In this paper, we propose Online LASSO - a version of LASSO that is configured for streaming data. In standard LASSO, the penalty parameter is typically chosen by cross-validation, a procedure which requires the entire dataset upfront and repeated fitting. The main contribution of this work is in finding an easy and principled choice for the penalty parameter for every incoming data point, in cases where the input features are uncorrelated. The proposed Online LASSO has several benefits: i) it is memory and time efficient ii) it is easy to implement, iii) it does not require an initial batch of data to start, iv) it does not require any tuning (e.g., step size or tolerance), and finally v) it converges to the performance of the optimal predictor and correct selection of features. We demonstrate these capabilities and compare Online LASSO with standard LASSO as well as other adaptive LASSO variations and provide a discussion on their performances.

While systems analysis has been studied for decades in the context of control theory, it has only been recently used to improve the convergence of Denoising Diffusion Probabilistic Models. This work describes a novel improvement to Third-Order Langevin Dynamics (TOLD), a recent diffusion method that performs better than its predecessors. This improvement, abbreviated TOLD++, is carried out by critically damping the TOLD forward transition matrix similarly to Dockhorn’s Critically-Damped Langevin Dynamics (CLD). Specifically, it exploits eigen-analysis of the forward transition matrix to derive the optimal set of dynamics under the original TOLD scheme. TOLD++ is theoretically guaranteed to converge faster than TOLD, and its faster convergence is verified on the Swiss Roll toy dataset and CIFAR-10 dataset according to the FID metric.

An important and often overlooked aspect of particle filtering methods is the estimation of unknown static parameters. A simple approach for addressing this problem is to augment the unknown static parameters as auxiliary states that are jointly estimated with the time-varying parameters of interest. This can be impractical, especially when the system of interest is high-dimensional. Multiple particle filtering (MPF) methods were introduced to try to overcome the curse of dimensionality by using a "divide and conquer" approach, where the vector of unknowns is partitioned into a set of subvectors, each estimated by a separate particle filter. Each particle filter weighs its own particles by using predictions and estimates communicated from the other filters. Currently, there is no principled way to implement MPF methods where the particle filters share unknown parameters or states. In this work, we propose a fusion strategy to allow for the sharing of unknown static parameters in the MPF setting. Specifically, we study the systems which are separable in states and observations. It is proved that optimal Bayesian fusion can be obtained for state-space models with non-interacting states and observations. Simulations are performed to show that MPF with fusion strategy can provide more accurate estimates within fewer time steps comparing to existing algorithms.

The curse of dimensionality has been a long-standing problem in the field of particle filters (PFs), and prevents their use in real complex systems characterized by large number of unknowns. Recently a two-stage PF (TPF) for high dimensions was proposed, showing promising results with modest number of particles. The TPF modifies the proposal distribution by tempering each state dimension towards the most likely particle proposed and carrying out regular filtering using the constructed proposal. However, it is limited to cases where the measurement equations are completely separable. We propose a new filter inspired by the TPF principle as well as multiple PF (MPF), that can be applied to any setup and that provides a posterior distribution of the tempering coefficient that is updated recursively. Simulations show comparable, and in some cases, even better results than those of a recently proposed improved MPF for high dimensions.

Nonlinear state-space models are powerful tools to describe dynamical structures in complex time series. In a streaming setting where data are processed one sample at a time, simultaneous inference of the state and its nonlinear dynamics has posed significant challenges in practice. We develop a novel online learning framework, leveraging variational inference and sequential Monte Carlo, which enables flexible and accurate Bayesian joint filtering. Our method provides an approximation of the filtering posterior which can be made arbitrarily close to the true filtering distribution for a wide class of dynamics models and observation models. Specifically, the proposed framework can efficiently approximate a posterior over the dynamics using sparse Gaussian processes, allowing for an interpretable model of the latent dynamics. Constant time complexity per sample makes our approach amenable to online learning scenarios and suitable for real-time applications.

Regime-switching state-space models (RS-SSMs) are an important class of statistical models that can be used to represent real-world phenomena. Unlike regular state-space models, RS-SSMs allow for dynamic uncertainty in the state transition and observations distributions, making them much more expressive. Unfortunately, there are no existing Bayesian inference techniques for joint estimation of regimes, states, and model parameters in generic RS-SSMs. In this work, we develop a particle Gibbs sampling algorithm for Bayesian learning in RS-SSMs. We demonstrate the proposed inference approach on a synthetic data experiment related to an ecological application, where the goal is in estimating the abundance and demographic rates of penguins in the Antarctic.

