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This paper is Part I of a series of two papers where we address sequential estimation of wide-sense stationary autoregressive moving average (ARMA) state processes by particle filtering. In Part I, we present estimation methods for ARMA processes of known model order, where the parameters are first known and then unknown. The driving noise of the ARMA process is Gaussian with unknown variance. We derive the transition density of the ARMA state for settings that correspond to different assumptions of a priori knowledge. Instead of estimating all the unknown parameters of the model, we treat them by Rao-Blackwellization. We propose a particle filtering method, with appropriate variations according to available information, for sequential estimation of the unknown state as it evolves with time. We demonstrate the performance of the proposed methods by extensive computer simulations. [ABSTRACT FROM PUBLISHER]

This paper provides performance bounds for compressed sensing in the presence of Poisson noise using expander graphs. The Poisson noise model is appropriate for a variety of applications, including low-light imaging and digital streaming, where the signal-independent and/or bounded noise models used in the compressed sensing literature are no longer applicable. In this paper, we develop a novel sensing paradigm based on expander graphs and propose a maximum a posteriori (MAP) algorithm for recovering sparse or compressible signals from Poisson observations. The geometry of the expander graphs and the positivity of the corresponding sensing matrices play a crucial role in establishing the bounds on the signal reconstruction error of the proposed algorithm. We support our results with experimental demonstrations of reconstructing average packet arrival rates and instantaneous packet counts at a router in a communication network, where the arrivals of packets in each flow follow a Poisson process. [ABSTRACT FROM AUTHOR]

This paper addresses the out-of-sequence measurement (OOSM) problem for mixed linear/nonlinear state-space models, which is a class of nonlinear models with a tractable, conditionally linear substructure. We develop two novel algorithms that utilize the linear substructure. The first algorithm effectively employs the Rao–Blackwellized particle filtering framework for updating with the OOSMs, and is based on storing only a subset of the particles and their weights over an arbitrary, predefined interval. The second algorithm adapts a backward simulation approach to update with the delayed (out-of-sequence) measurements, resulting in superior tracking performance. Extensive simulation studies show the efficacy of our approaches in terms of computation time and tracking performance. Both algorithms yield estimation improvements when compared with recent particle filter algorithms for OOSM processing; in the considered examples they achieve up to 10% enhancements in estimation accuracy. In some cases, the proposed algorithms even deliver accuracy that is similar to the lower performance bounds. Because the considered setup is common in various estimation scenarios, the developed algorithms enable improvements in different types of filtering applications. [ABSTRACT FROM PUBLISHER]

In this paper, the problem of estimating the unknown degree of sparsity from compressive measurements without the need to carry out a sparse recovery step is investigated. While the sparsity order can be directly inferred from the effective rank of the observation matrix in the multiple snapshot case, this appears to be impossible in the more challenging single snapshot case. It is shown that specially designed measurement matrices allow to rearrange the measurement vector into a matrix such that its effective rank coincides with the effective sparsity order. In fact, it is proven that matrices that are composed of a Khatri–Rao product of smaller matrices generate measurements that allow to infer the sparsity order. Moreover, if some samples are used more than once, one of the matrices needs to be Vandermonde. These structural constraints reduce the degrees of freedom in choosing the measurement matrix, which may incur in a degradation in the achievable coherence. Thus, this paper also addresses suitable choices of the measurement matrices. In particular, Khatri–Rao and Vandermonde matrices are analyzed in terms of their coherence and a new design for Vandermonde matrices that achieves a low coherence is proposed. [ABSTRACT FROM AUTHOR]

The demand for accurate localization in complex environments continues to increase despite the difficulty in extracting positional information from measurements. Conventional range-based localization approaches rely on distance estimates obtained from measurements (e.g., delay or strength of received waveforms). This paper goes one step further and develops localization techniques that rely on all probable range values rather than on a single estimate of each distance. In particular, the concept of soft range information (SRI) is introduced, showing its essential role for network localization. We then establish a general framework for SRI-based localization and develop algorithms for obtaining the SRI using machine learning techniques. The performance of the proposed approach is quantified via network experimentation in indoor environments. The results show that SRI-based localization techniques can achieve performance approaching the Cramér–Rao lower bound and significantly outperform the conventional techniques especially in harsh wireless environments. [ABSTRACT FROM AUTHOR]

