Predictive models for identification of gravitational waves by applying data from LIGO observatory

This paper explores the possibility of identifying gravitational waves by statistically processing data obtained from the experiment performed by the Laser Interferometer Gravitational-Wave Observatory (LIGO observatory). For an analysis of the measurement data arrays, the parameter z from the Doppler formula and the theory of covariance functions has been used. The trend of oscillation vectors of detectors obtained at the Hanford and Livingston observatories was assessed by applying the least square method. In addition, this procedure partially eliminates random errors in the data obtained from measurements carried out by the observatory. Upon assessment of the impact of gravitational waves on the changes in the values of the parameters of interferometer laser beams, the estimates of the auto-covariance and cross-covariance functions of vibration vectors of detectors measured at the observatories were calculated by varying the quantised interval on the time scale. The covariance of algebraic addition of relevant vectors and single vectors was used in the calculation of the estimates of covariance functions. The average value of the parameter z from the Doppler formula was calculated according to the formula created by using the expression of cross-covariance function of algebraic addition Hanford Gravitational Wave-Livingston Gravitational Wave (HGW-LGW) vector and single LGW vector. The speed and the direction of spread of the gravitational waves' component HGW -> LGW in respect of the vector of the gravitational waves were established. The calculations were performed using the author's original software based on MATLAB procedures.