The quality of importance distribution is vital to adaptive importance sampling, especially in high dimensional sampling spaces where the target distributions are sparse and hard to approximate. This requires that the proposal distributions are expressive and easily adaptable. Because of the need for weight calculation, point evaluation of the proposal distributions is also needed. The Gaussian process has been proven to be a highly expressive non-parametric model for conditional density estimation whose training process is also straightforward. In this paper, we introduce a class of adaptive importance sampling methods where the proposal distribution is constructed in a way that Gaussian processes are combined autoregressively. By numerical experiments of sampling from a high dimensional target distribution, we demonstrate that the method is accurate and efficient compared to existing methods.

In this paper we propose a powerful frequency, phase angle, and amplitude estimation solution for an unbalanced three-phase power system based on multiple model adaptive estimation. The proposed model utilizes the existence of a conditionally linear and Gaussian substructure in the power system states by marginalizing out the frequency component. This substructure can be effectively tracked by a bank of Kalman filters where each filter employs a different angular frequency value. Compared to other Bayesian filtering schemes for estimation in three-phase power systems, the proposed model reformulation is simpler, more robust, and more accurate as validated with numerical simulations on synthetic data.

The population Monte Carlo (PMC) algorithm is a popular adaptive importance sampling (AIS) method used for approximate computation of intractable integrals. Over the years, many advances have been made in the theory and implementation of PMC schemes. The mixture PMC (M-PMC) algorithm, for instance, optimizes the parameters of a mixture proposal distribution in a way that minimizes that Kullback-Leibler divergence to the target distribution. The parameters in M-PMC are updated using a single step of expectation maximization (EM), which limits its accuracy. In this work, we introduce a novel M-PMC algorithm that optimizes the parameters of a mixture proposal distribution, where parameter updates are resolved via stochastic optimization instead of EM. The stochastic gradients w.r.t. each of the mixture parameters are approximated using a population of Markov chain Monte Carlo samplers. We validate the proposed scheme via numerical simulations on an example where the considered target distribution is multimodal.

In this paper, we propose a novel Bayesian approach for estimating a gene network’s topology using particle Gibbs sampling. The conditional posterior distributions of the unknowns in a state-space model describing the time evolution of gene expressions are derived and employed for exact Bayesian posterior inference. Specifically, the proposed scheme provides the joint posterior distribution of the unknown gene expressions, the adjacency matrix describing the topology of the network, and the coefficient matrix describing the strength of the gene interactions. We validate the proposed method with numerical simulations on synthetic data experiments.

Altitude estimation is important for successful control and navigation of unmanned aerial vehicles (UAVs). UAVs do not have indoor access to GPS signals and can only use on-board sensors for reliable estimation of altitude. Unfortunately, most existing navigation schemes are not robust to the presence of abnormal obstructions above and below the UAV. In this work, we propose a novel strategy for tackling the altitude estimation problem that utilizes multiple model adaptive estimation (MMAE), where the candidate models correspond to four scenarios: no obstacles above and below the UAV; obstacles above the UAV; obstacles below the UAV; and obstacles above and below the UAV. The principle of Occam's razor ensures that the model that offers the most parsimonious explanation of the sensor data has the most influence in the MMAE algorithm. We validate the proposed scheme on synthetic and real sensor data.

The population Monte Carlo (PMC) algorithm is a powerful adaptive importance sampling (AIS) methodology used for estimating expected values of random quantities w.r.t. some target probability distribution. At each iteration, a Markov transition kernel is used to propagate a set of particles. Importance weights of the particles are computed and then used to resample the particles that are most representative of the target distribution. At the end of the algorithm, the set of all particles and weights can be used to perform estimation. The resampling step is an adaptive mechanism of the PMC algorithm that allows for particles to locate the most significant regions of the sampling space. In this letter, we generalize the adaptation procedure of PMC sampling by providing a perspective based on stochastic optimization rather than resampling. The proposed method is more flexible than standard PMC as it allows the parameter adaptation to be resolved using any stochastic optimization method. We show that under certain conditions, the standard PMC algorithm is a special case of the proposed approach.

Adaptive importance sampling (AIS) methods are a family of algorithms which can be used to approximate Bayesian posterior distributions. Many AIS algorithms exist in the literature, where the differences arise in the manner by which the proposal distribution is adapted at each iteration. The adaptive population importance sampler (APIS), for example, deterministically samples from a mixture distribution and uses the local information given by the samples and weights to adapt the location parameter of each proposal. The update rules by nature are heuristic, but effective, especially in the case that the target posterior is multimodal. In this work, we introduce a novel AIS scheme which incorporates modern techniques in stochastic optimization to improve the methodology for higher-dimensional posterior inference. More specifically, we derive update rules for the parameters of each proposal by means of deterministic mixture sampling and show that the method outperforms other state-of-the-art approaches in high-dimensional scenarios.

