Petar M. Djuric

Gaussian sum particle filtering

We use the Gaussian particle filter to build several types of Gaussian sum particle filters. These filters approximate the filtering and predictive distributions by weighted Gaussian mixtures and are basically banks of Gaussian particle filters. Then, we extend the use of Gaussian particle filters and Gaussian sum particle filters to dynamic state space (DSS) models with non-Gaussian noise. With non-Gaussian noise approximated by Gaussian mixtures, the non-Gaussian noise models are approximated by banks of Gaussian noise models, and Gaussian mixture filters are developed using algorithms developed for Gaussian noise DSS models. As a result, problems involving heavy-tailed densities can be conveniently addressed. Simulations are presented to exhibit the application of the framework developed herein, and the performance of the algorithms is examined.

Parameter estimation of chirp signals

The problem of the parameter estimation of chirp signals is addressed. Several closely related estimators are proposed whose main characteristics are simplicity, accuracy, and ease of online or offline implementation. For moderately high signal-to-noise ratios they are unbiased and attain the Cramer-Rao bound. Monte Carlo simulations verify the expected performance of the estimators. It should be easy to extend this approach to signals having polynomials of any degree in the exponent. All the derivations will be done under the assumption that the signal-to-noise ratio is sufficiently high. >

Frequency tracking in power networks in the presence of harmonics

Three new techniques for frequency measurement are proposed. The first is a modified zero-crossing method using curve fitting of voltage samples. The second method is based on polynomial fitting of the discrete Fourier transform (DFT) quasi-stationary phasor data for calculation of the rate of change of the positive sequence phase angle. The third method operates on a complex signal obtained by the standard technique of quadrature demodulation. All three methods are characterized by immunity to reasonable amounts of noise and harmonics in power systems. The performance of the proposed techniques is illustrated for several scenarios by computer simulation. >

Resampling algorithms and architectures for distributed particle filters

In this paper, we propose novel resampling algorithms with architectures for efficient distributed implementation of particle filters. The proposed algorithms improve the scalability of the filter architectures affected by the resampling process. Problems in the particle filter implementation due to resampling are described, and appropriate modifications of the resampling algorithms are proposed so that distributed implementations are developed and studied. Distributed resampling algorithms with proportional allocation (RPA) and nonproportional allocation (RNA) of particles are considered. The components of the filter architectures are the processing elements (PEs), a central unit (CU), and an interconnection network. One of the main advantages of the new resampling algorithms is that communication through the interconnection network is reduced and made deterministic, which results in simpler network structure and increased sampling frequency. Particle filter performances are estimated for the bearings-only tracking applications. In the architectural part of the analysis, the area and speed of the particle filter implementation are estimated for a different number of particles and a different level of parallelism with field programmable gate array (FPGA) implementation. In this paper, only sampling importance resampling (SIR) particle filters are considered, but the analysis can be extended to any particle filters with resampling.

Resampling algorithms for particle filters: a computational complexity perspective

Newly developed resampling algorithms for particle filters suitable for real-time implementation are described and their analysis is presented. The new algorithms reduce the complexity of both hardware and DSP realization through addressing common issues such as decreasing the number of operations and memory access. Moreover, the algorithms allow for use of higher sampling frequencies by overlapping in time the resampling step with the other particle filtering steps. Since resampling is not dependent on any particular application, the analysis is appropriate for all types of particle filters that use resampling. The performance of the algorithms is evaluated on particle filters applied to bearings-only tracking and joint detection and estimation in wireless communications. We have demonstrated that the proposed algorithms reduce the complexity without performance degradation.

Target Tracking by Particle Filtering in Binary Sensor Networks

We present particle filtering algorithms for tracking a single target using data from binary sensors. The sensors transmit signals that identify them to a central unit if the target is in their neighborhood; otherwise they do not transmit anything. The central unit uses a model for the target movement in the sensor field and estimates the targets trajectory, velocity, and power using the received data. We propose and implement the tracking by employing auxiliary particle filtering and cost-reference particle filtering. Unlike auxiliary particle filtering, cost-reference particle filtering does not rely on any probabilistic assumptions about the dynamic system. In the paper, we also extend the method to include estimation of constant parameters, and we derive the posterior Cramer-Rao bounds (PCRBs) for the states. We show the performances of the proposed methods by extensive computer simulations and compare them to the derived bounds.

