Avishy Carmi

Methods for Sparse Signal Recovery Using Kalman Filtering With Embedded Pseudo-Measurement Norms and Quasi-Norms

We present two simple methods for recovering sparse signals from a series of noisy observations. The theory of compressed sensing (CS) requires solving a convex constrained minimization problem. We propose solving this optimization problem by two algorithms that rely on a Kalman filter (KF) endowed with a pseudo-measurement (PM) equation. Compared to a recently-introduced KF-CS method, which involves the implementation of an auxiliary CS optimization algorithm (e.g., the Dantzig selector), our method can be straightforwardly implemented in a stand-alone manner, as it is exclusively based on the well-known KF formulation. In our first algorithm, the PM equation constrains the l 1 norm of the estimated state. In this case, the augmented measurement equation becomes linear, so a regular KF can be used. In our second algorithm, we replace the l 1 norm by a quasi-norm lp , 0 ¿ p < 1. This modification considerably improves the accuracy of the resulting KF algorithm; however, these improved results require an extended KF (EKF) for properly computing the state statistics. A numerical study demonstrates the viability of the new methods.

Bayesian compressive sensing for phonetic classification

In this paper, we introduce a novel bayesian compressive sensing (CS) technique for phonetic classification. CS is often used to characterize a signal from a few support training examples, similar to k-nearest neighbor (kNN) and Support Vector Machines (SVMs). However, unlike SVMs and kNNs, CS allows the number of supports to be adapted to the specific signal being characterized. On the TIMIT phonetic classification task, we find that our CS method outperforms the SVM, kNN and Gaussian Mixture Model (GMM) methods. Our CS method achieves an accuracy of 80.01%, one of the best reported result in the literature to date.

Stereovision-Based Estimation of Relative Dynamics Between Noncooperative Satellites: Theory and Experiments

Estimating the relative pose and motion of cooperative satellites using on-board sensors is a challenging problem. When the satellites are noncooperative, the problem becomes even more complicated, as there might be poor a priori information about the motion and structure of the target satellite. In this paper, the mentioned problem is solved by using only visual sensors, which measurements are processed through robust filtering algorithms. Using two cameras mounted on a chaser satellite, the relative state with respect to a target satellite, including the position, attitude, and rotational and translational velocities, is estimated. The new approach employs a stereoscopic vision system for tracking a set of feature points on the target spacecraft. The perspective projection of these points on the two cameras constitutes the observation model of an iterated extended Kalman filter (IEKF) estimation scheme. Using new theoretical results, the information contained in the visual data is quantified using the Fisher information matrix. It is shown that, even in the noncooperative case, there is information that can be extracted pertaining to the relative attitude and target structure. Finally, a method is proposed for rendering the relative motion filtering algorithm robust to uncertainties in the targets inertia tensor. This is accomplished by endowing the IEKF with a maximum a posteriori identification scheme for determining the most probable inertia tensor from several available hypotheses. The performance of the new filtering algorithm is validated by Monte-Carlo simulations. Also a preliminary experimental evaluation is provided.

Overview of Bayesian sequential Monte Carlo methods for group and extended object tracking

This work presents the current state-of-the-art in techniques for tracking a number of objects moving in a coordinated and interacting fashion. Groups are structured objects characterized with particular motion patterns. The group can be comprised of a small number of interacting objects (e.g. pedestrians, sport players, convoy of cars) or of hundreds or thousands of components such as crowds of people. The group object tracking is closely linked with extended object tracking but at the same time has particular features which differentiate it from extended objects. Extended objects, such as in maritime surveillance, are characterized by their kinematic states and their size or volume. Both group and extended objects give rise to a varying number of measurements and require trajectory maintenance. An emphasis is given here to sequential Monte Carlo (SMC) methods and their variants. Methods for small groups and for large groups are presented, including Markov Chain Monte Carlo (MCMC) methods, the random matrices approach and Random Finite Set Statistics methods. Efficient real-time implementations are discussed which are able to deal with the high dimensionality and provide high accuracy. Future trends and avenues are traced.

Attitude Estimation from Vector Observations Using Genetic-Algorithm-Embedded Quaternion Particle Filter

A novel algorithm is presented for the estimation of spacecraft attitude quaternion from vector observations in gyro-equipped spacecraft. The new estimator is a particle filter that uses approximate numerical representation techniques for performing the otherwise exact time propagation and measurement update of potentially non-Gaussian probability density functions in inherently nonlinear systems. The new method can be applied using various kinds of vector observations. In this paper, the case of a low-Earth-orbit spacecraft, acquiring noisy geomagnetic field measurements via a three-axis magnetometer, is considered. A genetic algorithm is used to estimate the gyro bias parameters, avoiding the need to augment the particle filters state and rendering the estimator computationally efficient. Contrary to conventional filters, which address the quaternions unit norm constraint via special (mostly ad hoc) techniques, the new filter maintains this constraint naturally. An extensive simulation study is used to compare the new filter to three extended Kalman filters and to the unscented Kalman filter in Gaussian and non-Gaussian scenarios. The new algorithm is shown to be robust with respect to initial conditions and to possess a fast convergence rate. An evaluation of the Cramer-Rao estimation error lower bound demonstrates the filters asymptotic statistical efficiency and optimality.