This paper investigates the particle filtering problem for a class of nonlinear/non-Gaussian systems under the dynamic event-triggered protocol. In order to avert frequent data transmission and reduce the communication overhead, a dynamic event-triggered transmission mechanism is adopted to decide whether the data should be transmitted or not. We first consider a scenario where all sensor nodes selectively transmit their newly obtained measurements to a central node, and a full likelihood function at the central node is derived by fusing the transmitted measurements and the information embodied in the non-triggered measurements. Based on the derived full likelihood function, a centralized auxiliary particle filtering algorithm is proposed to select those particles that are more likely to match the current measurement information. Next, based on the diffusion strategy, a distributed auxiliary particle filtering algorithm is further developed, where the local measurements and the local posteriors (approximated by the Gaussian mixture models) are exchanged among neighboring nodes under the dynamic event-triggered communication strategy. Finally, the effectiveness of the proposed filtering schemes is demonstrated via Monte Carlo simulations in a target tracking problem with received-signal-strength sensors. [ABSTRACT FROM AUTHOR]

This work presents sequential Bayesian detection and estimation methods for nonlinear dynamic stochastic systems using measurements affected by three sources of uncertainty: stochastic, set-theoretic and data association uncertainty. Following Mahler's framework for information fusion, the paper develops the optimal Bayes filter for this problem in the form of the Bernoulli filter for interval measurements. Two numerical implementations of the optimal filter are developed. The first is the Bernoulli particle filter (PF), which turns out to require a large number of particles in order to achieve a satisfactory performance. For the sake of reduction in the number of particles, the paper also develops an implementation based on box particles, referred to as the Bernoulli Box-PF. A box particle is a random sample that occupies a small and controllable rectangular region of nonzero volume in the target state space. Manipulation of boxes utilizes the methods of interval analysis. The two implementations are compared numerically and found to perform remarkably well: the target is reliably detected and the posterior probability density function of the target state is estimated accurately. The Bernoulli Box-PF, however, when designed carefully, is computationally more efficient. [ABSTRACT FROM AUTHOR]

This paper develops estimators for locating a rigid body using the time measurements, and the Doppler as well if it is moving, between the sensors in the rigid body and a few landmarks outside. The challenge of rigid body localization is that in addition to the position, we are also interested in obtaining the rotation parameters of the rigid body that must belong to the special orthogonal group. The proposed estimators are non-iterative and have two steps: preliminary and refinement. The preliminary step provides a coarse estimate and the refinement step improves the first step estimate to yield an accurate solution. When the rigid body is stationary, we are able to locate the body with accuracy higher than the solutions of comparable complexity found in the literature. When the rigid body is moving, we develop an estimator that contains the additional unknowns of angular and translational velocities. Simulations show that the proposed estimators, in both stationary and moving cases, can approach the Cramer-Rao Lower Bound performance under Gaussian noise over the small error region. [ABSTRACT FROM AUTHOR]

Much effort has been devoted to recovering sparse signals from one-bit measurements in recent years. However, it is still quite challenging to recover signals with high fidelity, which is desired in practical one-bit compressive sensing (1-bit CS) applications. We introduce the notion of Schur-concavity in this paper and propose to construct signals by taking advantage of Schur-Concave functions, which are capable of enhancing sparsity. Specifically, the Schur-concave functions can be employed to measure the degree of concentration, and the sparse solutions are obtained at the minima. As a representative of the Schur-concave family, the normalized $\ell _1$ Shannon entropy function ($\ell _1$ -SEF) is exploited. The resulting optimization problem is nonconvex. Hence, we convert it into a series of weighted ${\ell _1}$ -norm subproblems, which are solved iteratively by a generalized fixed-point continuation algorithm. Numerical results are provided to illustrate the effectiveness and superiority of the proposed 1-bit CS algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of observability of a linear dynamical system from compressive measurements and the knowledge of its external inputs. Observability of a high-dimensional system state in general requires a correspondingly large number of measurements. We show that if the initial state vector admits a sparse representation, the number of measurements can be significantly reduced by using random projections for obtaining the measurements. Our analysis gives sufficient conditions for the restricted isometry property of the observability matrix to hold, which leads to guarantees for the observability of the system. Our results depend only on the properties of system transfer and observation matrices, and are derived using tools from probability theory and compressed sensing. Unlike the prior work in this direction, our results are applicable to systems with an arbitrary nonzero system transfer matrix. Moreover, our results are stronger than the existing results in the regime where they are comparable. [ABSTRACT FROM AUTHOR]

