Sumeetpal S. Singh

Sequential Monte Carlo methods for multitarget filtering with random finite sets

Random finite sets (RFSs) are natural representations of multitarget states and observations that allow multisensor multitarget filtering to fit in the unifying random set framework for data fusion. Although the foundation has been established in the form of finite set statistics (FISST), its relationship to conventional probability is not clear. Furthermore, optimal Bayesian multitarget filtering is not yet practical due to the inherent computational hurdle. Even the probability hypothesis density (PHD) filter, which propagates only the first moment (or PHD) instead of the full multitarget posterior, still involves multiple integrals with no closed forms in general. This article establishes the relationship between FISST and conventional probability that leads to the development of a sequential Monte Carlo (SMC) multitarget filter. In addition, an SMC implementation of the PHD filter is proposed and demonstrated on a number of simulated scenarios. Both of the proposed filters are suitable for problems involving nonlinear nonGaussian dynamics. Convergence results for these filters are also established.

Particle methods for change detection, system identification, and control

Particle methods are a set of powerful and versatile simulation-based methods to perform optimal state estimation in nonlinear non-Gaussian state-space models. The ability to compute the optimal filter is central to solving important problems in areas such as change detection, parameter estimation, and control. Much recent work has been done in these areas. The objective of this paper is to provide a detailed overview of them.

Sequential monte carlo implementation of the phd filter for multi-target tracking

Random finite sets are natural represen- tations of multi-target states and observations that al- low multi-sensor multi-target tmcking to fit in the uni- fying random set framework for Data fision. Although a rigorous foundation has been developed in the form of Finite Set Statistics, optimal Bayesian multi-target filtering is not yet practical. Sequential Monte Carlo (SMC) approzimations of the optimal filter are compu- tationally ezpensive. A practical altemative to the opti- mal filter is the Probability Hypothesis Density (PHD) filter, which propagates the PHD or first moment in- stead of the full multi-target posterior. The propagation of the PHD involves multiple integrals which do not ad- mit closed form. We propose to approzimate the PHD by a set of weighted random samples which are propa- gated over time using a generalised SMC method. The resulting algorithm is very attractive as it is general enough to handle non-linear non-Gaussian dynamics and the computational complezity is independent of the (time-varying) number of targets.

An Overview of Sequential Monte Carlo Methods for Parameter Estimation in General State-Space Models

Abstract Nonlinear non-Gaussian state-space models arise in numerous applications in control and signal processing. Sequential Monte Carlo (SMC) methods, also known as Particle Filters, provide very good numerical approximations to the associated optimal state estimation problems. However, in many scenarios, the state-space model of interest also depends on unknown static parameters that need to be estimated from the data. In this context, standard SMC methods fail and it is necessary to rely on more sophisticated algorithms. The aim of this paper is to present a comprehensive overview of SMC methods that have been proposed to perform static parameter estimation in general state-space models. We discuss the advantages and limitations of these methods.

Tracking an unknown time-varying number of speakers using TDOA measurements: a random finite set approach

Speaker location estimation techniques based on time-difference-of-arrival measurements have attracted much attention recently. Many existing localization ideas assume that only one speaker is active at a time. In this paper, we focus on a more realistic assumption that the number of active speakers is unknown and time-varying. Such an assumption results in a more complex localization problem, and we employ the random finite set (RFS) theory to deal with that problem. The RFS concepts provide us with an effective, solid foundation where the multispeaker locations and the number of speakers are integrated to form a single set-valued variable. By applying a sequential Monte Carlo implementation, we develop a Bayesian RFS filter that simultaneously tracks the time-varying speaker locations and number of speakers. The tracking capability of the proposed filter is demonstrated in simulated reverberant environments

On Particle Methods for Parameter Estimation in State-Space Models

Nonlinear non-Gaussian state-space models are ubiquitous in statistics, econometrics, information engineering and signal processing. Particle methods, also known as Sequential Monte Carlo (SMC) methods, provide reliable numerical approximations to the associated state inference problems. However, in most applications, the state-space model of interest also depends on unknown static parameters that need to be estimated from the data. In this context, standard particle methods fail and it is necessary to rely on more sophisticated algorithms. The aim of this paper is to present a comprehensive review of particle methods that have been proposed to perform static parameter estimation in state-space models. We discuss the advantages and limitations of these methods and illustrate their performance on simple models.

Integrated voice/data call admission control for wireless DS-CDMA systems

This paper addresses the call admission control problem for multiservice wireless code division multiple access (CDMA) cellular systems when the physical layer channel and receiver structure at the base station are taken into account. The call admission problem is formulated as a semi-Markov decision process with constraints on the blocking probabilities and signal-to-interference ratio (SIR). By using previous results in large random matrices, the SIR constraints incorporate linear multiuser detectors and fading channels. We show that the optimal call admission policy can be computed via a linear programming-based algorithm.

Auxiliary Particle Implementation of Probability Hypothesis Density Filter

Optimal Bayesian multi-target filtering is, in general, computationally impractical owing to the high dimensionality of the multi-target state. The probability hypothesis density (PHD) filter propagates the first moment of the multi-target posterior distribution. While this reduces the dimensionality of the problem, the PHD filter still involves intractable integrals in many cases of interest. Several authors have proposed sequential Monte Carlo (SMC) implementations of the PHD filter. However these implementations are the equivalent of the bootstrap particle filter, and the latter is well known to be inefficient. Drawing on ideas from the auxiliary particle filter (APF), we present an SMC implementation of the PHD filter, which employs auxiliary variables to enhance its efficiency. Numerical examples are presented for two scenarios, including a challenging nonlinear observation model.

Simulation-based optimal sensor scheduling with application to observer trajectory planning

Sensor scheduling has been a topic of interest to the target tracking community for some years now. Recently, research into it has enjoyed fresh impetus with the current importance and popularity of applications in Sensor Networks and Robotics. The sensor scheduling problem can be formulated as a controlled Hidden Markov Model. In this paper, we address precisely this problem and consider the case in which the state, observation and action spaces are continuous valued vectors. This general case is important as it is the natural framework for many applications. We present a novel simulation-based method that uses a stochastic gradient algorithm to find optimal actions.1

Adaptive step-size algorithms for blind interference suppression in DS/CDMA systems

This paper develops adaptive step-size blind LMS algorithms and adaptive forgetting factor blind RLS algorithms for code-aided suppression of multiple access interference (MAI) and narrowband interference (NBI) in DS/CDMA systems. These algorithms optimally adapt both the step size (forgetting factor) and the weight vector of the blind linear multiuser detector using the received measurements. Simulations are provided to compare the proposed algorithms with previously studied blind RLS and blind LMS algorithms. They show that the adaptive step-size blind LMS algorithm and adaptive forgetting factor blind RLS algorithm field significant improvements over the standard blind LMS algorithm and blind RLS algorithm in dynamic environments where the number of interferers are time-varying.