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The sequential Monte Carlo, also called the Bayesian particle filter, approximates a posterior probability density function of a latent target state from noisy sensor measurements using a set of Monte Carlo samples. These samples are predicted using an importance density function and then updated using the Bayes's rule. The updated samples and their corresponding weights provide an estimate of the latent state. The said filtering process is iterated over time for tracking dynamic target states. It is critical to have enough particles in regions of the target state space that contribute to the posterior. The auxiliary and the improved auxiliary particle filters accomplish this by a process that mimics drawing from an importance density that leverages the incoming observation into the sampling step. However these filters are known to fail when the sensor measurements are highly informative and the diffusion over the state transition is large. This paper presents an improvement to the auxiliary particle filter by taking two support points that act as limits in a univariate state space within which particles are samples. The choice of the limits is adaptive. The proposed method is successfully tested using a nonlinear model using simulations. [ABSTRACT FROM AUTHOR]

nimble is an R package for constructing algorithms and conducting inference on hierarchical models. The nimble package provides a unique combination of flexible model specification and the ability to program model-generic algorithms. Specifically, the package allows users to code models in the BUGS language, and it allows users to write algorithms that can be applied to any appropriate model. In this paper, we introduce the nimbleSMC R package. nimbleSMC contains algorithms for state-space model analysis using sequential Monte Carlo (SMC) techniques that are built using nimble. We first provide an overview of state-space models and commonly-used SMC algorithms. We then describe how to build a state-space model in nimble and conduct inference using existing SMC algorithms within nimbleSMC. SMC algorithms within nimbleSMC currently include the bootstrap filter, auxiliary particle filter, ensemble Kalman filter, IF2 method of iterated filtering, and a particle Markov chain Monte Carlo (MCMC) sampler. These algorithms can be run in R or compiled into C++ for more efficient execution. Examples of applying SMC algorithms to linear autoregressive models and a stochastic volatility model are provided. Finally, we give an overview of how model-generic algorithms are coded within nimble by providing code for a simple SMC algorithm. This illustrates how users can easily extend nimble's SMC methods in high-level code.

Copyright of Journal of Signal Processing is the property of Journal of Signal Processing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Multi-target tracking is widely applied in video surveillance systems. As we know, although the standard particle cardinalized probability hypothesis density filter can estimate state of targets, it is difficult to define the proposal distribution function in prediction stage. Since the robust particles cannot be effectively drawn, the actual tracking accuracy should be enhanced. In this paper, an innovative unscented transform–based particle cardinalized probability hypothesis density filter is derived. Considering the different state spaces, we use the auxiliary particle method and then draw robust particles from the modified distributions in order to estimate the position of targets. Simultaneously, we present the recursion of the optimized Kalman gain to improve the general unscented transform for the velocity estimates. Using the track label, we further integrate them in the framework of the jump Markov model. The simulation results show that the proposed filter has advances in the multi-target tracking scenes. Moreover, the experiments indicate that the filter can track mobile targets with satisfactory results. [ABSTRACT FROM AUTHOR]

The Kim filter (KF) approximation is widely used for the likelihood calculation of dynamic linear models with Markov regime-switching parameters. However, despite its popularity, its approximation error has not yet been examined rigorously. Therefore, this study investigates the reliability of the KF approximation for maximum likelihood (ML) and Bayesian estimations. To measure the approximation error, we compare the outcomes of the KF method with those of the auxiliary particle filter (APF). The APF is a numerical method that requires a longer computing time, but its numerical error can be sufficiently minimized by increasing simulation size. According to our extensive simulation and empirical studies, the likelihood values obtained from the KF approximation are practically identical to those of the APF. Furthermore, we show that the KF method is reliable, particularly when regimes are persistent and sample size is small. From the Bayesian perspective, we show that the KF method improves the efficiency of posterior simulation. This study contributes to the literature by providing evidence to justify the use of the KF method in both ML and Bayesian estimations. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Signal Processing is the property of Journal of Signal Processing and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We introduce a new approach to latent state filtering and parameter estimation for a class of stochastic volatility models (SVMs) for which the likelihood function is unknown. The a-stable stochastic volatility model provides a flexible framework for capturing asymmetry and heavy tails, which is useful when modeling financial returns. However, the a-stable distribution lacks a closed form for the probability density function, which prevents the direct application of standard Bayesian filtering and estimation techniques such as sequential Monte Carlo and Markov chain Monte Carlo. To obtain filtered volatility estimates, we develop a novel approximate Bayesian computation (ABC) based auxiliary particle filter, which provides improved performance through better proposal distributions. Further, we propose a new particle based MCMC (PMCMC) method for joint estimation of the parameters and latent volatility states. With respect to other extensions of PMCMC, we introduce an efficient single filter particle Metropolis-within-Gibbs algorithm which can be applied for obtaining inference on the parameters of an asymmetric a-stable stochastic volatility model. We show the increased efficiency in the estimation process through a simulation study. Finally, we highlight the necessity for modeling asymmetric a-stable SVMs through an application to propane weekly spot prices. [ABSTRACT FROM AUTHOR]