In this paper, a new information fusion and state estimation algorithm is proposed for extended object tracking. An extended object has a spatial extent that is relatively larger than a sensor's resolution, and thus, multiple measurements are obtained from the object at each sensor scan. For example, in lidar-based tracking applications, a car can be considered as an extended object where a lidar sensor measures multiple laser lights reflected from various points on the car's surface. The extended object tracking is a challenging task since multiple measurements from the object need to be systematically assimilated to estimate the shape as well as the kinematic states (e.g., position and velocity) of the object. In particular, the multiple measurements along with sensor-to-object geometry provide positive (where the object exists) and negative (where the object should not exist) information, and these two types of information need to be incorporated in the estimation process. In the proposed algorithm, novel measurement models are developed for each type of information based on Gaussian process regression and virtual measurement generation. Based on those models, the extended object tracking problem is formulated as a Bayesian inference problem for which the unscented Kalman filter is used for its robustness and efficiency. The effectiveness of the proposed algorithm is demonstrated with illustrative car tracking examples. [ABSTRACT FROM AUTHOR]

The problem of the optimal allocation (in the expected mean square error sense) of a measurement budget for particle filtering is addressed. We propose three different optimal intermittent filters, whose optimality criteria depend on the information available at the time of decision making. For the first, the stochastic program filter, the measurement times are given by a policy that determines whether a measurement should be taken based on the measurements already acquired. The second, called the offline filter, determines all measurement times at once by solving a combinatorial optimization program before any measurement acquisition. For the third one, which we call online filter, each time a new measurement is received, the next measurement time is recomputed to take all the information that is then available into account. We prove that in terms of expected mean square error, the stochastic program filter outperforms the online filter, which itself outperforms the offline filter. However, these filters are generally intractable. For this reason, the filter estimate is approximated by a particle filter. Moreover, the mean square error is approximated using a Monte-Carlo approach, and different optimization algorithms are compared to approximately solve the combinatorial programs (a random trial algorithm, greedy forward and backward algorithms, a simulated annealing algorithm, and a genetic algorithm). Finally, the performance of the proposed methods is illustrated on two examples: a tumor motion model and a common benchmark for particle filtering. [ABSTRACT FROM AUTHOR]

In this paper, a new framework for sequential Bayesian estimation in sensor networks is proposed, which consists of two processes: censoring of measurements at local sensors and fusion of both received measurements and missing ones at the fusion center (FC). In our scheme, each local sensor maintains a Kalman filter (KF) for a linear Gaussian system or an extended Kalman filter (EKF) for a nonlinear system and the FC runs a particle filter (PF) to track the system state. Informative measurements are selected for transmission by an innovation based per-sensor censoring process executed at the sensors at each time. Though the less informative measurements are not sent to the FC, their absence still conveys some information, and the proposed scheme exploits such information from the missing messages. Numerical results show that, under the same bandwidth constraint, the proposed scheme outperforms the one that ignores missing data information and the one that selects sensors randomly for information transmission. [ABSTRACT FROM PUBLISHER]