Importance sampling (IS) is a Monte Carlo methodology that allows for the approximation of a target distribution using weighted samples generated from another proposal distribution. Adaptive importance sampling (AIS) implements an iterative version of IS, which adapts the parameters of the proposal distribution in order to improve estimation of the target. While the adaptation of the location (mean) of the proposals has been largely studied, an important challenge of AIS relates to the difficulty of adapting the scale parameter (covariance matrix). In the case of weight degeneracy, adapting the covariance matrix using the empirical covariance results in a singular matrix, which leads to a poor performance in subsequent iterations of the algorithm. In this letter, we propose a novel scheme which exploits recent advances in the IS literature to prevent the so-called weight degeneracy. The method efficiently adapts the covariance matrix of a population of proposal distributions and achieves a significant performance improvement in high-dimensional scenarios. We validate the new method through computer simulations.

In this paper we report our efforts to streamline the curriculum of a lecture-based course on signals and systems with exercises using the Matlab computing environment. We use a computer framework to generate individualized variations of problems, which are assigned to teams of students as well as to individual students. Feedback from students revealed that the new components were helpful for better understanding of the materials and hold strong promise in our new approach to interactive and hands-on learning. Furthermore, we discuss an auto-grading system that will provide students with instantaneous feedback and ease the task of evaluating projects in the next offering of the course.

We present a novel Rao-Blackwellized multiple particle filtering method for inference of correlated latent states observed via nonlinear functions. We adopt a state-space framework and model the dynamic correlated states using a mixing matrix, embedded in white Gaussian noise. The critical challenges in practice are the lack of knowledge about the mixing parameters and the possibly large dimensionality of the state. We address these issues by implementing Rao-Blackwellization of the unknown parameters and adopting a divide-and-conquer approach. The former strategy amounts to marginalizing out some of the variables; the latter breaks the space of the system in subsystems, and runs a separate particle filter for each of them. The resulting Rao-Blackwellized multiple particle filtering accurately estimates the correlated latent states, as shown by the provided simulation results.

In this paper, we consider state-space models where the latent processes represent correlated mixtures of fractional Gaussian processes embedded in white Gaussian noises. The observed data are nonlinear functions of the latent states. The fractional Gaussian processes have interesting properties including long-memory, self-similarity and scale-invariance, and thus, are of interest for building models in finance and econometrics. We propose sequential Monte Carlo (SMC) methods for inference of the latent processes where each method is based on different assumptions about the parameters of the state-space model. The methods are extensively evaluated via simulations of the popular stochastic volatility model.

Multiple importance sampling (MIS) methods approximate moments of complicated distributions by drawing samples from a set of proposal distributions. Several ways to compute the importance weights assigned to each sample have been recently proposed, with the so-called deterministic mixture (DM) weights providing the best performance in terms of variance, at the expense of an increase in the computational cost. A recent work has shown that it is possible to achieve a tradeoff between variance reduction and computational effort by performing an a priori random clustering of the proposals (partial DM algorithm). In this paper, we propose a novel “heretical” MIS framework, where the clustering is performed a posteriori with the goal of reducing the variance of the importance sampling weights. This approach yields biased estimators with a potentially large reduction in variance. Numerical examples show that heretical MIS estimators can outperform, in terms of mean squared error, both the standard and the partial MIS estimators, achieving a performance close to that of DM with less computational cost.

This paper presents an analysis on optimal mobile sensor configuration for multiple-target-tracking (MTT) with Received-Signal-Strength-Indicator (RSSI) based measurements. The analysis is based on the underlying assumption that the complexity of this inherently high-dimensional problem is reduced by employing a multi-agent distributed tracking system. The assumed system assigns a single target of interest (TOI) to each agent and treats the remaining targets as interference sources. The measurement interference due to these sources is effectively compensated for by exchanging TOI information between agents, and fusing this information during the estimation process. Proper sensor placement within such an environment represents a unique challenge and optimal solutions are fundamentally different from a conventional MTT scenario. The main results of this paper include formulation and subsequent simplification of the optimality criterion along with a suboptimal solution yielding competitive performance and superior efficiency. Simulation results are presented demonstrating the performance of the proposed solution and comparisons are made to existing techniques.

