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Whenever we apply methods for processing data, we make a number of model assumptions. In reality, these assumptions are not always correct. Robust methods can withstand model inaccuracies, that is, despite some incorrect assumptions they can still produce good results. We often want to know how robust employed methods are. To that end we need to have a yardstick for measuring robustness. In this paper,...
Particle filters have become very popular signal processing tools for problems that involve nonlinear tracking of an unobserved signal of interest given a series of related observations. In this paper we propose a new scheme for particle filtering when the observed data are possibly contaminated with outliers. An outlier is an observation that has been generated by some (unknown) mechanism different...
The time evolution of molecular species in a biochemical system is a discrete-state continuous-time Markov process, which can be described by a chemical master equation. The traditional methods for solving the chemical master equation are based on Monte Carlo methods, such as the stochastic simulation algorithm (SSA). In prior work, we proposed a method for simulation of the time evolution based on...
The idea of monitoring atmospheric events using radio waves has been implemented in the past. The concept has also been employed to detect meteors, that is, ionized trails created by meteors. The approach exploits the property of ionized trails to reflect radio waves and the use of bistatic radar and forward scattering. In this paper we present a setup of a data acquisition (DAQ) system based on software...
In previous literature on cooperative relay communications, the emphasis has been on the study of multi-hop networks. In this paper we address mesh wireless networks that use decode-and-forward relays for which we derive the optimal node decision rules in case of binary transmission. We also obtain the expression for the overall bit error probability. We compare the mesh networks with multi-hop networks...
The traditional methods for solving the chemical master equation are based on Monte Carlo methods, such as the stochastic simulation algorithm (SSA) and its accelerated versions. Methods for modeling biochemical networks based on moment propagation are a relatively unexplored area. In a prior paper, we addressed first-order reactions and presented a new method for propagating the first two moments...
Population Monte Carlo is a statistical method that is used for generation of samples approximately from a target distribution. The method is iterative in nature and is based on the principle of importance sampling. In this paper, we show that in problems where some of the parameters are conditionally linear on the remaining parameters, we can improve the computational efficiency of population Monte...
One of the most basic problems in science and engineering is the assessment of a considered model. The model should describe a set of observed data and the objective is to find ways of deciding if the model should be rejected. It seems that this is an ill-conditioned problem because we have to test the model against all the possible alternative models. In this paper we use the Kolmogorov-Smirnov statistic...
One of the most criticized aspects of particle filtering algorithms is their dependence on model assumptions. However, a rigorous study of the effect of modeling errors on the performance of such algorithms is still missing. In this paper, the problem of using an inaccurate discrete state-space model is considered and a systematic methodology for studying the effects on its performance is proposed...
In this paper, a data-driven extension of the variational algorithm is proposed. Based on a few selected sensors, target tracking is performed distributively without any information about the observation model. Tracking under such conditions is possible if one exploits the information collected from extra inter-sensor RSSI measurements. The target tracking problem is formulated as a kernel matrix...
In the literature, there are claims stating that particle filters cannot be used for high dimensional systems because their random measures degenerate to single particles. While this may be true for standard implementations of particle filtering, it may not be true for alternative implementations. In this paper we build on our previous work for tracking multiple targets with multiple particle filters,...
We introduce a method for sequential minimization of a certain class of (possibly non-convex) cost functions with respect to a high dimensional signal of interest. The proposed approach involves the transformation of the optimization problem into one of estimation in a discrete-time dynamical system. In particular, we describe a methodology for constructing an artificial state-space model which has...
Cost-reference particle filtering is a methodology for tracking unknowns in a system without reliance on probabilistic information about the noises in the system. The methodology is based on analogous principles as the ones of standard particle filtering. Unlike the random measures of standard particle filters that are composed of particles and weights, the random measures of cost-reference particle...
In this paper we address the problem of applying particle filtering to complex systems. In general, we consider complex systems as ones with nonlinearities and high dimensionality of the state space. We examine strategies for filtering where the state space is partitioned into subspaces and where each subspace is explored by its own particle filter. These particle filters are interconnected and communicate...
There are two distinct problems in the stochastic analysis of biochemical networks, and they are known as the forward and inverse problems. Solutions of the former problem are used for simulating a system of molecular species in time according to the random laws that govern the reactions in which the species participate. Solutions of the latter problem provide estimates of the unknowns in the system...
Advances in the development of models that can satisfactorily describe biochemical networks are extremely valuable for understanding life processes. In order to get full description of such networks, one has to solve the inverse problem, that is, estimate unknowns (rates and populations of various species) or choose models from a set of hypothesized models using experimental data. In this paper we...
Sequential Monte Carlo (SMC) methods, also referred to as particle filters, have been successfully applied to a variety of highly nonlinear problems such as target tracking with sensor networks. In this paper, we propose the application of a new class of SMC methods named cost-reference particle filters (CRPFs) to target tracking with mobile sensors. CRPF techniques have been shown to be a flexible...
In this paper, we present a new method for stochastic simulation of coupled chemical reactions. In this method we obtain recursive expressions for propagating the first two moments of the probability distributions over time. Its advantage over other simulation methods is that it does not require Monte Carlo simulations, and hence it performs several orders of magnitude faster than existing Monte Carlo...
Cost-reference particle filtering (CRPF) allows for tracking of nonlinear dynamic states without a prior knowledge of the probability distributions of the noises in the state-space representation of the system. In this paper we consider a setup where the system unknowns consist of linear and nonlinear states. We propose an efficient scheme for estimation of the states by combining CRPF with the recursive...
Standard particle filters have shown excellent performance in many challenging scenarios of target tracking, and therefore they often are the method of choice. In cases when there is no knowledge about the noise distributions in the studied system, one cannot use these methods or will use them with assumptions that in general may lead to very poor results. An alternative to standard particle filters...
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