This paper considers the problem of recovering a structured signal from a relatively small number of noisy measurements with the aid of a similar signal which is known beforehand. We propose a new approach to integrate prior information into the standard recovery procedure by maximizing the correlation between the prior knowledge and the desired signal. We then establish performance guarantees (in terms of the number of measurements) for the proposed method under sub-Gaussian measurements. Specific structured signals including sparse vectors, block-sparse vectors, and low-rank matrices are also analyzed. Furthermore, we present an interesting geometrical interpretation for the proposed procedure. Our results demonstrate that if prior information is good enough, then the proposed approach can (remarkably) outperform the standard recovery procedure. Simulations are provided to verify our results. [ABSTRACT FROM AUTHOR]

This paper studies how to optimally capture side information to aid in the reconstruction of high-dimensional signals from low-dimensional random linear and noisy measurements, by assuming that both the signal of interest and the side information signal are drawn from a joint Gaussian mixture model. In particular, we derive sufficient and (occasionally) necessary conditions on the number of linear measurements for the signal reconstruction minimum mean squared error (MMSE) to approach zero in the low-noise regime; moreover, we also derive closed-form linear side information measurement designs for the reconstruction MMSE to approach zero in the low-noise regime. Our designs suggest that a linear projection kernel that optimally captures side information is such that it measures the attributes of side information that are maximally correlated with the signal of interest. A number of experiments both with synthetic and real data confirm that our theoretical results are well aligned with numerical ones. Finally, we offer a case study associated with a panchromatic sharpening (pan sharpening) application in the presence of compressive hyperspectral data that demonstrates that our proposed linear side information measurement designs can lead to reconstruction peak signal-to-noise ratio (PSNR) gains in excess of 2 dB over other approaches in this practical application. [ABSTRACT FROM AUTHOR]

In phase retrieval problems, a signal of interest (SOI) is reconstructed based on the magnitude of a linear transformation of the SOI observed with additive noise. The linear transform is typically referred to as a measurement matrix. Many works on phase retrieval assume that the measurement matrix is a random Gaussian matrix, which, in the noiseless scenario with sufficiently many measurements, guarantees invertability of the transformation between the SOI and the observations, up to an inherent phase ambiguity. However, in many practical applications, the measurement matrix corresponds to an underlying physical setup, and is therefore deterministic, possibly with structural constraints. In this paper, we study the design of deterministic measurement matrices, based on maximizing the mutual information between the SOI and the observations. We characterize necessary conditions for the optimality of a measurement matrix, and analytically obtain the optimal matrix in the low signal-to-noise ratio regime. Practical methods for designing general measurement matrices and masked Fourier measurements are proposed. Simulation tests demonstrate the performance gain achieved by the suggested techniques compared to random Gaussian measurements for various phase recovery algorithms. [ABSTRACT FROM AUTHOR]

The Markov Chain Distributed Particle Filter (MCDPF) is an algorithm for the nodes in a sensor network to cooperatively run a particle filter, based on each sensor making updates to a local particle set using only local measurements, and then having particles exchanged between neighboring sensors based on a Markov chain on the network. This paper extends previously-known almost sure convergence results for the MCDPF to prove that the MCDPF convergences to the optimal filter in mean square as the number of particles and the number of Markov chain steps both go to infinity. The convergence proof derives an explicit error bound, showing that the convergence is inverse square-root in both parameters. A numerical example is provided to support the theoretical result. [ABSTRACT FROM PUBLISHER]

This paper considers the problem of tracking multiple acoustic sources using a single acoustic vector sensor (AVS). Firstly, a particle filtering (PF) approach is developed to track the direction of arrivals of fixed and known number of sources. Secondly, a more realistic tracking scenario which assumes that the number of acoustic sources is unknown and time-varying is considered. A random finite set (RFS) framework is employed to characterize the randomness of the state process, i.e., the dynamics of source motion and the number of active sources, as well as the measurement process. As deriving a closed-form solution for the multi-source probability density is difficult, a particle filtering approach is employed to arrive at a computationally tractable approximation of the RFS densities. The proposed RFS-PF algorithm is able to simultaneously detect and track multiple sources. Simulations under different tracking scenarios demonstrate the ability of the proposed approaches in tracking multiple acoustic sources. [ABSTRACT FROM PUBLISHER]

