Error Analysis on the linear digital average of several consecutive phase code intervals received by a fast moving LORAN receiver

One of the factors affecting the positioning error in Loran-C receivers is the accuracy of measuring the time of receiving the signals required to calculate the time difference. Generally, the third zero crossing of the Loran-C signal is used as the basis for determining the receiving time of the pulse, the accuracy of which is highly dependent on the signal-to-noise ratio. The linear digital average algorithm helps to increase the signal-to-noise ratio by averaging the pulses of the consecutive pulse coding intervals received by the Loran-C receiver. The linear digital average in a high-speed receiver, despite the reduction of noise power, distorts the average pulse due to the delay of the participant's pulses. In other words, in fast receivers, in addition to the signal-to-noise ratio and the envelope-to-cycle difference, its distortion is also an important factor in accuracy of the third zero crossing detection. This paper seeks to analyze the effects of the motion vector of the receiver on linear digital average efficiency and to determine the threshold of the receiver’s velocity to measure the third zero crossing of the average pulse with the desired accuracy. By decomposition of the average pulse into two desirable and undesirable parts, it is getting possible to define the average pulse distortion with known characteristics such as envelope-to-cycle difference and the amplitude attenuation coefficient, and the distortion volume is obtained as a function of velocity vector. The proposed analytical framework is simulated to show the impact of the velocity vector.