scholarly journals Unbiased estimation of the solution to Zakai’s equation

2020 ◽  
Vol 26 (2) ◽  
pp. 113-129
Author(s):  
Hamza M. Ruzayqat ◽  
Ajay Jasra
Keyword(s):  
Continuous Time ◽  
Unbiased Estimation ◽  
Finite Variance ◽  
Linear Filtering ◽  
Multilevel Monte Carlo ◽  
Zakai Equation ◽  
Unbiased Estimators ◽  
First Order ◽  
Multilevel Monte Carlo Method ◽  
Filtering Problem

AbstractIn the following article, we consider the non-linear filtering problem in continuous time and in particular the solution to Zakai’s equation or the normalizing constant. We develop a methodology to produce finite variance, almost surely unbiased estimators of the solution to Zakai’s equation. That is, given access to only a first-order discretization of solution to the Zakai equation, we present a method which can remove this discretization bias. The approach, under assumptions, is proved to have finite variance and is numerically compared to using a particular multilevel Monte Carlo method.

Embedding non-linear filtering in autonomous underwater vehicle dynamics via the Kolmogorov backward equation

2021 ◽  
pp. 014233122110196
Author(s):  
Ravish H. Hirpara ◽  
Shambhu N. Sharma
Keyword(s):  
State Vector ◽  
Autonomous Underwater Vehicle ◽  
Underwater Vehicle ◽  
Linear Filtering ◽  
Homogeneous Markov Process ◽  
Non Linear ◽  
Backward Equation ◽  
Noise Correction ◽  
Ito Process ◽  
Correction Terms

This paper revisits the state vector of an autonomous underwater vehicle (AUV) dynamics coupled with the underwater Markovian stochasticity in the ‘non-linear filtering’ context. The underwater stochasticity is attributed to atmospheric turbulence, planetary interactions, sea surface conditions and astronomical phenomena. In this paper, we adopt the Itô process, a homogeneous Markov process, to describe the AUV state vector evolution equation. This paper accounts for the process noise as well as observation noise correction terms by considering the underwater filtering model. The non-linear filtering of the paper is achieved using the Kolmogorov backward equation and the evolution of the conditional characteristic function. The non-linear filtering equation is the cornerstone formalism of stochastic optimal control systems. Most notably, this paper introduces the non-linear filtering theory into an underwater vehicle stochastic system by constructing a lemma and a theorem for the underwater vehicle stochastic differential equation that were not available in the literature.

A CALIBRATED MODEL SEISMIC SYSTEM

Geophysics ◽  
1972 ◽  
Vol 37 (3) ◽  
pp. 445-455 ◽  
Author(s):  
C. N. G. Dampney ◽  
B. B. Mohanty ◽  
G. F. West
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Elastic Waves ◽  
Critical Examination ◽  
Two Dimensional ◽  
Linear Filtering ◽  
Analog Model ◽  
Basic Assumptions ◽  
Electronic Circuitry ◽  
Seismic System

Simple electronic circuitry and axially polarized ceramic transducers are employed to generate and detect elastic waves in a two‐dimensional analog model. The absence of reverberation and the basic simplicity. of construction underlie the advantages of this system. If the form of the fundamental wavelet in the model itself, as modified by the linear filtering effects of the remainder of the system, can be found, then calibration is achieved. This permits direct comparison of theoretical and experimental seismograms for a given model if its impulse response is known. A technique is developed for calibration and verified by comparing Lamb’s theoretical and experimental seismograms for elastic wave propagation over the edge of a half plate. This comparison also allows a critical examination of the basic assumptions inherent in a model seismic system.

Properties and applications of stochastic processes with stationarynth-order increments

1974 ◽  
Vol 6 (3) ◽  
pp. 512-523 ◽  
Author(s):  
B. Picinbono
Keyword(s):  
Stochastic Processes ◽  
Stationary Process ◽  
General Description ◽  
Linear Filtering ◽  
Stationary Increments ◽  
Physical Problems

Many physical problems are described by stochastic processes with stationary increments. We present a general description of such processes. In particular we give an expression of a process in terms of its increments and we show that there are two classes of processes: diffusion and asymptotically stationary. Moreover, we show that thenth increments are given by a linear filtering of an arbitrary stationary process.

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