This paper is concerned with quantifying shift-variance of linear systems with continuous-time input and discrete-time output. We first introduce a notion of \mbi \mu-shift-invariance for the system. It specifies how the system should respond when the input signal is shifted. For generalized sampling processes, the property is characterized by the sampling kernel, and is shown to be equivalent to lack of aliasing and to shiftability. We then define a shift-variance level which describes how far the system can be possibly away from the set of systems that are \mbi \mu-shift-invariant. The level is defined to be the maximum of the induced norms of the commutators of the system and the shift-operators (both continuous-time or discrete-time are necessarily involved). A shift-variance measure is then defined to be the ratio of the shift-variance level to the system norm, further divided by two so that the measure is between zero and unity. For generalized sampling, we obtain analytical formulas for the shift-variance level and the shift-variance measure. The results allow us to analyze the shift-variance of, among others, the discrete-time wavelet transform (DWT) and the short-time Fourier transform (STFT). We obtain a simple relation between the shift-variance levels at all scales of the DWT, and show that the shift-variance measures are identical at all scales. We calculate the shift-variance level and the shift-variance measure of some typical DWTs and the STFTs. [ABSTRACT FROM AUTHOR]

The recently emerged compressive sensing (CS) framework aims to acquire signals at reduced sample rates compared to the classical Shannon-Nyquist rate. To date, the CS theory has assumed primarily real-valued measurements; it has recently been demonstrated that accurate and stable signal acquisition is still possible even when each measurement is quantized to just a single bit. This property enables the design of simplified CS acquisition hardware based around a simple sign comparator rather than a more complex analog-to-digital converter; moreover, it ensures robustness to gross nonlinearities applied to the measurements. In this paper we introduce a new algorithm—restricted-step shrinkage (RSS)—to recover sparse signals from 1-bit CS measurements. In contrast to previous algorithms for 1-bit CS, RSS has provable convergence guarantees, is about an order of magnitude faster, and achieves higher average recovery signal-to-noise ratio. RSS is similar in spirit to trust-region methods for nonconvex optimization on the unit sphere, which are relatively unexplored in signal processing and hence of independent interest. [ABSTRACT FROM AUTHOR]

Target tracking is investigated using particle filtering of data collected by distributed sensors. In lieu of a fusion center, local measurements must be disseminated across the network for each sensor to implement a centralized particle filter (PF). However, disseminating raw measurements incurs formidable communication overhead as large volumes of data are collected by the sensors. To reduce this overhead and thus enable distributed PF implementation, the present paper develops a set-membership constrained (SMC) PF approach that i) exhibits performance comparable to the centralized PF; ii) requires only communication of particle weights among neighboring sensors; and iii) can afford both consensus-based and incremental averaging implementations. These attractive attributes are effected through a novel adaptation scheme, which is amenable to simple distributed implementation using min- and max-consensus iterations. The resultant SMC-PF exhibits high gain over the bootstrap PF when the likelihood is peaky, but not in the tail of the prior. Simulations corroborate that for a fixed number of particles, and subject to peaky likelihood conditions, SMC-PF outperforms the bootstrap PF, as well as recently developed distributed PF algorithms, by a wide margin. [ABSTRACT FROM AUTHOR]

A key challenge when designing particle filters in high-dimensional state spaces is the construction of a proposal distribution that is close to the posterior distribution. Recent advances in particle flow filters provide a promising avenue to avoid weight degeneracy; particles drawn from the prior distribution are migrated in the state space to the posterior distribution by solving partial differential equations. Numerous particle flow filters have been proposed based on different assumptions concerning the flow dynamics. Approximations are needed in the implementation of all of these filters; as a result, the particles do not exactly match a sample drawn from the desired posterior distribution. Past efforts to correct the discrepancies involve expensive calculations of importance weights. In this paper, we present new filters which incorporate deterministic particle flows into an encompassing particle filter framework. The valuable theoretical guarantees concerning particle filter performance still apply, but we can exploit the attractive performance of the particle flow methods. The filters we describe involve a computationally efficient weight update step, arising because the embedded particle flows we design possess an invertible mapping property. We evaluate the proposed particle flow particle filters’ performance through numerical simulations of a challenging multitarget multisensor tracking scenario and complex high-dimensional filtering examples. [ABSTRACT FROM PUBLISHER]

