Evaluation of Direction Finding Method using the VLF Data Measured by Akebono

Abstract:

Investigating characteristics of plasma waves observed by scientific satellites in the Earth’s magnetosphere and plasmasphere is the effective key to understand not only generation mechanisms of the waves but also a plasma environment which influences its generation and propagation conditions. In particular, direction finding of plasma waves is most important for understanding these characteristics.

 The wave distribution function (WDF) method was proposed for direction finding of VLF waves in the Earth’s magnetosphere/plasmasphere. This method assumes that the observed signals are combinations of a continuum of superposed plane waves of different frequencies, propagating in different directions with no mutual phase coherence. Under this assumption, the WDF method can estimate a WDF as directional distribution of wave energy density by using a spectral matrix which is composed by cross spectra of observed signals. However, the WDF estimation is ill-posed problem, that is, the solution is not determined uniquely. Models as additional information for WDF must be needed to determine the solution uniquely. Many models have been proposed until now such as the Gaussian distribution model, and Markov random field model. The estimation using these models works well if the sample number of observed signals is large enough to calculate spectral matrices exactly. Actually the number of sample observed by satellites is very few. We therefore must take into account that the spectral matrix which can be used for WDF estimation contains uncertainty.

 First, to treat the uncertainty, we used the Bayesian inference, and we introduced probability density distribution which determines relationship between observed and theoretical spectral matrices. Second, we studied Markov chain Monte Carlo (MCMC) methods as a Bayesian inference method for WDF estimation. The performance of proposed inference methods is evaluated by using computer-generated data. The PFX subsystem of EXOS-D (Akebono) satellite measures two components of electric field and three components of magnetic field in the VLF range using wire and loop antennas, respectively. The measurement of the five components enables us to estimate wave directions without ambiguity. By using the PFX data, we also evaluated the performance of our proposed method.