We propose approaches to the problem of multi-paths beam tracking in millimeter-wave (mmWave) mobile communications. Precise angle tracking is necessary to take advantage of beamforming technology in this mmWave band. The mobile channel is a highly nonlinear function with respect to the state that comprises the beam angle and the channel path gain. Therefore, the beam angle tracking is challenging and crucial. We propose a couple of particle filtering frameworks for beam tracking and show outperforming result of an auxiliary particle filtering approach over recently proposed tracking approaches. [ABSTRACT FROM AUTHOR]

Autonomous unmanned aerial vehicles (UAVs) require highly reliable navigation information. Generally, navigation systems with the inertial navigation system (INS) and global navigation satellite system (GNSS) have been widely used. However, the GNSS is vulnerable to jamming and spoofing. The terrain referenced navigation (TRN) technique can be used to solve this problem. In this study, to obtain reliable navigation information even if a GNSS is not available or the degree of terrain roughness is not determined, we propose a federated filter based INS/GNSS/TRN integrated navigation system. We also introduce a TRN system that combines batch processing and an auxiliary particle filter to ensure stable flight of UAVs even in a long-term GNSS-denied environment. As an altimeter sensor for the TRN system, an interferometric radar altimeter (IRA) is used to obtain reliable navigation accuracy in high altitude flight. In addition, a parallel computing technique with general purpose computing on graphics processing units (GPGPU) is applied to process a high resolution terrain database and a nonlinear filter in real-time on board. Finally, the performance of the proposed system is verified through software-in-the-loop (SIL) tests and captive flight tests in a GNSS unavailable environment.

State of charge (SOC) estimation of lithium batteries is one of the most important unresolved problems in the field of electric vehicles. Due to the changeable working environment and numerous interference sources on vehicles, it is more difficult to estimate the SOC of batteries. Particle filter is not restricted by the Gaussian distribution of process noise and observation noise, so it is more suitable for the application of SOC estimation. Three main works are completed in this paper by taken LFP (lithium iron phosphate) battery as the research object. Firstly, the first-order equivalent circuit model is adapted in order to reduce the computational complexity of the algorithm. The accuracy of the model is improved by identifying the parameters of the models under different SOC and minimum quadratic fitting of the identification results. The simulation on MATLAB/Simulink shows that the average voltage error between the model simulation and test data was less than 24.3 mV. Secondly, the standard particle filter algorithm based on SIR (sequential importance resampling) is combined with the battery model on the MATLAB platform, and the estimating formula in recursive form is deduced. The test data show that the error of the standard particle filter algorithm is less than 4% and RMSE (root mean square error) is 0.0254. Thirdly, in order to improve estimation accuracy, the auxiliary particle filter algorithm is developed by redesigning the importance density function. The comparative experimental results of the same condition show that the maximum error can be reduced to less than 3.5% and RMSE is decreased to 0.0163, which shows that the auxiliary particle filter algorithm has higher estimation accuracy.

Sequential Monte Carlo algorithms, or particle filters, are Bayesian filtering algorithms, which propagate in time a discrete and random approximation of the a posteriori distribution of interest. Such algorithms are based on importance sampling with a bootstrap resampling step, which aims at struggling against weight degeneracy. However, in some situations (informative measurements, high-dimensional model), the resampling step can prove inefficient. In this paper, we revisit the fundamental resampling mechanism, which leads us back to Rubin's static resampling mechanism. We propose an alternative rejuvenation scheme in which the resampled particles share the same marginal distribution as in the classical setup, but are now independent. This set of independent particles provides a new alternative to compute a moment of the target distribution and the resulting estimate is analyzed through a CLT. We next adapt our results to the dynamic case and propose a particle filtering algorithm based on independent resampling. This algorithm can be seen as a particular auxiliary particle filter algorithm with a relevant choice of the first-stage weights and instrumental distributions. Finally, we validate our results via simulations, which carefully take into account the computational budget. [ABSTRACT FROM PUBLISHER]

