Assessing the quality of parameter estimates for models describing the motion of single molecules in cellular environments is an important problem in fluorescence microscopy. In this work, we consider the fundamental data model, where molecules emit photons at random time instances and these photons arrive at random locations on the detector according to complex point spread functions (PSFs). The randomness and non-Gaussian PSF of the detection process, and the random trajectory of the molecule, make inference challenging. Moreover, the presence of other closely spaced molecules causes further uncertainty in the origin of the measurements, which impacts the statistical precision of the estimates. We quantify the limits of accuracy of model parameter estimates and separation distance between closely spaced molecules (known as the resolution problem) by computing the Cramér--Rao lower bound (CRLB), or equivalently the inverse of the Fisher information matrix (FIM), for the variance of estimates. Results on the CRLB obtained from the fundamental model are crucial, in that they provide a lower bound for more practical scenarios. While analytic expressions for the FIM can be derived for static and deterministically moving molecules, the analytical tools to evaluate the FIM for molecules whose trajectories follow stochastic differential equations are still for the most part missing. We address this by presenting a general sequential Monte Carlo (SMC) based methodology for both parameter inference and computing the desired accuracy limits for nonstatic molecules and a non-Gaussian fundamental detection model. For the first time, we are able to estimate the FIM for stochastically moving molecules observed through the Airy and Born and Wolf detection models. This is achieved by estimating the score and observed information matrix via SMC. We summarize the outcome of our numerical work by delineating the qualitative behaviors for the accuracy limits as functions of various experimental settings like collected photon count, molecule diffusion, etc. We also verify that we can recover known results from the static molecule case.

The particle Gibbs algorithm can be used for Bayesian parameter estimation in Markovian state space models. Sometimes the resulting Markov chains mix slowly when the component particle filter suffers from degeneracy. This effect can be somewhat alleviated using backward simulation. In this paper we show how a simple modification to this scheme, which we refer to as refreshed backward simulation, can further improve the mixing. This works by sampling new state values simultaneously with the corresponding ancestor indexes. Although the necessary conditional distributions cannot be sampled directly, we provide suitable Markov kernels which target them. The efficacy of this new scheme is demonstrated with a simulation example.

Recursive maximum likelihood (RML) is a popular methodology for estimating unknown static parameters in state-space models. We describe how a completely decentralized version of RML can be implemented in dynamic graphical models through the propagation of suitable messages that are exchanged between neighbouring nodes of the graph. The resulting algorithm can be interpreted as a generalization of the celebrated belief propagation algorithm to compute likelihood gradients. This algorithm is applied to solve the sensor registration and localisation problem for sensor networks. An exact implementation is given for dynamic linear Gaussian models without loop. If loops are present, a loopy version of the algorithm is described. For non-linear non Gaussian scenarios, a sequential Monte Carlo (SMC) or particle filter implementation is sketched

In this paper we present a novel optimization method for on-line maximum likelihood estimation (MLE) of the static parameters of a general state space model. Our approach is based on viewing the particle filter as a controlled Markov chain, where the control is the unknown static parameters to be identified. The algorithm relies on the computation of the gradient of the particle filter using a score function approach

Particle filtering techniques are a popular set of simulation-based methods to perform optimal state estimation in nonlinear nonGaussian dynamic models. However, in applications related to control and identification, it is often necessary to be able to compute the derivative of the optimal filter with respect to parameters of the dynamic model. Several methods have already been proposed in the literature. In experiments, the approximation errors increase with the dataset length. We propose here original particle methods to approximate numerically the filter derivative. In simulations, these methods do not suffer from the problem mentioned. Applications to batch and recursive parameter estimation are presented.

Using time-difference-of-arrival (TDOA) measurements to perform speaker localization has received much interest recently. Motivated by the significant progress in TDOA single speaker localization, this paper presents a TDOA multi-speaker location tracking algorithm based on Bayesian particle filtering. The development is based on the random finite set framework, which provides an effective treatment to the problem of an unknown time-varying number of active speakers. The proposed method can be viewed as a generalization of the existing single-speaker particle filter. Using a simulated reverberant room, we demonstrate the tracking capability of the proposed particle filter.

Tracking multiple speakers in an acoustic environment involves jointly estimating the number of speakers and their states. This important problem in signal processing is challenging in theory as well as implementation. The paper presents a novel and fundamentally well-grounded framework for tracking multiple speakers using random finite sets. Simulations are also presented to demonstrate the performance in tracking a randomly varying number of speakers in a reverberant room.

We consider the problem of blind multiuser detection. We adopt a Bayesian approach where unknown parameters are considered random and integrated out. Computing the maximum a posteriori estimate of the input data sequence requires solving a combinatorial optimization problem. We propose here to apply the Cross-Entropy method recently introduced by Rubinstein. The performance of cross-entropy is compared to Markov chain Monte Carlo. For similar Bit Error Rate performance, we demonstrate that Cross-Entropy outperforms a generic Markov chain Monte Carlo method in terms of operation time.

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.

In the discrete-time envelope-constrained filtering problem, the gain of the filter is minimised subject to the constraint that the filter output to a prescribed input fits into a given envelope. A novel adaptive algorithm for solving this problem based on stochastic optimisation is presented. The algorithm is simple to implement on-line and convergence is demonstrated in numerical examples. Under mild regularity assumptions, convergence follows from standard stochastic approximation results.

A novel access control strategy for cellular DS-CDMA networks is proposed within the framework of Markov Decision Processes. This paper considers the scenario where users in the network are partitioned into two groups, realtime and non-realtime; and only non-realtime users may be “access controlled” as they are more delay tolerant. The transmission rate of non-realtime users are then regulated via time-division multiplexing to satisfy the QoS requirements. The ACS proposed is optimal because it maximises the transmission rate of non-realtime users while ensuring that QoS requirement of all users are satisfied.

This paper considers the call admission control problem for multi-service wireless CDMA cellular systems with buffering. The call admission problem is formulated as a semi-Markov decision process with constraints on the blocking probabilities and SIR. By using recent results in large random matrices, the SIR constraints incorporate multi-class voice/data services and fading channels. We show that the optimal call admission policy can be computed via a linear programming based algorithm.

The task of polling a roaming mobile user in a cellular network to determine its location is known as paging and it requires the use of limited wireless resources. Current cellular mobile communication systems use a broadcast (blanket) paging strategy where all the cells in a location area are polled for the mobile station. This is wasteful in resources due to increased signalling load. We formulate the paging problem as an optimal search problem and derive efficient sequential paging strategies for roaming mobile users. Using the theory of partially observed Markov decision processes (POMDP) we design a smart distributor which sequentially pages roaming mobile users to minimise signalling load.

We develop an adaptive forgetting factor blind RLS algorithm for code-aided suppression of multiple access interference (MAI) and narrow-band interference (NBI) in DS/CDMA systems. The algorithm optimally adapts both the forgetting factor and the weight vector of the linear multiuser detector using the received measurements. Simulations show that the proposed algorithm is superior to the blind RLS algorithm in dynamic environments.