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.

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.

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 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 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.

In this work, we propose new particle filter based blind equalization algorithms for FIR channels subject to additive noise of arbitrary distributions. These algorithms employ artificial evolution methods to jointly generate samples from the missing data and from the unknown channel parameters, which are assumed time-invariant. To achieve these results we introduce a new importance function, which leads to greatly improved performance compared to more obvious alternatives as verified via numerical simulations using Weibull envelope noise processes, in which the performance of the trained MLSE equalizer is approached to a narrow margin

This work introduces the use of particle filters for joint blind equalization/decoding of convolutionally coded signals transmitted over frequency selective channels. As in the equalization-only case, we show how to evaluate the optimal importance function recursively via a bank of Kalman filters. Numerical simulation investigations using both stochastic and deterministic particle selection strategies show the outstanding superiority of the deterministic joint equalization/decoding method over approaches that perform blind equalization using particle filters prior to optimal decoding.