In this research, a non-infrastructure-based and low-cost indoor navigation method is proposed through the integration of smartphone built-in microelectromechanical systems (MEMS) sensors and indoor map information using an auxiliary particle filter (APF). A cascade structure Kalman particle filter algorithm is designed to reduce the computational burden and improve the estimation speed of the APF by decreasing its update frequency and the number of particles used in this research. In the lower filter (Kalman filter), zero velocity update and non-holonomic constraints are used to correct the error of the inertial navigation-derived solutions. The innovation of the design lies in the combination of upper filter (particle filter) map-matching and map-aiding methods to further constrain the navigation solutions. This proposed navigation method simplifies indoor positioning and makes it accessible to individual and group users, while guaranteeing the system's accuracy. The availability and accuracy of the proposed algorithm are tested and validated through experiments in various practical scenarios. [ABSTRACT FROM AUTHOR]

Estimating the hidden hemodynamic states that underlie measured blood oxygen level dependent (BOLD) signals is an important model inversion challenge in functional neuroimaging. Various filtering techniques are proposed in the literature. Those are Gaussian type approximated estimation techniques like Extended Kalman filter (EKF), Unscented Kalman filter (UKF), Cubature Kalman filter (CKF) as well as stochastic inference techniques like standard particle filters (PF) and auxiliary particle filter (APF). In this technical note, we compare particle filter type algorithms and Gaussian approximated inference methods. We also implement a particular type of particle filter that approximates the optimal proposal function by the Extended Kalman filter (PF-EKF). We show that the allegation that Extended Kalman type approximated methods are poor in performance is not true. On the contrary, they are better. We tested this assertion under different parameter sets, inputs, a wide range of noise conditions and unknown initial condition. This finding is important for developing fast and accurate alternative model inversion schemes, which is the topic of our subsequent paper. [ABSTRACT FROM AUTHOR]

We propose a new technique for mobile tracking in wideband code-division multiple-access (WCDMA) systems employing multiple receive antennas. To achieve a high estimation accuracy, the algorithm utilizes the time difference of arrival (TDOA) measurements in the forward link pilot channel, the angle of arrival (AOA) measurements in the reverse-link pilot channel, as well as the received signal strength. The mobility dynamic is modelled by a first-order autoregressive (AR) vector process with an additional discrete state variable as the motion offset, which evolves according to a discrete-time Markov chain. It is assumed that the parameters in this model are unknown and must be jointly estimated by the tracking algorithm. By viewing a nonlinear dynamic system such as a jump-Markov model, we develop an efficient auxiliary particle filtering algorithm to track both the discrete and continuous state variables of this system as well as the associated system parameters. Simulation results are provided to demonstrate the excellent performance of the proposed adaptive mobile positioning algorithm in WCDMA networks.

This paper proposes a novel particle filter, namely, the auxiliary iterated extended Kalman particle filter (AIEKPF). To generate the importance density, based on the auxiliary particle filtering (APF) technique the proposed filter uses the iterated extended Kalman filter (IEKF) to integrate the latest measurements into state transition density. This new filter can match the posterior density well, because of the robustness of the APF and the importance density generated by the IEKF. The performance of the presented particle filter is evaluated by two different estimation problems with the noise of Gaussian distribution and Gamma distribution, respectively. The experimental results illustrate that the AIEKPF is superior to the extended Kalman filter and some existing particle filters, such as the standard particle filter (PF), the extended Kalman particle filter, the unscented Kalman particle filter (UKPF) and the auxiliary extended Kalman particle filter, where the number of particles is relatively small, such as 200 and 1,000. However, with an increase of particles, the superiority of the proposed method may decline compared with the PF and APF as showed in the experiments. Also, the AIEKPF has less running time than the UKPF under the same conditions, and from the viewpoint of the average effective sample sizes, it is clear that the AIEKPF has the slightest degeneracy in all filters presented in the experiments. [ABSTRACT FROM AUTHOR]

This article estimates models of high-frequency index futures returns using “around-the-clock” 5-min returns that incorporate the following key features: multiple persistent stochastic volatility factors, jumps in prices and volatilities, seasonal components capturing time of the day patterns, correlations between return and volatility shocks, and announcement effects. We develop an integrated MCMC approach to estimate interday and intraday parameters and states using high-frequency data without resorting to various aggregation measures like realized volatility. We provide a case study using financial crisis data from 2007 to 2009, and use particle filters to construct likelihood functions for model comparison and out-of-sample forecasting from 2009 to 2012. We show that our approach improves realized volatility forecasts by up to 50% over existing benchmarks and is also useful for risk management and trading applications. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