We report on a university-based pilot initiative to introduce students in grades 9–12 to electrical engineering practices. The after-school program consisted of two modules of four two-hour sessions and targeted students from two different local schools. They were exposed to hands-on electronic activities as well as programming practices related to image processing. The data collected from weekly surveys revealed that students found the program more challenging and engaging as the course progressed and they were motivated to pursue future engineering study. Additional schools in the region have requested the opportunity for their students to participate in the program at the university.

Particle filtering has been widely accepted as an important methodology for processing data represented by state-space models characterized by nonlinearities and/or non-Gaussianities. It is also well documented that particle filtering deteriorates quickly in performance when the dimension of the tracked state becomes large. This limits its application in many science/engineering problems. Previously we have proposed a way of alleviating this deficiency based on the use of multiple particle filtering. According to the approach, a number of particle filters are assigned to track different subsets of the state with time. In this paper, we propose a new method for accurate and efficient implementation of multiple particle filtering. We provide simulation results that demonstrate the performance of the new method.

We investigate the problem of real-time self-tracking of tagged objects in a new system with low-cost “smart” tags. These tiny and battery-less devices will play a pivotal role in the infrastructure of the Internet of Things (IoT). With capabilities of low-power computation and tag-to-tag backscattered communication, no readers will be needed for running the Radio Frequency Identification (RFID) system. In order to allow for low-cost tags, self-tracking has to be performed with simple algorithms while still exhibiting high accuracy. In this paper we propose a linear observation model for which Kalman filtering (KF) is the optimal method. We also consider a nonlinear model for which we apply particle filtering (PF) of reduced complexity as the tracking method. The performance and computational complexity of the different methods are compared by computer simulations.

In many practical scenarios, including those dealing with large data sets, calculating global estimators of unknown variables of interest becomes unfeasible. A common solution is obtaining partial estimators and combining them to approximate the global one. In this paper, we focus on minimum mean squared error (MMSE) estimators, introducing two efficient linear schemes for the fusion of partial estimators. The proposed approaches are valid for any type of partial estimators, although in the simulated scenarios we concentrate on the combination of Monte Carlo estimators due to the nature of the problem addressed. Numerical results show the good performance of the novel fusion methods with only a fraction of the cost of the asymptotically optimal solution.

Multiple importance sampling (MIS) methods use a set of proposal distributions from which samples are drawn. Each sample is then assigned an importance weight that can be obtained according to different strategies. This work is motivated by the trade-off between variance reduction and computational complexity of the different approaches (classical vs. deterministic mixture) available for the weight calculation. A new method that achieves an efficient compromise between both factors is introduced in this letter. It is based on forming a partition of the set of proposal distributions and computing the weights accordingly. Computer simulations show the excellent performance of the associated partial deterministic mixture MIS estimator.

In this paper an analysis is conducted regarding the likelihood function of an RSSI-based sensor measurement that is affected by a target of interest (TOI) and an interfering target source. The interferer's true location is unknown but is assumed to be Gaussian distributed with known parameters. This analysis is motivated by its potential application within a multi-agent distributed tracking system, where each agent is tasked with tracking a single TOI while treating others as sources of interference. By exchanging TOI information, each agent can use the results established here to effectively compensate for “out-of-scope” target interference by fusing this external information. An exact analytical form is established for the aforementioned likelihood and a Gaussian approximation is analytically developed. An application of these results is presented through an example scenario, with computer simulation results demonstrating performance.

In this paper we introduce a new multiple particle filtering approach for problems where the state-space of the system is of high-dimension. We propose to break the space into subspaces and to perform separate particle filtering in each of them. The two critical operations of particle filtering, the particle propagation and weight computation of each particle filter are performed wherever necessary with the aid of parametric distributions received from other subspaces. The proposed method is demonstrated by computer simulations and the results show an excellent performance when compared to other implementations of multiple particle filtering.

Predicting the course of influenza rates is extremely useful for the efficacy of planned vaccination programs. In this paper we address this problem by stating a dynamic state-space model that mathematically describes both the evolution of influenza rates and the observations obtained by a surveillance system. We then propose a prediction method based on particle filtering that accommodates the nonlinear nature of the model. Using real data we estimate the necessary model functions prior to the prediction step. Computer simulations reveal promising results of the proposed method.

