Integrating Sensor Time Series Reconstruction for Amplitude Correction
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Solution Overview
Problem
Existing methods for correcting time series measured using integrating sensors are incomplete and often incorrect, as they fail to account for the physical properties of the sensors, leading to underestimation of signal amplitudes due to centroid formation.
Innovation Solution
A method that corrects time series by accounting for the integration time and duty cycle of integrating sensors, which involves redefining sampling points to be in the middle of the integration time, allowing for averaging over a symmetrical integration interval to estimate the centroid of the signal, and using a sinc function to correct amplitude underestimation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If integrating sensors are used to measure time series, then measurement capability is improved, but signal amplitude is underestimated due to centroid formation
Solution Approach 1:
The patent applies parameter changes by modifying the sampling time definition from the start of integration to the middle of integration (t_s' = t_s + delta). This parameter shift compensates for the centroid formation effect, allowing the measured signal amplitude to accurately represent the true signal amplitude at the corrected sampling point.
Solution Approach 2:
The patent replaces the physical measurement system's inherent centroid formation effect with a mathematical correction approach. By introducing a time shift parameter and applying sinc function-based amplitude correction, the method substitutes the physical sensor limitation with computational compensation, recovering the true signal amplitude.
2Measurement precision
If integration time is extended to improve signal integration, then measurement sensitivity is improved, but temporal resolution and amplitude accuracy deteriorate
Solution Approach 1:
The patent uses parameter changes by defining the sampling time as the midpoint of the integration interval (t_s' = t_s + delta) and applying amplitude correction based on the duty cycle parameter. This allows the system to maintain extended integration times for improved signal-to-noise ratio while recovering temporal accuracy through mathematical correction.
Solution Approach 2:
The patent introduces an intermediary correction factor (sinc function based on duty cycle) that mediates between the extended integration time and the true signal amplitude. This intermediary mathematical operation bridges the gap between the integrated measurement and the actual instantaneous signal value.
3Measurement precision
If sampling frequency is increased to improve temporal resolution, then time series accuracy is improved, but the centroid formation effect becomes more significant
Solution Approach 1:
The patent applies parameter changes by shifting the sampling time definition to the integration midpoint and applying amplitude correction proportional to the duty cycle. This correction becomes more effective at higher sampling frequencies, as the time shift parameter (delta) represents a smaller fraction of the sampling period, reducing the distortion.
4Measurement precision
If duty cycle is increased to improve signal capture, then measurement completeness is improved, but amplitude underestimation increases
Solution Approach 1:
The patent directly addresses duty cycle effects by applying amplitude correction based on the duty cycle parameter. The correction factor sinc(pi * duty_cycle) compensates for the amplitude underestimation that increases with duty cycle, allowing the system to capture more complete signal information while maintaining amplitude accuracy.
Data Source
AI summary
Method for correcting amplitude underestimations in time series, which were measured on sequences of multi-dimensional signals, wherein the multi-dimensional signals were sampled with one or more integrating sensors, such that the time series are degraded by a center of gravity/centroid formation, which can be characterized by a duty cycle of the integrating sensors. According to the invention, a centroid formation of the time series is corrected based on the duty cycle, the duty cycle or the integration time of the sensors.