The curse of outlier measurements in estimation problems is a well-known issue in a variety of fields. Therefore, outlier removal procedures, which enables the identification of spurious measurements within a set, have been developed for many different scenarios and applications. In this paper, we propose a statistically motivated outlier removal algorithm for time differences of arrival (TDOAs), or equivalently range differences (RD), acquired at sensor arrays. The method exploits the TDOA-space formalism and works by only knowing relative sensor positions. As the proposed method is completely independent from the application for which measurements are used, it can be reliably used to identify outliers within a set of TDOA/RD measurements in different fields (e.g., acoustic source localization, sensor synchronization, radar, remote sensing, etc.). The proposed outlier removal algorithm is validated by means of synthetic simulations and real experiments. [ABSTRACT FROM PUBLISHER]

This paper studies the classification of high-dimensional Gaussian signals from low-dimensional noisy, linear measurements. In particular, it provides upper bounds (sufficient conditions) on the number of measurements required to drive the probability of misclassification to zero in the low-noise regime, both for random measurements and designed ones. Such bounds reveal two important operational regimes that are a function of the characteristics of the source: 1) when the number of classes is less than or equal to the dimension of the space spanned by signals in each class, reliable classification is possible in the low-noise regime by using a one-vs-all measurement design; 2) when the dimension of the spaces spanned by signals in each class is lower than the number of classes, reliable classification is guaranteed in the low-noise regime by using a simple random measurement design. Simulation results both with synthetic and real data show that our analysis is sharp, in the sense that it is able to gauge the number of measurements required to drive the misclassification probability to zero in the low-noise regime. [ABSTRACT FROM PUBLISHER]

This paper addresses the problem of simultaneously localizing multiple targets and estimating the positions of the sensors in a sensor network using particle filters. We develop a new technique called multitarget simultaneous localization and mapping (MSLAM) that has better performance than the well-known FastSLAM when there are several targets in the surveillance area. The proposed algorithm is based on the parallel partition particle filter, especially designed for multiple target tracking, and the truncated unscented Kalman filter for updating the sensors' positions. [ABSTRACT FROM PUBLISHER]

This paper proposes a novel framework for delay-tolerant particle filtering that is computationally efficient and has limited memory requirements. Within this framework the informativeness of a delayed (out-of-sequence) measurement (OOSM) is estimated using a lightweight procedure and uninformative measurements are immediately discarded. The framework requires the identification of a threshold that separates informative from uninformative; this threshold selection task is formulated as a constrained optimization problem, where the goal is to minimize state estimation error whilst controlling the computational requirements. We develop an algorithm that provides an approximate solution for the optimization problem. Simulation experiments provide an example where the proposed framework processes less than 40% of all OOSMs with only a small reduction in state estimation accuracy. [ABSTRACT FROM PUBLISHER]

This paper deals with vector (or multivariate) random fields in space and/or time with second-order moments, for which a framework is needed for specifying not only the properties of each component but also the possible cross relationships among the components. We derive basic properties of the covariance matrix function of the vector random field and propose three approaches to construct covariance matrix functions for Gaussian or non-Gaussian random fields. The first approach is to take derivatives of a univariate covariance function, the second one is to work on the univariate random field whose index domain is in a higher dimension and the third one is based on the scale mixture of separable spatio-temporal covariance matrix functions. To illustrate these methods, many parametric or semiparametric examples are formulated. [ABSTRACT FROM AUTHOR]

Posterior Cramér-Rao bounds (CRBs) are derived for the estimation performance of three Gaussian process-based state-space models. The parametric CRB is derived for the case with a parametric state transition and a Gaussian process-based measurement model. We illustrate the theory with a target tracking example and derive both parametric and posterior filtering CRBs for this specific application. Finally, the theory is illustrated with a positioning problem, with experimental data from an office environment where the obtained estimation performance is compared to the derived CRBs. [ABSTRACT FROM AUTHOR]