This paper deals with the problem of real-time indoor tracking of tagged objects in Ultra High Frequency Radio Frequency Identification systems with asynchronous measurements. A new and more realistic model of the system is proposed, where the probability of detecting a tag by a reader is described by a function of both the distance and the angle between the tag and the reader's antenna. The model also accounts for the possibility of a tag being in a dead-zone where the tag cannot be detected. For tracking, we propose the use of the particle filtering methodology that takes into account the asynchronous nature of the measurements. The parameters for modeling the resulting system are obtained from real-world experiments and the performance of the algorithm is shown by extensive computer simulations.

In this paper we consider the problem of target tracking in a network of mobile agents that receive asynchronous measurements. The agents measure received signal strengths from the target and broadcast the information to the remaining agents engaged in the tracking. We propose several non-centralized schemes based on particle filtering that account for the lack of synchronization. We demonstrate the proposed methods by computer simulations and compare their performance to the synchronous scenario. The obtained results reveal that the proposed strategies efficiently compensate for the asynchronism of the measurements.

This paper reports on the latest efforts of the Center for Science and Mathematics Education and the Department of Electrical and Computer Engineering at Stony Brook University to provide high school students with an early exposure to engineering activities. Several programs, events and activities have been offered over the last few years and here we discuss the Engineering Summer Camp. This two-week residential camp for high school students in their sophomore or junior years exposes them to hands-on electrical and computer engineering research and educational activities. Students participate in exercises that range from fabricating a fiber voice link to developing an embedded processing system for measuring temperature. The purpose of this effort is to attract, inspire and educate engineers of the future.

Chirp signals are usually encountered in target tracking problems including radar and sonar systems. The multimodality characterizing the distribution of the chirp signal parameters makes their estimation very challenging. In this paper we apply marginalized population Monte Carlo (MPMC) sampling to the problem of parameter estimation of chirp signals in noise. MPMC reduces the dimension of the vector of unknowns by marginalizing the complex amplitudes, which are conditionally linear on the chirp rates and frequencies. A Gibbs sampling scheme is combined with the MPMC method to further improve the performance. Computer simulations illustrate the validity of the proposed approach.

This paper analyzes and validates an enhanced implementation of the multiple particle filter that improves its accuracy when applied to high dimensional problems. The algorithm combines the divide et impera philosophy of the multiple particle filter, which avoids the collapse of traditional particle filters, with game theory strategies that provide with a powerful tool to improve the performance. The problem of multiple target tracking with received signal strength measurements is addressed and the results show remarkable improvement over both standard particle filtering and multiple particle filtering.

In this paper we model and simulate a biological system describing the evolution of cancer stem cells into tumors. Starting from some basic hypotheses about the behavior of these cells, we develop a model that mimics the evolution of a system of cancer stem cells and show how random-set-theory naturally leads to a generation algorithm. Computer simulations demonstrate the potential of our approach by using simple random sampling rules and a lattice environment.

In this paper we consider the problem of target tracking in a network of mobile agents. We propose a scheme with agents that are endowed with processing and decision-making capabilities and without a central unit that controls them and/or fuses information. The agents measure received signal strengths from the targets and communicate it to the remaining agents engaged in the tracking. Each agent applies particle filtering for tracking and uses an algorithm for optimal agent deployment for the next time instant. We describe the details of the tracking from its initialization to its completion. We demonstrate the proposed method by computer simulations.

In this paper, we propose a model for proliferation of cancer stem cells and a procedure for estimating the unknowns of the model. Understanding the proliferation of cancer stem cells is critical for the development of anti-cancer therapies. We propose to use a nonlinear and non-Gaussian state-space model for studying the proliferation process. For estimation of the unknowns we apply particle filtering, which is particularly appropriate given the nature of the model. In addition, we deal with a very large dimension of the state-space and very sparse time series of measurements. Computer simulations show promising results in a simple scenario generated with synthetic data.

In signal processing, it is typical to develop or use a method based on a given model. In practice, however, we almost never know the actual model and we hope that the assumed model is in the neighborhood of the true one. If deviations exist, the method may be more or less sensitive to them. Therefore, it is important to know more about this sensitivity, or in other words, how robust the method is to model deviations. To that end, it is useful to have a metric that can quantify the robustness of the method. In this paper we propose a procedure for developing a variety of metrics for measuring robustness. They are based on a discrete random variable that is generated from observed data and data generated according to past data and the adopted model. This random variable is uniform if the model is correct. When the model deviates from the true one, the distribution of the random variable deviates from the uniform distribution. One can then employ measures for differences between distributions in order to quantify robustness. In this paper we describe the proposed methodology and demonstrate it with simulated data.

