Pranab K. Mandal

On the “near-universal proxy” argument for theoretical justification of information-driven sensor management

In sensor management applications, sometimes it may be difficult to find a goal function that meaningfully represents the desired qualities of the estimate, such as when we do not have a clear performance metric or when the computation cost of the goal function is prohibitive. An alternative is to use goal functions based on information theory, such as the Rényi divergence (also called α-divergence). One strong argument in favor of information-driven sensor management is that the Rényi divergence is a “near-universal” proxy for arbitrary task-driven risk functions, implying that these could be replaced by a Rényi divergence-based criterion, and this would usually result in satisfactory performance. In this paper, we present a rebuttal to that argument, which implies that finding theoretical justification for information-driven sensor management still seems to be an open problem.

Particle Based Smoothed Marginal MAP Estimation for General State Space Models

We consider the smoothing problem for a general state space system using sequential Monte Carlo (SMC) methods. The marginal smoother is assumed to be available in the form of weighted random particles from the SMC output. New algorithms are developed to extract the smoothed marginal maximum a posteriori (MAP) estimate of the state from the existing marginal particle smoother. Our method does not need any kernel fitting to obtain the posterior density from the particle smoother. The proposed estimator is then successfully applied to find the unknown initial state of a dynamical system and to address the issue of parameter estimation problem in state space models.

Exact Moment Matching for Efficient Importance Functions in SMC Methods

In this article we introduce a new proposal distribution to be used in conjunction with the sequential Monte Carlo (SMC) method of solving non-linear filtering problem. The proposal distribution incorporates all the information about the to be estimated current state form both the available state and observation processes. This makes it more effective than the state transition density which is more commonly used but ignores the recent observation. Because of its Gaussian nature it is also very easy to implement. We show further that the introduced proposal performs better than other similar importance functions which also incorporate both state and observations.

Acceptance probability of IP-MCMC-PF: revisited

Tracking of multiple objects via particle filtering faces the difficulty of dealing effectively with high dimensional state spaces. One efficient solution consists of integrating Markov chain Monte Carlo (MCMC) sampling at the core of the particle filter. To accomplish such integration, a few different approaches have been proposed in the literature during the last decade. In this paper, we introduce the derivation of the acceptance probability of the interacting population MCMC particle filter (IP-MCMC-PF), one of the most recent approaches to MCMC-based particle filtering. Additionally, we show that the previous expression known in the literature was incomplete.

Parameter estimation in a general state space model from short observation data: A SMC based approach

In this article, we propose a SMC based method for estimating the static parameter of a general state space model. The proposed method is based on maximizing the joint likelihood of the observation and unknown state sequence with respect to both the unknown parameters and the unknown state sequence. This in turn, casts the problem into simultaneous estimations of state and parameter. We show the efficacy of this method by numerical simulation results.

A two-stage particle filter in high dimension

Particle Filter (PF) is a popular sequential Monte Carlo method to deal with non-linear non-Gaussian filtering problems. However, it suffers from the so-called curse of dimensionality in the sense that the required number of particle (needed for a reasonable performance) grows exponentially with the dimension of the system. One of the techniques found in the literature to tackle this is to split the high-dimensional state in to several lower dimensional (sub)spaces and run a particle filter on each subspace, the so-called multiple particle filter (MPF). It is also well-known from the literature that a good proposal density can help to improve the performance of a particle filter. In this article, we propose a new particle filter consisting of two stages. The first stage derives a suitable proposal density that incorporates the information from the measurements. In the second stage a PF is employed with the proposal density obtained in the first stage. Through a simulated example we show that in high-dimensional systems, the proposed two-stage particle filter performs better than the MPF with much fewer number of particles.

A multi-channel multiple access scheme using frequency offsets — Modelling and analysis

A system using frequency offset based transmit-reference (TR) modulation allows multiple nodes to transmit simultaneously and asynchronously without any mutual timing coordination. Thus, such a system provides inherent capabilities for a multiple access in the medium access control (MAC) layer to coordinate the shared use of the common wireless medium among the nodes of the wireless sensor network (WSN). However, certain characteristics of a frequency offset based system limits its performance, for example, the number of available frequency offsets is limited as it depends on several system parameters, and the number of simultaneous communications using different frequency offsets is limited due to inter-user interference. In this paper, we introduce an extended version of the performance model of a basic slotted-Aloha system, that captures the basic phenomena of a multi-channel system with a limited set of channels and a limit to the number of simultaneously used channels. An analysis of this model reveals the potential of a MAC protocol for TR modulation with frequency offsets.

Bayes Formula for Optimal Filter with n-ple Markov Gaussian Errors

We consider the nonlinear filtering problem where the observation noise process is n-ple Markov Gaussian. A Kallianpur–Striebel type Bayes formula for the optimal filter is obtained.