This article describes a sensor network approach to tracking a single object in the presence of static and moving occluders using a network of cameras. To conserve communication bandwidth and energy, we combine a task-driven approach with camera subset selection. In the task-driven approach, each camera first performs simple local processing to detect the horizontal position of the object in the image. This infonnation is then sent to a cluster head to track the object. We assume the locations of the static occluders to be known, but only prior statistics on the positions of the moving occluders are available. A noisy perspective camera measurement model is introduced, where occlusions are captured through occlusion indicator functions. An auxiliary particle filter that incorporates the occluder information is used to track the object. The camera subset selection algorithm uses the minimum mean square error of the best linear estimate of the object position as a metric, and tracking is performed using only the selected subset of cameras. Using simulations and preselected subsets of cameras, we investigate (i) the dependency of the tracker performance on the accuracy of the moving occluder priors, (ii) the trade-off between the number of cameras and the occluder prior accuracy required to achieve a prescribed tracker performance, and (hi) the importance of having occluder priors to the tracker performance as the number of occluders increases. We find that computing moving occluder priors may not be worthwhile, unless it can be obtained cheaply and to high accuracy. We also investigate the effect of dynamically selecting the subset of camera nodes used in tracking on the tracking performance. We show through simulations that a greedy selection algorithm performs close to the brute-force method and outperforms other heuristics, and the performance achieved by greedily selecting a small fraction of the cameras is close to that of using all the cameras. [ABSTRACT FROM AUTHOR]

This is the third part of a three part article series examining methods for Bayesian estimation and tracking. In the first part we presented the general theory of Bayesian estimation where we showed that Bayesian estimation methods can be divided into two very general classes: a class where the observation-conditioned posterior densities are propagated in time through a predictor/corrector method and a second class where the first two moments are propagated in time, with state and observation moment prediction steps followed by state moment update steps that use the latest observations. In the second part, we make the assumption that all densities are Gaussian and, after applying an affine transformation and approximating all nonlinear functions by interpolating polynomials, we recover the sigma point class of Kalman filters. In this third part, we show that approximating a non-Gaussian density by a set of Monte Carlo samples drawn from an importance density leads to particle filter methods, where the posterior density is propagated in time and moment integrals are approximated by sample moments. These methods include the sequential importance sampling bootstrap, optimal, and auxiliary particle filters and more general Monte Carlo particle filters. WIREs Comput Stat 2012 doi: 10.1002/wics.1210 For further resources related to this article, please visit the WIREs website [ABSTRACT FROM AUTHOR]

We compare two Monte Carlo (MC) procedures, sequential importance sampling (SIS) and Markov chain Monte Carlo (MCMC), for making Bayesian inferences about the unknown states and parameters of state–space models for animal populations. The procedures were applied to both simulated and real pup count data for the British grey seal metapopulation, as well as to simulated data for a Chinook salmon population. The MCMC implementation was based on tailor-made proposal distributions combined with analytical integration of some of the states and parameters. SIS was implemented in a more generic fashion. For the same computing time MCMC tended to yield posterior distributions with less MC variation across different runs of the algorithm than the SIS implementation with the exception in the seal model of some states and one of the parameters that mixed quite slowly. The efficiency of the SIS sampler greatly increased by analytically integrating out unknown parameters in the observation model. We consider that a careful implementation of MCMC for cases where data are informative relative to the priors sets the gold standard, but that SIS samplers are a viable alternative that can be programmed more quickly. Our SIS implementation is particularly competitive in situations where the data are relatively uninformative; in other cases, SIS may require substantially more computer power than an efficient implementation of MCMC to achieve the same level of MC error. [ABSTRACT FROM AUTHOR]

To improve tracking accuracy, an adaptive model set interacting multiple model auxiliary particle filter (AMSIMMAPF)algorithm is presented, based on the turning model. The instant angular velocity is identified by the turning model and the model set is updated by this angle. The auxiliary particle filter can avoid weight degeneracy, sample the impoverishment and not restricted by assumptions of linearity or Gaussian noise. So it is selected in the respective model to improve its accuracy. The results of theoretical analysis and simulation verify that the algorithm has more precise filter result and less computation load, when compared with the interacting multiple model particle filter (IMMPF)algorithm. [ABSTRACT FROM AUTHOR]