Population Monte Carlo is a statistical method that is used for generation of samples approximately from a target distribution. The method is iterative in nature and is based on the principle of importance sampling. In this paper, we show that in problems where some of the parameters are conditionally linear on the remaining parameters, we can improve the computational efficiency of population Monte Carlo by generating samples of the nonlinear parameters only and marginalizing the linear parameters. We demonstrate the marginalized population Monte Carlo on the problem of frequency estimation of closely spaced sinusoids.

This paper reports on the latest efforts of the MARIACHI1program at Stony Brook University, a unique endeavor that detects and studies ultra-high-energy cosmic rays. This is done by using a novel detection technique based on radar-like technology and traditional scintillator ground detectors. Using the phenomena of cosmic rays and meteors as vehicles to motivate research and educational activities, innovative hands-on modules in physics, engineering and cyberinfrastructure based on a learning by doing philosophy are offered to high school teachers and students. Participants at all levels are engaged in research projects, seminars, and workshops, where they will learn to use tools needed in MARIACHI by means of mobile technology.

One of the most criticized aspects of particle filtering algorithms is their dependence on model assumptions. However, a rigorous study of the effect of modeling errors on the performance of such algorithms is still missing. In this paper, the problem of using an inaccurate discrete state-space model is considered and a systematic methodology for studying the effects on its performance is proposed. The methodology is based on the use of the Kolmogorov-Smirnov statistic, which in this case is a distance metric between the posterior characterization when respectively correct and incorrect model assumptions are made. An example with functional and distributional inaccuracies is studied.

Advances in the development of models that can satisfactorily describe biochemical networks are extremely valuable for understanding life processes. In order to get full description of such networks, one has to solve the inverse problem, that is, estimate unknowns (rates and populations of various species) or choose models from a set of hypothesized models using experimental data. In this paper we discuss signal processing techniques for resolving the inverse problem of biochemical networks using the stochastic approach based on Bayesian theory. The proposed methods are tested in simple scenarios and the results are promising and suggest application of these methods to more complex networks.

MARIACHI is a unique endeavor that integrates research at the frontier of our knowledge of the universe, with a broad program of training, education, advancement, and mentoring. Its scientific goal is to detect ultra-high-energy cosmic rays whose origin may provide insight into the evolution of the universe. The detection technique is novel and is based on radar-like technology (where signal processing plays a crucial role) and traditional scintillator ground detectors. The wide educational program flows from the research concept and involves students at all levels (high-school, undergraduate and graduate) working with a multidisciplinary team of scientists, engineers and educators.

Cost-reference particle filtering (CRPF) allows for tracking of nonlinear dynamic states without a prior knowledge of the probability distributions of the noises in the state-space representation of the system. In this paper we consider a setup where the system unknowns consist of linear and nonlinear states. We propose an efficient scheme for estimation of the states by combining CRPF with the recursive least square (RLS) algorithm. We applied the method to the problem of target tracking using biased bearing measurements. Simulation results show a very accurate performance of the proposed approach.

In this paper, we present a new method for stochastic simulation of coupled chemical reactions. In this method we obtain recursive expressions for propagating the first two moments of the probability distributions over time. Its advantage over other simulation methods is that it does not require Monte Carlo simulations, and hence it performs several orders of magnitude faster than existing Monte Carlo methods. Simulation results are presented for some examples of coupled first-order reactions.

There are two distinct problems in the stochastic analysis of biochemical networks, and they are known as the forward and inverse problems. Solutions of the former problem are used for simulating a system of molecular species in time according to the random laws that govern the reactions in which the species participate. Solutions of the latter problem provide estimates of the unknowns in the system that is represented by the biochemical network. The estimates are obtained from measurements that are functions of the number of molecules of some of the species. In the two problems, we have underlying assumptions about the probabilistic models of the studied network. In this paper we present two new methods for addressing these problems. For solving the forward problem we propose a method that does not employ Monte Carlo simulations, whereas for solving the inverse problem we use particle filtering.

Particle filtering is a sequential signal processing methodology that uses discrete random measures composed of particles and weights to approximate probability distributions of interest. The quality of approximation depends on many factors including the number of particles used for filtering and the way new particles are generated by the filter. The problem of good approximation becomes increasingly challenging as the dimension of the state space increases. In this paper, we address a possible solution for improved particle filtering in high dimensional cases by using a set of particle filters operating on partitioned subspaces of the complete state space. We provide simulation results that show the feasibility of the proposed approach.

