TY - GEN

T1 - Probability functional of a vector non-Gaussian Markov process

AU - Lyandres, V.

N1 - Publisher Copyright:
© 1999 IEEE.

PY - 1999/1/1

Y1 - 1999/1/1

N2 - A large number of investigations have been carried out on the sufficient statistical characterization of different origins of interference. In some communication, radar and acoustic applications the Gaussian noise model is often not appropriate. For synthesis of an optimal signal detection algorithm we need an adequate statistical description of the interference, but the probability density function (PDF) of any limited dimension only specifies a certain equivalence class of random processes. Their sample paths may be quite different, so such a finite description cannot be considered to be an exhaustive approach. In this regard, it would be very attractive to describe a process by a single "continuous probability density", or a probability functional. In this paper we consider the explicit statistical description of a continuous vector Markov process in the form of its probability functional. Such a process is represented as a solution of a certain system of stochastic differential equations with parameters depending on the probability density function and correlation interval of the process components. Such a generative approach is very attractive as a tool for simulating real noise as it gives the opportunity to describe analytically a correlated non-Gaussian process and since it provides synthesis of optimal signal detection algorithms in the corresponding interference environment.

AB - A large number of investigations have been carried out on the sufficient statistical characterization of different origins of interference. In some communication, radar and acoustic applications the Gaussian noise model is often not appropriate. For synthesis of an optimal signal detection algorithm we need an adequate statistical description of the interference, but the probability density function (PDF) of any limited dimension only specifies a certain equivalence class of random processes. Their sample paths may be quite different, so such a finite description cannot be considered to be an exhaustive approach. In this regard, it would be very attractive to describe a process by a single "continuous probability density", or a probability functional. In this paper we consider the explicit statistical description of a continuous vector Markov process in the form of its probability functional. Such a process is represented as a solution of a certain system of stochastic differential equations with parameters depending on the probability density function and correlation interval of the process components. Such a generative approach is very attractive as a tool for simulating real noise as it gives the opportunity to describe analytically a correlated non-Gaussian process and since it provides synthesis of optimal signal detection algorithms in the corresponding interference environment.

UR - http://www.scopus.com/inward/record.url?scp=85039969732&partnerID=8YFLogxK

U2 - 10.1109/HOST.1999.778735

DO - 10.1109/HOST.1999.778735

M3 - Conference contribution

AN - SCOPUS:85039969732

T3 - Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics, SPW-HOS 1999

SP - 247

EP - 250

BT - Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics, SPW-HOS 1999

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 1999 IEEE Signal Processing Workshop on Higher-Order Statistics, SPW-HOS 1999

Y2 - 14 June 1999 through 16 June 1999

ER -