Measuring the Moment and the Magnitude of the Abrupt Change of the Gaussian Process Bandwidth

Abstract

The maximum likelihood algorithm is introduced for measuring the unknown moment of abrupt change and bandwidth jump of a fast-fluctuating Gaussian random process. This algorithm can be technically implemented much simpler than the ones obtained by means of common approaches. The technique for calculating the characteristics of the synthesized measurer is presented and the closed analytical expressions for the conditional biases and variances of the resulting estimates are found using the additive local Markov approximation of the decision statistics. By statistical simulation methods, it is confirmed that the presented measurer is operable, while the theoretical formulas describing its performance well approximate the corresponding experimental data in a wide range of the parameter values of the analyzed random process.

Keywords

• abrupt change of random process
• unknown bandwidth
• maximum likelihood method
• discontinuous parameter
• local markov approximation method
• bias of estimate
• variance of estimate
• statistical simulation