State space method for reducing phase fluctuations for the radio waves travelling through the ionosphere at 26 MHz

In this work one of the most important problems in the radio astronomy has been attacked. In radio astronomy antenna arrays are used with very long baselines in order to obtain good angular resolutions. For the baseline of 3000 km the two element array gives an effect of a parabolic antenna as if it has 3000 km radius. The antennas see different parts of the Ionosphere because of the large distance between the antennas. These different regions seen by the two antennas have different random dynamic structures with a small correlation of these dynamic time varying structures. These different changes in two different regions of the Ionosphere cause different random phase changes of received waves by the antennas. The effects are large for the frequencies at 26 MHz regions. The observations are important at this frequency region for different reasons. Because of the random phase fluctuations of the received waves, random phase drifts of the local oscillators and the limited observation time, the correlation between the signals obtained from the receivers is below the detection level. Therefore, detection becomes even impossible. In this work, the differential ionospheric phase error is modeled as quasi-sinusoidal exponential phase because of the periodic structure of ionospheric irregularity blobs. The differential oscillator drift is modeled as a linear change with a random slope. Finally, the total differential phase error is expressed as a matrix equation with approximate parameters. Applying the recursive Kalman Filter algorithm to the matrix equation the true phase is estimated. With the new phase, the correlation function is reconstructed. This process improved the S/N ratio in great extends. The method has been applied to the radio star 3C144 and very good results have been obtained. Because of improvements in the processing speeds of the computers lately, the method seems to be valuable.