Modern aviation often relies on global navigation satellite systems (GNSS) for positioning accuracy. However, today's electronic warfare technology presents an integrity risk for such systems. Therefore, it is increasingly desirable for aircraft not to depend exclusively on GNSS. Celestial navigation, on the other hand, is a promising alternative due to its resistance to electromagnetic interference. This paper describes a new way to solve the aircraft positioning problem through an errorstate Kalman filter (ESKF) for autonomous astronomical-based navigation by adapting an observation model developed for planetary rovers to the context of aviation. Its efficiency to reduce inertial navigation system errors is demonstrated through Monte Carlo simulations of randomly generated aircraft trajectories.

We propose in this paper two adapt-then-combine (ATC) distributed particle filters for cooperative estimation of 3D orientations. The first algorithm represents rotations as elements of the Special Orthogonal Group and builds Gaussian parametric approximations on a Lie Algebra to fuse posterior probability densities. The second algorithm, in turn, represents the orientations as unit-norm quaternions and resorts to directional statistics, fusing von Mises-Fisher parametric approximations. The proposed algorithms performances are then evaluated via numerical simulations.

We present in this paper a fully distributed algorithm for simultaneous positioning of cooperative aircraft and distributed tracking of a noncooperative target. We model the probability of connection between the aircraft and the probability of an aircraft detecting the target and implement the simultaneous positioning and tracking algorithm using dynamic factor graphs that incorporate geometric average fusion.

This paper proposes new distributed particle filters for tracking the state of a dynamic system that evolves on the Special Euclidean Group. The algorithms are based on the Random Exchange diffusion technique and build compressed parametric approximations to the particles using Lie algebras. Via numerical simulations, we observe that the proposed methods perform similarly to a centralized particle filter, surpassing an extended Kalman filter by a large margin.

This paper introduces a novel distributed diffusion algorithm for tracking the state of a dynamic system that evolves on the Stiefel manifold. To compress information exchanged between nodes, the algorithm builds a Gaussian parametric approximation to the particles that are previously projected onto the tangent space to the Stiefel manifold and mapped to real vectors. Observations from neighboring nodes are then assimilated for a general nonlinear observation model. Performance results are compared to those of competing linear diffusion Extended Kalman Filters and other particle filters.

In this paper, we introduce new distributed diffusion algorithms to track a sequence of hidden random matrices that evolve on the special orthogonal group. The algorithms are based on the Adapt-then-Combine and the Random Exchange methods, and diffuse Gaussian approximations of posterior densities computed in the Lie algebra of the special orthogonal group. Simulation results show that, in scenarios with nonlinear observation functions, the proposed algorithms perform closely to the centralized particle filter estimator and can outperform competing Extended Kalman Filters.

This paper introduces a new distributed Adapt-then-Combine (ATC) diffusion algorithm for cooperative tracking of an un-known state vector that evolves on the unit hypersphere. The adapt step is implemented for a general nonlinear observation model and a dynamic state model defined on the hypersphere using a marginal particle filter (PF). The combine step in turn uses parallel transport to build Gaussian parametric approximations on a common tangent space to the spherical manifold. Performance results are compared to those of competing linear diffusion Extended Kalman Filters and non-cooperative PFs.

In this paper, we extend previous particle filtering methods whose states were constrained to the (real) Stiefel manifold to the complex case. The method is then applied to a Bayesian formulation of the subspace tracking problem. To implement the proposed particle filter, we modify a previous MCMC algorithm so as to simulate from densities defined on the complex manifold. Also, to compute subspace estimates from particle approximations, we extend existing averaging methods to complex Grassmannians. As we verify via numerical simulations, the proposed method is advantageous over traditional SVD-based subspace tracking algorithms for scenarios with low signal-to-noise ratio.

We introduce in this paper novel Bayesian distributed estimation algorithms for tracking the hidden state of a system that evolves on a spherical manifold. In the proposed method, different nodes on a partially-connected network run particle filters (PFs) that assimilate local data and cooperate with their neighbors via Random Exchange (RndEx) and Adapt-then-Combine (ATC) diffusion techniques. To implement the diffusion filters, we introduce parametric approximations that abide by the geometric restrictions imposed on the state variables. Numerical simulations show that the proposed methodology outperforms equivalent non-cooperative PF algorithms and competing extended Kalman Filter (EKF) approaches.

