JAIF - Articles to Appear in a Future Issue

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"Early Fusion and Query Modification in Their Dual Late Fusion Forms"

Leszek Kaliciak (AmbieSense, UK), Hans Myrhaug (AmbieSense, UK), Ayse Goker (AmbieSense, UK), Dawei Song (The Open University, UK)

In this paper, we prove that specific widely used models in Content-based Image Retrieval for information fusion are interchangeable. In addition, we show that even advanced, non-standard fusion strategies can be represented in dual forms. These models are often classified as representing early or late fusion strategies. We also prove that the standard query modification method with specific similarity measurements can be represented in a late fusion form.

"Bias Estimation for Moving Optical Sensor Measurements with Targets of Opportunity"

Djedjiga Belfadel (University of Connecticut, USA), Richard Osborne III (University of Connecticut, USA), Yaakov Bar-Shalom (University of Connecticut, USA)

Integration of space based sensors into a Ballistic Missile Defense System (BMDS) allows for detection and tracking of threats over a larger area than ground based sensors. This paper examines the effect of sensor bias error on the tracking quality of a Space Tracking and Surveillance System (STSS) for the highly non-linear problem of tracking a ballistic missile. The STSS constellation consists of two or more satellites (on known trajectories) for tracking ballistic targets. Each satellite is equipped with an IR sensor that provides azimuth and elevation to the target. The tracking problem is made more difficult due to a constant or slowly varying bias error present in each sensor's line of sight measurements. It is important to correct for these bias errors so that the multiple sensor measurements and/or tracks can be referenced as accurately as possible to a common tracking coordinate system. The measurements provided by these sensors are assumed time-coincident (synchronous) and perfectly associated. The line of sight (LOS) measurements from the sensors can be fused into measurements which are the Cartesian target position, i.e., linear in the target state. We evaluate the Cram\'er-Rao Lower Bound (CRLB) on the covariance of the bias estimates, which serves as a quantification of the available information about the biases. Statistical tests on the results of simulations show that this method is statistically efficient, even for small sample sizes (as few as two sensors and six points on the (unknown) trajectory of a single target of opportunity. We also show that the RMS position error is significantly improved with bias estimation compared with the target position estimation using the original biased measurements.


Particle filtering with observations in a manifold:  A proof of convergence and two worked examples

Salem Said and Jonathan H. Manton

Particle filtering is currently a popular numerical method for solving stochastic filtering problems. This paper outlines its application to continuous time filtering problems with observations in a manifold. Such problems include a variety of important engineering situations and have received independent interest in the mathematical literature. The paper begins  by stating a general stochastic filtering problem where the observation process, conditionally on the unknown signal, is an elliptic diffusion in a differentiable manifold. Using a geometric structure (a Riemannian metric and a connection) which is adapted to the observation model, it expresses the solution of this problem in the form of a Kallianpur-Striebel formula. The paper proposes a new particle filtering algorithm which implements this formula using sequential Monte Carlo strategy. This algorithm is based on an original use of the concept of connector map, which is here applied for the first time in the context of filtering problems. The paper proves the convergence of this algorithm, under the assumption that the underlying manifold is compact, and illustrates it with two worked examples. In the first example, the observations lie in the special orthogonal group $SO(3)$. The second example is concerned with the case of observations in the unit sphere $S^2$.

Multitarget tracking with the von Mises-Fisher filter and probabilistic data association

