Non-linear filtering of stochastic processes and optimal signal transmission through a feedback channel

1988 ◽  
pp. 95-102
Author(s):  
O. A. Glonti
Keyword(s):  
Stochastic Processes ◽  
Signal Transmission ◽  
Linear Filtering ◽  
Feedback Channel ◽  
Non Linear ◽  
Optimal Signal ◽  
Filtering Of Stochastic Processes

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.

scholarly journals Simulations with Australian dragon lizards suggest movement-based signal effectiveness is dependent on display structure and environmental conditions

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Xue Bian ◽  
Angela Pinilla ◽  
Tom Chandler ◽  
Richard Peters
Keyword(s):  
Research Methods ◽  
Environmental Conditions ◽  
Comparative Studies ◽  
Habitat Structure ◽  
Signal Transmission ◽  
Lizard Species ◽  
Local Adaptations ◽  
Signal Divergence ◽  
Colour Signals ◽  
Optimal Signal

AbstractHabitat-specific characteristics can affect signal transmission such that different habitats dictate the optimal signal. One way to examine how the environment influences signals is by comparing changes in signal effectiveness in different habitats. Examinations of signal effectiveness between different habitats has helped to explain signal divergence/convergence between populations and species using acoustic and colour signals. Although previous research has provided evidence for local adaptations and signal divergence in many species of lizards, comparative studies in movement-based signals are rare due to technical difficulties in quantifying movements in nature and ethical restrictions in translocating animals between habitats. We demonstrate herein that these issues can be addressed using 3D animations, and compared the relative performance of the displays of four Australian lizard species in the habitats of each species under varying environmental conditions. Our simulations show that habitats differentially affect signal performance, and an interaction between display and habitat structure. Interestingly, our results are consistent with the hypothesis that the signal adapted to the noisier environment does not show an advantage in signal effectiveness, but the noisy habitat was detrimental to the performance of all displays. Our study is one of the first studies for movement-based signals that directly compares signal performance in multiple habitats, and our approach has laid the foundation for future investigations in motion ecology that have been intractable to conventional research methods.

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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