This work develops robust diffusion recursive least-squares algorithms to mitigate the performance degradation often experienced in networks of agents in the presence of impulsive noise. The first algorithm minimizes an exponentially weighted least-squares cost function subject to a time-dependent constraint on the squared norm of the intermediate update at each node. A recursive strategy for computing the constraint is proposed using side information from the neighboring nodes to further improve the robustness. We also analyze the mean-square convergence behavior of the proposed algorithm. The second proposed algorithm is a modification of the first one based on the dichotomous coordinate descent iterations. It has a performance similar to that of the former, however, its complexity is significantly lower especially when input regressors of agents have a shift structure and it is well suited to practical implementation. Simulations show the superiority of the proposed algorithms over previously reported techniques in various impulsive noise scenarios. [ABSTRACT FROM AUTHOR]

We propose an algorithm for tracking an unknown number of targets based on measurements provided by multiple sensors. Our algorithm achieves low computational complexity and excellent scalability by running belief propagation on a suitably devised factor graph. A redundant formulation of data association uncertainty and the use of “augmented target states” including binary target indicators make it possible to exploit statistical independencies for a drastic reduction of complexity. An increase in the number of targets, sensors, or measurements leads to additional variable nodes in the factor graph but not to higher dimensions of the messages. As a consequence, the complexity of our method scales only quadratically in the number of targets, linearly in the number of sensors, and linearly in the number of measurements per sensor. The performance of the method compares well with that of previously proposed methods, including methods with a less favorable scaling behavior. In particular, our method can outperform multisensor versions of the probability hypothesis density (PHD) filter, the cardinalized PHD filter, and the multi-Bernoulli filter. [ABSTRACT FROM PUBLISHER]

Particle filter (PF) based multi-target tracking (MTT) methods suffer from the curse of dimensionality. Existing strategies to combat this assume posterior independence between target states, in order to then sample targets independently, or to perform joint sampling of closely spaced targets only. When many targets are in proximity, these strategies either perform poorly or are too computationally expensive. We make two contributions towards addressing these limitations. Firstly, we advocate an alternative view of the use of posterior independence which emphasizes the statistical effect of assuming posterior independence on the Monte Carlo (MC) approximation of posterior density. Our analysis suggests that assuming posterior independence can provide a better MC approximation of the prior distribution at the next time, and therefore the posterior at the next time, without regard for how sampling is performed. Secondly, we present a computationally efficient, measurement directed, joint sampling method to cope with the target coupling and measurement ambiguity when targets are near each other. Consequently, we develop a PF which employs posterior independence while sampling targets jointly. This PF is applicable to both the traditional thresholded and track-before-detect style pixelized models. Simulation results for a challenging tracking scenario show that the proposed PF substantially outperforms existing approaches. [ABSTRACT FROM PUBLISHER]

The linear periodically shift variant (LPSV) properties within critically sampled multirate FIR filter banks are generally analysed using deterministic signals. Periodic shift variance is, however, closely related to cyclostationarities introduced by the LPSV system into originally wide sense stationary (WSS) random signals passing through the system. We provide first a unified framework to measure both shift variance of the LPSV system and the amount of cyclostationarity it generates. In this respect, the key concept is the covariance operator associated to a random variable. Cyclostationarity of the variable translates to LPSV properties of the operators, and vice versa. We study several related concepts for the quantification of shift variance in operators and their interpretation in the stochastic setting. We then introduce a new concept called expected shift variance. Fourier-analytic expressions for the various measures are given, and subsequently used to derive explicit formulae for the case of critically sampled two-channel filter banks, as well as sharp upper bounds for unitary two-channel filter banks. Numerical evaluations of the measures show that they provide largely consistent rankings between various critically sampled two-channel filter banks. [ABSTRACT FROM PUBLISHER]