Many problems in statistical signal processing involve tracking the state of a dynamic system that evolves on a Stiefel manifold. To this aim, we introduce in this paper a novel particle filter algorithm that approximates the optimal importance function on the Stiefel manifold and is capable of handling nonlinear observation functions. To sample from the required importance function, we develop adaptations of previous MCMC algorithms. We verify via numerical simulations that, in a scenario with a strongly nonlinear observation model, the new proposed method outperforms existing algorithms that use the prior importance function at the cost, however, of increased computational complexity.

This paper formulates the general Adapt-then-Combine (ATC) and Random Exchange (RndEx) diffusion filters for an arbitrary nonlinear state-space model. Subsequently, we propose two novel marginal Particle Filter implementations of the general ATC and RndEx filters using respectively a pure Sequential Monte Carlo (SMC) strategy and a hybrid Gaussian/SMC methodology. The proposed algorithms are assessed via simulation in a numerical example of cooperative target tracking with received-signal-strength (RSS) sensors.

This paper deals with state inference and parameter identification in Jump Markov Non-Linear System. The state inference problem is solved efficiently using a recently proposed Rao-Blackwellized Particle Filter, where the discrete state is integrated out analytically. Within the RBPF framework, Recursive Maximum Likelihood parameter identification is performed using gradient ascent algorithms. The proposed learning method has the advantage over (online) Expectation Maximization methods, that it can be easily applied to cases where the probability density functions defining the Jump Markov Non-Linear System are not members of the exponential family. Two benchmark problems illustrate the parameter identification performance.

We introduce in this paper the Random Exchange Diffusion Bernoulli Filter (RndEx-BF), which enables joint target detection and tracking by a network of collaborative sensors. RndEx-BF is a fully distributed algorithm that, unlike consensus-based solutions, does not require iterative internode communication between sensor measurements. Internode communication cost is further reduced by a novel hybrid GMM/SMC implementation of the proposed filter. Experimental results show that RndEx-BF approaches the performance of a flooding-based implementation of the optimal centralized Bernoulli filter with much lower bandwidth requirements.

In many estimation problems of interest, the unknown parameters reside on spherical manifolds. As most common filtering algorithms assume that parameters have Gaussian prior distributions, their application to such problems leads to suboptimal performance. In this letter, we propose a model in which the unknown unit-norm parameter vectors have Fisher-Bingham (F-B) prior distributions. We show that if the observations relate to the parameters via Gaussian likelihoods, the F-B priors form a conjugate model that yields closed-form, recursive estimators that naturally take into account the restrictions on the unknowns. We apply this model to a communication setup with multiple gain-controlled FIR frequency-selective channels, deriving a novel maximum a posteriori (MAP) channel parameter estimator and a blind equalizer based on Rao-Blackwellized particle filters. As we verify via Monte Carlo numerical simulations, the F-B model leads to superior performance compared to previous algorithms that adopt mismatched Gaussian prior models.

This paper introduces a novel distributed particle filtering algorithms for the blind equalization of frequency-selective channels in a setup where a single transmitter broadcasts to multiple remote receivers. The algorithm computes particle-independent non-parametric approximations of some posterior probability functions, which are propagated between nodes via minimum-consensus iterations. We verify via numerical simulations that the proposed algorithms exhibit bit error rate (BER) performances markedly superior to that of particle-filtering-based isolated receivers with communication requirements far inferior to that of previous distributed algorithms.

We introduce in this paper a new fully distributed particle filter (PF) algorithm based on random information diffusion that is capable of performing joint multi-frame detection and tracking of a single moving emitter using a cooperative network of multiple received-signal-strength (RSS) sensors. Unlike previous consensus-based distributed PF schemes, the proposed Random Exchange Diffusion Particle Filter (ReDif-PF) does not require multiple iterative inter-node communication in the time interval between the arrival of two consecutive sensor measurements. Inter-node communication cost is further reduced by suitable parametric approximations.

