Regularization Algorithm for Speed and Acceleration Signal Noise
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Solution Overview
Problem
Existing speed and acceleration measurement devices face issues with noise amplification at high sampling rates, leading to erroneous signals, and low sampling rates result in signal distortion and loss of accuracy.
Innovation Solution
The method employs regularization algorithms to mitigate noise amplification by expressing position or displacement data as an integral equation, discretizing it, and using a regularization method to recover accurate speed and acceleration values, with techniques such as generalized cross-validation and minimum mean squared error to determine the regularization parameter.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If high sampling rate is used to calculate speed and acceleration from position data, then measurement resolution is improved, but noise amplification occurs causing erroneous signals
Solution Approach 1:
The patent changes the mathematical approach from direct difference methods to regularization algorithms, transforming the ill-posed differentiation problem into a stable solution by modifying the calculation parameters and methodology to suppress noise amplification while maintaining high sampling rate benefits
Solution Approach 2:
The patent introduces regularization algorithms as an intermediary computational method between position data and speed/acceleration output, acting as a mediator that processes the raw data through a stabilized mathematical framework to produce accurate results without direct noise amplification
2Reliability
If low sampling rate is used to reduce noise amplification, then signal stability is improved, but signal distortion and accuracy loss occur
Solution Approach 1:
The patent transforms the fundamental calculation methodology from simple differencing to regularization-based computation, changing how the system processes data to simultaneously achieve noise suppression and accuracy preservation without requiring low sampling rates
3Device complexity
If difference methods are used to calculate speed and acceleration from position data, then calculation simplicity is maintained, but noise amplification causes erroneous results
Solution Approach 1:
The patent modifies the computational parameters and mathematical framework from basic difference methods to regularization algorithms, maintaining computational tractability while fundamentally improving calculation reliability through stabilized mathematical operations
Data Source
AI summary
Speed and acceleration calculation and measuring methods and devices based on a regularization algorithm are disclosed. Speed and acceleration are calculated using the following steps: (1) acquiring position data or displacement data; and (2) using the position data or displacement data to calculate the speed and the acceleration with a disclosed regularization method. The disclosed methods and systems avoid the issue of noise amplification that arises when speed and acceleration are measured by existing speed and acceleration devices at high sampling rates. Noise amplification is prevented by first expressing the relationship between position data or displacement data and speed or acceleration into a typical Volterra integral equation of the first kind, and then using the disclosed regularization method to calculate speed and acceleration, thus suppressing noise amplification and accurately extracting speed and acceleration signal values.