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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,...
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...
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 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...
This paper reports on the latest efforts of the MARIACHI1 program at Stony Brook University, a unique endeavor that detects and studies ultra-high-energy cosmic rays. This is done by using a novel detection technique based on radar-like technology and traditional scintillator ground detectors. Using the phenomena of cosmic rays and meteors as vehicles to motivate research and educational activities,...
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,...
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...
MARIACHI is a unique endeavor that integrates research at the frontier of our knowledge of the universe, with a broad program of training, education, advancement, and mentoring. Its scientific goal is to detect ultra-high-energy cosmic rays whose origin may provide insight into the evolution of the universe. The detection technique is novel and is based on radar-like technology (where signal processing...
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...
We present particle filtering algorithms for tracking a single target using data from binary sensors. The sensors transmit signals that identify them to a central unit if the target is in their neighborhood; otherwise they do not transmit anything. The central unit uses a model for the target movement in the sensor field and estimates the target's trajectory, velocity, and power using the received...
This paper focuses on particle filtering techniques for tracking a single target using bearings-only measurements. The problem is formulated as fusing information collected from two or more sensors in the presence of additive noise and multiplicative/additive biases. Assuming the biases are nuisance parameters and marginalizing them out from the estimation problem, we propose an algorithm that combines...
Target tracking in wireless sensor networks with constrained resources is a challenging problem. In this paper we consider scenarios where sensors sense an object of interest and process the received measurements using adaptive thresholds to obtain quantized data in the form of two levels. The data are quantized to address resource constraints in sensor networks. The processed data are then sent to...
In this paper we propose a new cost-reference particle filter that exploits the concept of correlative learning. The objective of applying correlative learning is to obtain the centers of probability distributions that are used for particle generation. Such distributions should provide particles in regions of the state space that have low costs. The new cost-reference particle filter is compared to...
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