We describe in this paper a novel distributed particle filtering algorithm that performs blind equalization of frequency-selective channels in a setup with a single transmitter and multiple receivers. The algorithm employs parallel minimum consensus iterations to determine some a posteriori probability functions, providing equal approximations on all network nodes in a finite, deterministic, network-dependent number of steps. We verify via computer simulations that the new algorithm exhibits a bit error rate (BER) performance similar to that of the centralized particle-filter estimator with communication requirements milder than that of previous approaches, as the new method drops the need to evaluate quantities via average consensus.

We introduce in this paper a novel cooperative particle filter algorithm for tracking a moving emitter using received-signal strength (RSS) measurements with unknown observation noise variance. In the studied scenario, multiple RSS sensors passively observe independently attenuated and perturbed versions of the same broadcast signal transmitted by an emitter which is moving through the sensor field and cooperate to estimate the emitter state. The new algorithm differs from previous methods by employing a parametric approximation to reduce the associated communication burden.

We describe in this paper novel consensus-based distributed particle filtering algorithms which are applied to cooperative blind equalization of frequency-selective channels in a network with one transmitter and multiple receivers. The proposed algorithms employ parallel consensus averaging iterations to evaluate the product of some node-dependent quantities across the receiver network, thus eliminating the need for message broadcasts beyond each receiver's local neighborhood. Additionally, parallel minimum consensus iterations are used to assess the convergence of the quantized consensus averages and ensure accordingly the coherence of particle sets across the different network nodes. We verify via computer simulations that the consensus-based schemes exhibit a small performance gap compared to both centralized and communication-intensive broadcast solutions.

We introduce in this paper a new distributed sequential Monte Carlo (SMC) algorithm for blind equalization of frequency-selective broadcast channels. In the considered setup, multiple receiving nodes sense independently distorted versions of the same broadcast signal and cooperate to recover it. The proposed approach innovates by using parametric approximations based on the Variational Bayes (VB) method that allow the inter-node communication burden to be greatly reduced compared to previous communication-intensive distributed SMC algorithms. We verify via numerical simulations that the proposed method yields better performance than alternative methods that employ ad hoc parametric approximations, while preserving roughly the same computational cost.

We present in this article a novel particle-filter-based blind equalization algorithm suitable for FIR time-varying frequency-selective communication channels corrupted by unknown variance additive Gaussian noise. The proposed method is fully Bayesian, integrating out the unknown parameters via an original recursive method, unlike previous approaches that rely on suboptimal plug-in estimates. We verify via numerical simulations that the proposed method's performance approaches that of the trained MAP equalizer, exceeding that of the linear least squares Kalman equalizer for medium to low noise levels.

We propose in this paper a new particle filtering algorithm for blind equalization of FIR frequency-selective communication channels corrupted by additive Gaussian noise, assuming that both the channel order and noise variance are unknown. The proposed algorithm integrates out analytically the unknown parameters using a modified sequential importance sampling technique. We verify via numerical simulations that the proposed method leads to near optimal performance, greatly outperforming traditional methods under noise variance mismatch.

We present in this paper a modified density-assisted particle filter for indoor mobile robot localization in a situation where the environment map is subject to random uncertainties and is not perfectly known to the tracker. The proposed filter jointly estimates the robot's pose and the environment map parameters combining raw measurements from a range-finding laser scanner and the robot's odometric data. Experiments with real data show promising results even in adverse scenarios with abrupt maneuvers and heavily cluttered environments.

We introduce in this paper an improved particle filter for mobile robot localization using a parametric model of the environment. The proposed filter combines a clutter suppression routine for feature extraction with an optimized importance function and measurement-driven MCMC move steps. The filter is tested with both real and synthetic data and its performance is compared to competing algorithms found in the literature

We present a density-assisted particle filter (DAPF) algorithm for ballistic target tracking with unknown, fixed ballistic coefficient. The proposed algorithm uses an optimized importance function to update the particle population and then utilizes the updated particles and their respective importance weights to build a parametric approximation of the joint posterior probability density function (PDF) of the target state and the unknown ballistic coefficient. A new set of particles is then resampled according to this approximate pdf and propagated to the next iteration of the algorithm. Simulation results confirm previous claims in the literature that DAPFs are viable alternatives for sequential estimation in nonlinear dynamic models with unknown, static parameters.