Ivan Markovic, Mario Bukal, Josip Cesic and Ivan Petrovic

Directional data emerge in many scientific disciplines due to the nature of the observed phenomena or the working principles of a sensor. The problem of tracking with direction-only sensors is challenging since the motion of the target typically resides either in 3D or 2D Euclidean space, while the corresponding measurements reside either on the unit sphere or the unit circle, respectively. Furthermore, in multitarget tracking there is the need to deal with the problem of pairing sensors measurements with targets in the presence of clutter (the data association problem). In this paper we propose to approach multitarget tracking in clutter with direction-only data by setting it on the unit hypersphere, thus tracking the objects with a Bayesian estimator based on the von Mises-Fisher distribution and probabilistic data association. To achieve this goal we derive the probabilistic data association (PDA) filter and the joint probabilistic data association (JPDA) filter for the Bayesian von Mises-Fisher estimation on the unit hypersphere. The final PDA and JPDA filter equations are derived with respect to the Kullback-Leibler divergence by preserving the first moment of the hyperspherical distribution. Although the fundamental equations are given for the hyperspherical case, we focus on the filters on the unit 1-sphere (circle in $\BBRD{R}^2$) and the unit 2-sphere (surface of the unit ball in $\BBRD{R}^3$). The proposed approach is validated through synthetic data experiments on 100 Monte Carlo runs simulating multitarget tracking with noisy directional measurements and clutter. 

Direct Position Determination for TDOA-based Single Sensor Localization

Christian Steffes and Marc Oispuu

In this paper, four different localization techniques based on TDOA-measurements for single sensor passive emitter localization are proposed. The use of signal structure information allows TDOA-based localization with a single moving sensor node. A direct position estimation scheme is derived for the single sensor TDOA localization problem. The feasibility of the proposed method is shown in simulations. The position estimation accuracy of the single sensor TDOA and the direct technique are compared using simulation results and the Cram*aaer-Rao Lower Bound. Field experiments using an airborne sensor are conducted to prove the concept.

Uncertainty Propagation of Correlated Quaternion and Euclidean States using the Gauss-Bingham Density

Jacob E. Darling and Kyle J. Demars

A new probability density function, called the Gauss-Bingham density, is proposed and studied in the context of uncertainty propagation. The Gauss-Bingham density quantifies the correlation between a quaternion and Euclidean states on the cylindrical manifold on which these states naturally exist. The Gauss-Bingham density, including its canonical form, is developed. In order to approximate the temporal evolution of the uncertainty, an unscented transform for the Gauss-Bingham density is first developed. The sigma points are then transformed according to given (potentially) nonlinear system 
dynamics, and the maximum weighted log-likelihood parameters of the Gauss-Bingham density are recovered. Uncertainty propagation using the Gauss-Bingham density does not rely on a small angle assumption to project the uncertainty in the quaternion into a three parameter representation as does the predictor of the multiplicative extended Kalman filter, so its accuracy does not suffer when propagating large attitude uncertainties. Two simulations are presented to show the process and efficacy of uncertainty propagation using the Gauss-Bingham density and to compare it to the multiplicative extended Kalman filter.

Density Estimation on the rotation group using Diffusive wavelets

Nicolas Le Bihan, Julien Flamant and Jonathan H. Manton

This paper considers the problem of estimating probability density functions on the rotation group $SO(3)$. Two distinct approaches are proposed, one based on characteristic functions and the other on wavelets using the heat kernel. Expressions are derived for their Mean Integrated Squared Errors. The performance of the estimators is studied numerically and compared with the performance of an existing technique using the De La Vall*aaee Poussin kernel estimator. The heat-kernel wavelet approach appears to offer the best convergence, with faster convergence to the optimal bound and guaranteed positivity of the estimated probability density function.

Stochastic Filtering Using Periodic Cost Functions

Eyal Nitzan, Tirza Routtenberg and Joseph Tabrikian

Stochastic filters attempt to estimate an unobservable state of a stochastic dynamical system from a set of noisy measurements. In this paper, we consider circular stochastic filtering and develop two dynamic methods for estimation of circular states, named sample-based stochastic filtering via root-finding (SB-SFRF) and Fourier-based stochastic filtering via root-finding (FB-SFRF). The proposed SB-SFRF and FB-SFRF methods attempt to dynamically minimize Bayes periodic risks by using Fourier series representation of their corresponding cost functions. The performance of the proposed methods is 
evaluated in the problem of direction-of-arrival (DOA) tracking.

Methods for Deterministic Approximation of Circuylar Densities

Gerhard Kurz, Igor Gilitschenski, Roland Siegwart and Uwe D. Hanebeck


No abstract

Multivariate Angular Filtering Using Fourier Series

Florian Pfaff, Gerhard Kurz and Uwe D. Hanebeck


No abstract