An Envelope-to-Cycle Difference Compensation Method for eLoran Signals in Seawater Based on a Variable Step Size Least Mean Square Algorithm

The dispersion effect of seawater can cause the envelop distortion of underwater eLoran signals, which causes the envelope-to-cycle difference (ECD) to exceed the standard range. Furthermore, it results in incorrect cycle identification and significant positioning errors. However, few studies have focused on the distortion caused by the dispersion effect. In this study, we propose an accurate underwater eLoran ECD compensation method based on a variable step size least mean square (VSS-LMS) algorithm. First, a systematic modeling approach was employed to investigate the impact of dispersion effects on Loran signals. Second, the VSS-LMS algorithm was introduced to update the filter weight vector in response to discrepancies in the input signal. Finally, the input signal was subjected to an adaptive transversal filtering process, resulting in an output signal that adhered to the specifications of the ECD standard. The efficacy and superiority of the proposed algorithm were demonstrated by experimentation and simulation. When the depth of seawater exceeds 2 m, the ECD value of the original eLoran signal exceeds the standard range, precluding the possibility of cycle identification. However, when the depth of seawater reaches 4 m, the ECD of the signal compensated by the proposed algorithm adaptively compensates for the normal range, thereby enabling the accurate recognition of cycles.