Sensor localization methods based on Monte Carlo sampling approximate the sensor position distributions by a weighted set of samples. These approaches traditionally require complete knowledge of the probabilistic distributions of the uncertainties in the sensor system. In this paper, we propose alternative sampling-based methods which do not require complete knowledge of the probabilistic distributions. The sensor position distributions are represented by a set of samples and costs which are described by spatial parametric regions. Few parameters are needed to characterize these regions, and therefore the amount of information to be transmitted to the rest of the sensors to self-localize is simplified. Computer simulations show that the proposed methods are more robust and less computationally intensive than standard sampling approaches.

Cost-reference particle filtering (CRPF) is a methodology for recursive estimation of hidden states of dynamic systems. It is used for tracking nonlinear states when probabilistic assumptions about the state and observations noises are not made. Recently, we have proposed a CRPF algorithm for systems with conditionally linear states that combines the use of Kalman filtering for the linear states and CRPF for the nonlinear states. We have shown that this combined method yields improved results over the standard CRPF. In this paper, we further extend that approach by relaxing some of the assumptions about the noises in the system. As a result, the only statistical assumption that remains is that the noises are stationary and zero mean. We demonstrate the performance of the proposed method by computer simulations and compare it with standard CRPF, standard particle filtering (SPF), and marginalized particle filtering (MPF).

In many situations, solutions to nonlinear discrete- time filtering problems are available through approximations. Many of these solutions are based on approximating the posterior distributions of the states with Gaussian distributions. In this letter, we compare the performance of Gaussian-based filters including the extended Kalman filter, the unscented Kalman filter, and the Gaussian particle filter. To that end, we measure the distance between the posteriors obtained by these filters and the one estimated by a sequential Monte Carlo (particle filtering) method. As a distance metric, we apply the Kullback-Leibler and X2information measures. Through computer simulations, we rank the performance of the three filters.

We propose a distributed algorithm for sensor localization using beacon nodes. In this algorithm, beacon nodes broadcast distributions which contain information about their location. Nearby sensor nodes with unknown location information use this transmitted information and received beacon signal characteristics to estimate their positions. Sensors that estimate their positions become new beacons. A Monte Carlo method known as Importance Sampling is used for fusing these distributions and for obtaining approximations of the posterior distributions of the sensor locations. We also compute the Bayesian Cramér-Rao bounds for self-localization of sensors and study the impact of the beacons' prior location information and other system parameters. We analyze the performance of the proposed algorithm through computer simulations and compare it with numerically obtained bounds.

In this paper, we consider tracking time-varying number of targets which move along a two-dimensional area monitored by a network of wireless sensors. We propose a novel fusion algorithm based on particle filtering that accounts for both detection of the number of active targets in the field and estimation of their positions and velocities. The method uses measurements collected by acoustic sensors, where the measurements represent superposition of received powers of signals transmitted by the targets. Computer simulations are provided to illustrate the feasibility of the proposed method in scenarios with zero, one, and two targets.

An important application of sensor networks is target tracking and localization. To deal with sensor nodes with limited energy supply and communication band width we propose energy-efficient hierarchical architectures for solving the target tracking problem. In these networks, sensors form clusters and transmit minimal quantized information about a sensed event to a specialized node, known as a cluster head. Cluster heads are equipped with capability of communicating over large distances with a fusion center or a base station. We consider two different hierarchical architectures : (a) the target dynamics are probabilistically estimated at the cluster heads and their statistics combined at the fusion center, and (b) the cluster heads perform simple compression rules on the quantized sensor data and the fusion center estimates the target dynamics using these severely compressed data. Sequential Monte Carlo algorithms for estimation of the target dynamics are used. Through computer simulations the performances of these two architectures are studied.

In this paper, we investigate different variants of the recently proposed cost-reference particle filters (CRPFs) and study their application to the problem of tracking of a high-speed maneuvering target in the two-dimensional space. CRPFs drop all probabilistic assumptions required by conventional particle filters and, as a consequence, lead to practically more robust algorithms. We introduce some suitable and natural modifications of CRPFs in order to increase their efficiency and reduce their computational complexity. Computer simulations are provided to illustrate the performance of the new alternatives.

Recent advances of wireless sensor networks have presented some very interesting problems for signal processing. For practical reasons, many networks are composed of simple sensors that use very little power and do not consume much communication bandwidth. A class of sensors that satisfy these requirements are the tertiary sensors. They report an approaching event with one signal and a receding event with another signal. When the event is out of their range, they do not report anything. In this paper, we apply particle filtering for processing signals from tertiary sensor networks with the purpose of tracking events (targets) within the field of the sensor network. We present an algorithm for tracking and demonstrate its performance by computer simulations.