Distributed particle filtering in agent networks: A survey, classification, and comparison

Distributed particle filter (DPF) algorithms are sequential state estimation algorithms that are executed by a set of agents. Some or all of the agents perform local particle filtering and interact with other agents to calculate a global state estimate. DPF algorithms are attractive for large-scale, nonlinear, and non-Gaussian distributed estimation problems that often occur in applications involving agent networks (ANs). In this article, we present a survey, classification, and comparison of various DPF approaches and algorithms available to date. Our emphasis is on decentralized ANs that do not include a central processing or control unit.

Indoor Tracking: Theory, Methods, and Technologies

In the last decade, the research on and the technology for outdoor tracking have seen an explosion of advances. It is expected that in the near future, we will witness similar trends for indoor scenarios where people spend more than 70% of their lives. The rationale for this is that there is a need for reliable and high-definition real-time tracking systems that have the ability to operate in indoor environments, thus complementing those based on satellite technologies, such as the Global Positioning System (GPS). The indoor environments are very challenging, and as a result, a large variety of technologies have been proposed for coping with them, but no legacy solution has emerged. This paper presents a survey on indoor wireless tracking of mobile nodes from a signal processing perspective. It can be argued that the indoor tracking problem is more challenging than the problem on indoor localization. The reason is simple: From a set of measurements, one has to estimate not one location but a series of correlated locations of a mobile node. The paper illustrates the theory, the main tools, and the most promising technologies for indoor tracking. New directions of research are also discussed.

Asymptotic MAP criteria for model selection

The two most popular model selection rules in signal processing literature have been Akaikes (1974) criterion (AIC) and Rissanens (1978) principle of minimum description length (MDL). These rules are similar in form in that they both consist of data and penalty terms. Their data terms are identical, but the penalties are different, MDL being more stringent toward overparameterization. AIC penalizes for each additional model parameter with an equal incremental amount of penalty, regardless of the parameters role in the model, In most of the literature on model selection, MDL appears in a form that also suggests equal penalty for every unknown parameter. This MDL criterion, we refer to as naive MDL. In this paper, we show that identical penalization for every parameter is not appropriate and that the penalty has to depend on the model structure and type of model parameters. The approach to showing this is Bayesian, and it relies on large sample theory. We derive maximum a posteriori (MAP) rules for several different families of competing models and obtain forms that are similar to AIC and naive MDL. For some families, however, we find that the derived penalties are different. In those cases, our extensive simulations show that the MAP rule outperforms AIC and naive MDL.

A model selection rule for sinusoids in white Gaussian noise

The model selection problem for sinusoidal signals has often been addressed by employing the Akaike (1974) information criterion (AIC) and the minimum description length principle (MDL). The popularity of these criteria partly stems from the intrinsically simple means by which they can be implemented. They can, however, produce misleading results if they are not carefully used. The AIC and MDL have a common form in that they comprise two terms, a data term and a penalty term. The data term quantifies the residuals of the model, and the penalty term reflects the desideratum of parsimony. While the data terms of the AIC and MDL are identical, the penalty terms are different. In most of the literature, the AIC and MDL penalties are, however, both obtained by apportioning an equal weight to each additional unknown parameter, be it phase, amplitude, or frequency. By contrast, we demonstrate that the penalties associated with the amplitude and phase parameters should be weighted differently than the penalty attached to the frequencies. Following the Bayesian methodology, we derive a model selection criterion for sinusoidal signals in Gaussian noise which also contains the log-likelihood and the penalty terms. The simulation results disclose remarkable improvement in our selection rule over the commonly used MDL and AIC.