance" in the Cardinalized Probability Hypothesis Density Filter

The task of tracking extended objects or (partly) unresolvable group targets raises new challenges for both data association and track maintenance. Extended objects may give rise to more than one detection per opportunity where the scattering centers may vary from scan to scan. On the other end, group targets (i. e., a number of closely spaced targets moving in a coordinated fashion) often will not cause as many detections as there are individual targets in the group due to limited sensor resolution capabilities. In both cases, tracking and data association under the one target-one detection assumption are no longer applicable. This paper deals with the problem of maintaining a track for an extended object or group target with varying number of detections. Herein, object extension is represented by a random symmetric positive definite matrix. A recently published Bayesian approach to tackling this problem is analyzed and discussed. From there, a new approach is derived that is expected to overcome some of the weaknesses the Bayesian approach suffers from in certain applications.

/pdf/tracking-of-extended-objects-and-group-targets-using-random-2w15cyqeq7.pdf

Tracking of extended objects and group targets using random matrices — a new approach

The task of tracking extended objects or (partly) unresolvable group targets raises new challenges for both data association and track maintenance. Due to limited sensor resolution capabilities, group targets (i. e., a number of closely spaced targets moving in a coordinated fashion) may show a similar detection pattern as extended objects, namely a varying number of detections whose spread is determined by both the statistical sensor errors as well as the physical extension of the group or extended object. Different tracking approaches treating these situations have been proposed where physical extension is represented by a random symmetric positive definite matrix. This paper discusses some results that should give deeper insight into behavior and performance analysis of these approaches. Further improvements are presented.

/pdf/advances-on-tracking-of-extended-objects-and-group-targets-46msjfaa4v.pdf

Dietrich Franken

Papers

Tracking of Extended Objects and Group Targets Using Random Matrices

Improved fast covariance intersection for distributed data fusion

"Spooky Action at a Distance" in the Cardinalized Probability Hypothesis Density Filter

Tracking of extended objects and group targets using random matrices — a new approach

Advances on tracking of extended objects and group targets using random matrices