The recently introduced cost-reference particle filter (CRPF) methodology allows for recursive estimation of unobserved states of dynamic systems without a priori knowledge of probability distributions of the noise in the system. We use CRPFs in problems where we eliminate one more strong assumption about the state space model, the one of knowing the function governing the state evolution. We replace this function by a linearly combined set of basis functions where the linear combination coefficients are unknown. We show how CRPFs can be modified to cope with this scenario and demonstrate their performance for positioning a moving vehicle in a two-dimensional space.

A new approach for the computation of probability distributions for coupled first order chemical reactions is introduced. The approach is based on system theory, where the system states are chemical species and the signals are probabilities. We derive the transfer functions of the so defined systems and show that they can be applied to various reaction environments. The use of block diagrams offers a clear, visual, and convenient way to decompose a complicated reaction system into simpler sub-systems and vice versa. Since the state of the system is defined as a molecule species instead of molecule population, with this method, one can study chemical reactions involving any number of molecules.

Target tracking is a highly nonlinear problem that has been successfully addressed in recent years using sequential Monte Carlo (SMC) methods, usually called particle filters. We investigate the application of a new class of SMC techniques, termed cost reference particle filters (CRPFs), to the tracking of a high-speed maneuvering target. The new CRPF methodology drops all probabilistic assumptions (i.e., prior probabilities, knowledge of noise distributions and likelihood functions) that are common to conventional particle filters and, as a consequence, leads to practically more robust algorithms. The advantage of the proposed CRPF over the standard SMC filter in the context of maneuvering target tracking is illustrated through computer simulations.

In recent years the theory of particle filtering has continued to advance, and it has found increasing use in sequential signal processing. A weakness of particle filtering is that it is inadequate for problems that besides tracking of evolving states require the estimation of constant parameters. In this paper, we propose particle filters that do not have this limitation. We call these filters density assisted particle filters, of which special cases are the recently introduced Gaussian particle filters and Gaussian sum particle filters. An implementation of a density particle filter is shown on a relatively simple but important nonlinear model. Simulations are included that show the performance of this filter.

Accurate estimation of synchronization parameters is a fundamental issue in digital transmission. In this paper, we investigate a novel approach to joint synchronization and blind data detection in frequency non-selective fast fading channels, based on the application of sequential Monte Carlo (SMC) techniques. The algorithm is derived by modeling the transmission process as a dynamic system where the channel parameters and the transmitted symbols are unobserved state variables. The performance of the proposed technique is studied through computer simulations that illustrate the accuracy of timing recovery and the overall performance of the resulting receiver in terms of its symbol error rate (SER).

The paper addresses joint estimation of the timing epoch and detection of the transmitted symbols in a digital communication system. Most timing recovery techniques found in the literature are either approximately or heuristically derived, since optimal estimators are analytically intractable. Our approach to the problem relies on modeling the symbol timing as an autoregressive process. In this way, the digital communication system can be mathematically represented by a dynamic system in state-space form and the sequential Monte Carlo (SMC) methodology can be applied. SMC algorithms are powerful tools for Bayesian estimation that are based on representing the posterior distribution of the system state by a discrete measure with random support. This representation can be updated recursively, as new information becomes available, allowing for optimal estimation of both the transmitted symbols and their timing.

This paper addresses the problem of equalizing Multiple-Input Multiple-Output (MIMO) channels in Space-Time Coded (STC) systems. We propose to apply the Maximum Likelihood (ML) principle in order to compute the coefficients of a multidimensional Decision-Feedback Equalizer (DFE) that generalizes the classical DFE structure to the MIMO case. The equalizer coefficients are numerically computed by means of the Space Alternating Generalized Expectation-maximization (SAGE) algorithm. This algorithm is known to present local convergence problems due to the existence of multiple maxima in the likelihood function. To avoid this limitation, we suggest to incorporate a small number of a priori known symbols into the transmitted data. Since the aim of these symbols is not to improve performance but just to avoid misconvergence, we term the resulting equalizer as semiblind.

This paper addresses the problem of interference suppression in direct sequence code division multiple access (DS CDMA) systems. We propose a novel semiblind decision feedback (DF) receiver based on the maximum likelihood (ML) principle that simultaneously exploits the transmission of training sequences and the statistical information concerning the unknown transmitted symbols. The space alternating generalized expectation maximization (SAGE) algorithm allows an efficient iterative implementation of the receiver. Computer simulations show that the resulting multiuser detector attains practically the same performance as the theoretical DF minimum mean square error (MMSE) receiver.