The Gaussian mixture MCMC particle algorithm for dynamic cluster tracking

We present a new filtering algorithm for tracking multiple clusters of coordinated targets. Based on a Markov Chain Monte Carlo (MCMC) mechanism, the new algorithm propagates a discrete approximation of the underlying filtering density. A dynamic Gaussian mixture model is utilized for representing the time-varying clustering structure. This involves point process formulations of typical behavioral moves such as birth and death of clusters as well as merging and splitting. Following our previous work, we adopt here two strategies for increasing the sampling efficiency of the basic MCMC scheme: an evolutionary stage which allows improved exploration of the sample space, and an EM-based method for making optimized proposals based on the frame likelihood. The algorithms performance is assessed and demonstrated in both synthetic and real tracking scenarios.

On MCMC-Based particle methods for Bayesian filtering: Application to multitarget tracking

Nonlinear non-Gaussian state-space models arise in numerous applications in control and signal processing. In this context, one of the most successful and popular approximation techniques is sequential Monte Carlo (SMC) methods, also known as particle filters. Nevertheless, these methods tend to be inefficient when applied to high dimensional problems. In this paper, we present an overview of Markov chain Monte Carlo (MCMC) methods for sequential simulation from posterior distributions, which represent efficient alternatives to SMC methods. Then, we describe an implementation of this MCMC-Based particle algorithm to perform the sequential inference for multitarget tracking. Numerical simulations illustrate the ability of this algorithm to detect and track multiple targets in a highly cluttered environment.

Adaptive Particle Filtering for Spacecraft Attitude Estimation from Vector Observations

An extension is presented to the recently introduced genetic algorithm-embedded quaternion particle filter. Belonging to the class ofMonte Carlo sequential methods, the genetic algorithm-embedded quaternion particle filter is an estimator that uses approximate numerical representation techniques for performing the otherwise exact time propagation and measurement update of potentially non-Gaussian probability density functions in the inherently nonlinear attitude estimation problem. The spacecraft attitude is represented via the quaternion of rotation, and a genetic algorithm is used to estimate the gyrobiases, allowing one to estimate just the quaternion via the particlefilter. An adaptive version of the genetic algorithm-embedded quaternion particle filter is presented herein that extends the applicability of this filter to problems with highly uncertain measurement noise distributions. The adaptive algorithm estimates themeasurement noise distribution on the fly, alongwith the spacecraft attitude and gyro biases. A simulation study is used to demonstrate the performance of the adaptive algorithm using real data obtained from the Technion’s TechSAT satellite, whose three-axis magnetometer’s data are non-Gaussian. The simulation, which compares the performance of the filter to the nonadaptive genetic algorithm-embedded quaternion particle filter, demonstrates the viability of the new algorithm.

Fast Particle Filtering for Attitude and Angular-Rate Estimation from Vector Observations

Extending and consolidating the recently introduced quaternion particle filter for a spacecraft’s attitude estimation and its companion, the angular-rate particlefilter, this paper presents a novel algorithm for the estimation of both a spacecraft’s attitude and angular rate from vector observations. Belonging to the class of Monte Carlo sequential methods, the new estimator is a particle filter that uses approximate numerical representation techniques for performing the otherwise exact time propagation and measurement update of potentially non-Gaussian probability density functions in inherently nonlinear systems. The paper develops thefilter and its implementation in the case of a low-Earth-orbit spacecraft, acquiring noisy Geomagnetic field measurements via a three-axis magnetometer. The new estimator copeswith the curse of dimensionality related to the particle filtering technique by introducing innovative procedures that permit a significant reduction in the number of particles. This renders the new estimator computationally efficient and enables its implementationwith a remarkably small number of particles (relative to the dimension of the state). The results of a simulation study demonstrate the viability and robustness of the new filter and its fast convergence rate.

Kalman filtering for compressed sensing

Compressed sensing is a new emerging field dealing with the reconstruction of a sparse or, more precisely, a compressed representation of a signal from a relatively small number of observations, typically less than the signal dimension. In our previous work we have shown how the Kalman filter can be naturally applied for obtaining an approximate Bayesian solution for the compressed sensing problem. The resulting algorithm, which was termed CSKF, relies on a pseudo-measurement technique for enforcing the sparseness constraint. Our approach raises two concerns which are addressed in this paper. The first one refers to the validity of our approximation technique. In this regard, we provide a rigorous treatment of the CSKF algorithm which is concluded with an upper bound on the discrepancy between the exact (in the Bayesian sense) and the approximate solutions. The second concern refers to the computational overhead associated with the CSKF in large scale settings. This problem is alleviated here using an efficient measurement update scheme based on Krylov subspace method.