FDOA Geolocation Using Cross-Correlation Phase Interpolation
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Solution Overview
Problem
Existing methods for determining the location of a radio emitter using frequency and time difference of arrival (FDOA and TDOA) are prone to errors due to uncertainties in leading-edge timing, interpolation between signal samples, and irregularities in pulse rate, which affect the accuracy of geolocation.
Innovation Solution
A method and system that obtain in-phase and quadrature-phase (IQ) samples of a pulsed waveform, determine an approximation of TDOA, perform cross-correlations at multiple delays, refine the TDOA using amplitude interpolation, and calculate the rate of change of cross-correlation phase to accurately determine FDOA, which is then used to geolocate the emitter.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If leading-edge timing methods are used to determine TDOA, then the geolocation process can be initiated, but measurement precision deteriorates due to uncertainties in leading-edge timing
Solution Approach 1:
The patent performs cross-correlation at multiple delays (d_c, d_c+1, d_c-1) before final TDOA determination. This preliminary action of sampling at multiple delay points allows for interpolation to find the precise TDOA, eliminating the uncertainty of simple leading-edge timing while maintaining process efficiency.
Solution Approach 2:
The patent replaces the mechanical/electronic leading-edge detection method with a signal processing approach using cross-correlation and parabolic interpolation. This substitution transforms the TDOA measurement from a direct timing measurement to a calculated value derived from correlation amplitudes, significantly improving precision.
2Productivity
If simple TDOA approximation is used, then processing speed is maintained, but measurement precision deteriorates due to irregularities in pulse rate
Solution Approach 1:
The system performs cross-correlation at three delay points (d_c, d_c+1, d_c-1) as a preliminary step before final TDOA calculation. This preliminary sampling at multiple points allows accurate interpolation even with irregular pulse rates, while the overall process remains efficient by only performing these additional correlations when needed.
Solution Approach 2:
The patent changes the approach from direct time measurement to amplitude-based interpolation. By measuring correlation amplitudes at multiple delay points and interpolating to find the peak, the system achieves high precision TDOA measurement that is robust to pulse rate irregularities while maintaining processing efficiency.
3Ease of manufacture
If leading-edge timing method is used, then the method is simple to implement, but measurement precision deteriorates due to interpolation errors
Solution Approach 1:
The patent replaces simple leading-edge detection with cross-correlation-based amplitude measurement and parabolic interpolation. This substitution eliminates the interpolation errors inherent in leading-edge methods while keeping the implementation relatively simple through standard signal processing operations.
Solution Approach 2:
The patent introduces cross-correlation amplitude as an intermediary measurement between the raw signal and the final TDOA value. This intermediary step of measuring correlation amplitudes at multiple delays provides a more robust basis for TDOA determination, eliminating direct reliance on leading-edge timing and its associated interpolation errors.
Data Source
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AI summary
A method for determining a FDOA of a pulsed waveform received by two sensors includes obtaining a respective plurality of in-phase and quadrature-phase (IQ) samples indicative of a pulse envelope of the received pulsed waveform. The method includes determining a TDOA responsive to a leading edge of a pulse of the pulsed waveform and obtaining a first cross correlation of IQ samples at a delay (dc) closest to the TDOA, and respective second and third cross correlations at least one additional delay (dc+1 and dc-1) on either side of the closest delay. The method includes refining the approximation of the TDOA according to an interpolation of amplitudes of the cross-correlation and determining a respective rate of change of cross-correlation phase (Δϕ ). The method includes approximating a straight line fit to the rates of change of cross-correlation phase (dΔϕ/dt), the slope of the straight line representative of the FDOA.