The projection operator approach to the Fokker-Planck equation. II. Dichotomic and nonlinear Gaussian noise

1988 ◽  
Vol 52 (3-4) ◽  
pp. 979-1003 ◽  
Author(s):  
Sandro Faetti ◽  
Leone Fronzoni ◽  
Paolo Grigolini ◽  
Vincenzo Palleschi ◽  
Girolamo Tropiano
Keyword(s):  
Gaussian Noise ◽  
Projection Operator ◽  
Planck Equation ◽  
Operator Approach ◽  
Fokker Planck Equation ◽  
Fokker Planck

Cooperative target localization using multiple UAVs with out-of-sequence measurements

2017 ◽  
Vol 89 (1) ◽  
pp. 112-119 ◽  
Author(s):  
Xiaogang Wang ◽  
Wutao Qin ◽  
Yuliang Bai ◽  
Naigang Cui
Keyword(s):  
Time Delay ◽  
Probability Density ◽  
Gaussian Noise ◽  
Nonlinear Filtering ◽  
Planck Equation ◽  
Target Localization ◽  
Content Type ◽  
Fokker Planck Equation ◽  
Delay Measurement ◽  
Fokker Planck

Purpose The time delay would occurs when the measurements of multiple unmanned aerial vehicles (UAVs) are transmitted to the date processing center during cooperative target localization. This problem is often named as the out-of-sequence measurement (OOSM) problem. This paper aims to present a nonlinear filtering based on solving the Fokker–Planck equation to address the issue of OOSM. Design/methodology/approach According to the arrival time of measurement, the proposed nonlinear filtering can be divided into two parts. The non-delay measurement would be fused in the first part, in which the Fokker–Planck equation is utilized to propagate the conditional probability density function in the forward form. The time delay measurement is fused in the second part, in which the Fokker–Planck is used in the backward form approximately. The Bayes formula is applied in both parts during the measurement update. Findings Under the Bayesian filtering framework, this nonlinear filtering is not only suitable for the Gaussian noise assumption but also for the non-Gaussian noise assumption. The nonlinear filtering is applied to the cooperative target localization problem. Simulation results show that the proposed filtering algorithm is superior to the previous Y algorithm. Practical implications In this paper, the research shows that a better performance can be obtained by fusing multiple UAV measurements and treating time delay in measurement with the proposed algorithm. Originality/value In this paper, the OOSM problem is settled based on solving the Fokker–Planck equation. Generally, the Fokker–Planck equation can be used to predict the probability density forward in time. However, to associate the current state with the state related to OOSM, it would be used to propagate the probability density backward either.

scholarly journals GENERALIZED WIENER PROCESS AND KOLMOGOROV'S EQUATION FOR DIFFUSION INDUCED BY NON-GAUSSIAN NOISE SOURCE

2005 ◽  
Vol 05 (02) ◽  
pp. L267-L274 ◽  
Author(s):  
ALEXANDER DUBKOV ◽  
BERNARDO SPAGNOLO
Keyword(s):  
White Noise ◽  
Wiener Process ◽  
Anomalous Diffusion ◽  
Gaussian Noise ◽  
Gaussian White Noise ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Non Gaussian ◽  
Generalized Wiener Process ◽  
Fokker Planck

We show that the increments of generalized Wiener process, useful to describe non-Gaussian white noise sources, have the properties of infinitely divisible random processes. Using functional approach and the new correlation formula for non-Gaussian white noise we derive directly from Langevin equation, with such a random source, the Kolmogorov's equation for Markovian non-Gaussian process. From this equation we obtain the Fokker–Planck equation for nonlinear system driven by white Gaussian noise, the Kolmogorov–Feller equation for discontinuous Markovian processes, and the fractional Fokker–Planck equation for anomalous diffusion. The stationary probability distributions for some simple cases of anomalous diffusion are derived.

Approximate Fokker-Planck equation with colored Gaussian noise

1989 ◽  
Vol 39 (5) ◽  
pp. 2747-2748 ◽  
Author(s):  
A. M. Cetto ◽  
L. de la Peña ◽  
R. M. Velasco
Keyword(s):  
Gaussian Noise ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Colored Gaussian Noise ◽  
Fokker Planck

The projection approach to the Fokker-Planck equation. I. Colored Gaussian noise

1988 ◽  
Vol 52 (3-4) ◽  
pp. 951-978 ◽  
Author(s):  
Sandro Faetti ◽  
Leone Fronzoni ◽  
Paolo Grigolini ◽  
Riccardo Mannella
Keyword(s):  
Gaussian Noise ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Colored Gaussian Noise ◽  
Projection Approach ◽  
Fokker Planck

AN APPLICATION OF FOKKER–PLANCK EQUATION TO JOSEPHSON JUNCTION

1989 ◽  
Vol 9 (1) ◽  
pp. 109-120
Author(s):  
G. Liao ◽  
A.F. Lawrence ◽  
A.T. Abawi
Keyword(s):  
Josephson Junction ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck
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