Modeling physical systems often leads to discrete time state-space models with dependent process and measurement noises. For linear Gaussian models, the Kalman filter handles this case, as is well described in literature. However, for nonlinear or non-Gaussian models, the particle filter as described in literature provides a general solution only for the case of independent noise. Here, we present an extended theory of the particle filter for dependent noises with the following key contributions: i) The optimal proposal distribution is derived; ii) the special case of Gaussian noise in nonlinear models is treated in detail, leading to a concrete algorithm that is as easy to implement as the corresponding Kalman filter; iii) the marginalized (Rao–Blackwellized) particle filter, handling linear Gaussian substructures in the model in an efficient way, is extended to dependent noise; and, finally, iv) the parameters of a joint Gaussian distribution of the noise processes are estimated jointly with the state in a recursive way. [ABSTRACT FROM PUBLISHER]

We consider distributed state estimation in a wireless sensor network without a fusion center. Each sensor performs a global estimation task-based on the past and current measurements of all sensors-using only local processing and local communications with its neighbors. In this estimation task, the joint (all-sensors) likelihood function (JLF) plays a central role as it epitomizes the measurements of all sensors. We propose a distributed method for computing, at each sensor, an approximation of the JLF by means of consensus algorithms. This “likelihood consensus” method is applicable if the local likelihood functions of the various sensors (viewed as conditional probability density functions of the local measurements) belong to the exponential family of distributions. We then use the likelihood consensus method to implement a distributed particle filter and a distributed Gaussian particle filter. Each sensor runs a local particle filter, or a local Gaussian particle filter, that computes a global state estimate. The weight update in each local (Gaussian) particle filter employs the JLF, which is obtained through the likelihood consensus scheme. For the distributed Gaussian particle filter, the number of particles can be significantly reduced by means of an additional consensus scheme. Simulation results are presented to assess the performance of the proposed distributed particle filters for a multiple target tracking problem. [ABSTRACT FROM PUBLISHER]

We investigate the behavior of the mean-square error (MSE) of low-rank matrix reconstruction and its special case, matrix completion. We first derive the constrained Cramér–Rao bound (CRB) on the MSE matrix of any locally unbiased estimator, and then analyze the behavior of the constrained CRB when a subset of entries of the underlying matrix is randomly observed. We design an alternating minimization procedure to compute the maximum likelihood estimator (MLE) for the low-rank matrix, and demonstrate through numerical simulations that the performance of the MLE approaches the constrained CRB when the signal-to-noise ratio is high. Applying a Chapman–Robbins type Barankin bound allows us to derive lower bounds on the worst-case scalar MSE. We demonstrate that the worst-case scalar MSE is infinite even if the model is identifiable. However, the infinite scalar MSE is achieved only on a set of low-rank matrices with measure zero. We discuss the implications of these bounds and compare them with the empirical performance of the matrix LASSO estimator and the existing bounds in the literature. [ABSTRACT FROM PUBLISHER]

In this correspondence, we consider reconstruction of time-varying sparse signals in a sensor network with communication constraints. In each time interval, the fusion center transmits the predicted signal estimate and its corresponding error covariance to a selected subset of sensors. The selected sensors compute quantized innovations and transmit them to the fusion center. We present algorithms for sparse signal estimation in the described scenario, analyze their complexity, and demonstrate their near-optimal performance even in the case where sensors transmit a single bit (i.e., the sign of innovation) to the fusion center. [ABSTRACT FROM AUTHOR]

Signal propagation delays are hardly a problem for target tracking with standard sensors such as radar and vision due to the fact that the speed of light is much higher than the speed of the target. This contribution studies the case where the ratio of the target and the propagation speed is not negligible, as in the case of sensor networks with microphones, geophones or sonars for instance, where the signal speed in air, ground and water causes a state dependent and stochastic delay of the observations. The proposed approach utilizes an augmentation of the state vector with the propagation delay in a particle filtering framework to compensate for the negative effects of the delays. The model of the physics rules governing the propagation delays is used in interaction with the target motion model to yield an iterative prediction update step in the particle filter which is called the propagation delayed measurement particle filter (PDM-PF). The performance of PDM-PF is illustrated in a challenging target tracking scenario by making comparisons to alternative particle filters that can be used in similar cases. [ABSTRACT FROM AUTHOR]