We present in this paper two improved particle filter algorithms for ballistic target tracking. The first algorithm is a sampling/importance resampling (SIR) filter that uses an optimized importance function plus residual resampling to combat particle degeneracy, and also incorporates a Metropolis-Hastings (MH) move step to reduce particle impoverishment. The second proposed algorithm is an auxiliary particle filter (APF). Both algorithms show good performance results when compared to the ideal posterior Cramer-Rao lower bound for the mean square estimation error.

We introduce in this paper new mixed-state particle filter algorithms for direct target tracking in image sequences in a scenario where the true target template is unknown and changes randomly from frame to frame. We present two versions of the mixed-state particle filter tracker using respectively the sampling/importance resampling (SIR) technique and the alternative auxiliary particle filter (APF) method. Monte Carlo simulation results with heavily cluttered image sequences generated from real infrared airborne radar (IRAR) data show that the proposed algorithms have good performance and compare favorably to an alternative grid-based HMM filter by yielding similar steady-state root mean-square error (RMSE) at a much lower computational cost.

We propose in this letter a new approach to direct target tracking in cluttered image sequences using sequential importance sampling (SIS). We use Gauss-Markov random field modeling to describe the clutter correlation and incorporate the clutter and target signature models into the design of the SIS tracking algorithm. We quantify the performance of the SIS tracker using a simulated image sequence generated from real infrared airborne radar data and compare it to the performance of a grid-based hidden Markov model tracker. Simulation results show good performance for the proposed algorithms in a scenario of very low target-to-clutter ratio.

We present in this paper a clutter adaptive, multiframe Bayesian algorithm for joint detection and tracking of a multiaspect target in cluttered image sequences. The target template is randomly translated, rotated, scaled and sheared from frame to frame. Tracking performance studies with a sequence generated from real data infrared airbone radar (lRAR) imagery show a reduction in the steady-state position estimation error and in the target acquisition time when the Bayes detector/tracker is compared to the association of a bank of matched filter detectors and a linearized Kalman-Bucy tracker.

We introduce a new Bayesian algorithm for joint multiframe detection and tracking of multiaspect targets that move randomly in cluttered digital image sequences. Two versions of the algorithm are derived: a batch Bayes smoother and an on-line Bayes filter. Performance results with a simulated image sequence generated from real infrared airborne radar (IRAR) data show an improvement over the association of a bank of correlation detectors and a Kalman-Bucy tracker in a scenario with a heavily cluttered multiaspect target.

This paper develops the two-dimensional (2D) clutter adaptive, multiframe Bayes detector/tracker for targets with random signature. We model the background Clutter and the target signature as samples of two independent, spatially correlated, 2D noncausal Gauss-Markov random fields (GMrfs). The target's motion is modeled by a 2D hidden Markov model (HMM). We study, through Monte Carlo simulations, the performance of the adaptive multiframe detector/tracker, and show that the performance of the adaptive tracker is very close to the performance of the tracker when the clutter model is perfectly known.

We present a Bayesian algorithm for optimal multiframe detection and tracking of small extended targets in two-dimensional (2D) finite resolution images. The algorithm integrates detection and tracking into a single framework using as data a sequence of cluttered sensor snapshots. Performance studies using Monte Carlo simulations show substantial improvements when the proposed Bayes tracker is compared to the association of a correlation filter and a linearized Kalman-Bucy filter. Likewise, there are significant detection performance gains of up to 6 dB in peak signal-to-noise ratio (PSNR) when the multiframe Bayes detector is compared to a single frame likelihood ratio test (LRT) detector.

We present in this paper a multiframe Bayesian algorithm for the detection and tracking of heavily cluttered rigid bodies with random translational and rotational motion. Monte Carlo simulations with synthetic targets and clutter show that the proposed algorithm achieves substantial performance gains over the common association of a maximum likelihood position estimator and a linearized Kalman-Bucy filter.

We propose an optimal nonlinear Bayesian algorithm for joint detection and tracking of targets that move randomly in cluttered environments. We review the derivation of the optimal Bayesian detector/tracker and present Monte Carlo simulations that benchmark the detection and tracking performances in both spatially correlated and non-Gaussian clutter.