Loran Sky-Ground Wave Separation Using Time-Domain LM Fitting
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Solution Overview
Problem
Existing high-precision sky-ground wave separation methods for Loran systems face challenges in low signal-to-noise ratios and complex calculations, especially when signal multipaths increase, and the Levenberg-Marquart algorithm has not been applied for this purpose.
Innovation Solution
A method using the Levenberg-Marquart algorithm to separate Loran sky and ground waves by generating simulated signals, normalizing them, preprocessing with an initialization parameter, establishing a time-domain mathematical model, and fitting parameters to obtain delays and amplitudes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If frequency domain algorithms (Hybrid-WRELAX, EXIP-WRELAX) are used for sky-ground wave separation, then separation accuracy is improved, but calculation complexity increases significantly when signal multipaths increase
Solution Approach 1:
The patent replaces frequency domain algorithms with a time domain Levenberg-Marquart algorithm. This substitution changes the computational approach from frequency-based iterative methods to time-domain nonlinear least squares fitting, thereby reducing calculation complexity while maintaining separation accuracy
Solution Approach 2:
The patent transforms the separation problem by changing the domain of operation from frequency domain to time domain. By working directly with time-domain signals and applying the Levenberg-Marquart algorithm to fit the received signal model, the method achieves efficient parameter estimation without the computational burden of frequency domain transformations
2Measurement precision
If frequency domain algorithms are used for sky-ground wave separation, then separation accuracy is improved, but performance deteriorates in low signal-to-noise ratio conditions
Solution Approach 1:
The patent substitutes frequency domain methods with a time domain Levenberg-Marquart algorithm that is specifically designed to handle noisy signals. The algorithm's iterative nonlinear least squares approach provides robust parameter estimation even when signal-to-noise ratio is low, thereby improving reliability without sacrificing accuracy
3Measurement precision
If the number of signal multipaths increases, then separation accuracy can be maintained, but calculation process becomes extremely complicated
Solution Approach 1:
The patent replaces computationally intensive frequency domain iterative methods with a time domain Levenberg-Marquart algorithm. This substitution significantly reduces calculation time when handling multiple signal multipaths, as the time domain approach directly fits the signal model without requiring complex frequency domain transformations and iterations
Data Source
AI summary
Provided herein is a method for separating Loran sky and ground waves based on a Levenberg-Marquart algorithm, including: (1) collecting a plurality of Loran sky-ground wave signals followed by normalization to obtain a normalized signal; (2) preprocessing the normalized signal by inverse Fourier transform method to obtain an initialization parameter; (3) establishing a mathematical model for the Loran sky-ground wave signals in time domain; and (4) solving parameters of the mathematical model using the Levenberg-Marquart algorithm to separate the Loran sky and ground waves.