Adaptive AR Model Frequency Estimation in Noisy Signals
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Solution Overview
Problem
Existing methods for determining the frequency of periodic components in noisy signals, such as those from physiological sensors, face challenges in selecting the optimal model order for auto-regressive modeling, leading to incorrect estimates of dominant frequencies due to varying noise levels and differing model fits.
Innovation Solution
The method generates synthetic signals based on candidates for periodic signals in the frequency domain, specifically pure sinusoids, and compares them in the time domain with the input signal to determine the highest cross-correlation, thereby estimating the dominant periodic component, using techniques like auto-regressive modeling or Fourier transforms, and applying these to windowed signals with varying model orders to improve frequency resolution.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If a single model order is used for auto-regressive modeling, then the device complexity is reduced, but the measurement precision of frequency estimation deteriorates due to inability to adapt to varying noise levels
Solution Approach 1:
The patent applies dynamics by making the model order adaptive rather than fixed. The system dynamically selects the optimal model order based on the characteristics of the input signal and noise conditions, allowing the modeling parameters to change in response to varying signal conditions. This resolves the contradiction by enabling the system to achieve high measurement precision across different noise levels without requiring a permanently complex multi-model architecture.
Solution Approach 2:
The patent changes the model order parameter adaptively based on signal characteristics and noise levels. By monitoring signal properties and adjusting the model order parameter accordingly, the system achieves optimal frequency estimation accuracy for different operating conditions without maintaining multiple complete models, thus balancing complexity and precision.
2Measurement precision
If multiple models of different orders are fitted to the input signal, then the measurement precision of frequency estimation is improved, but the device complexity increases
Solution Approach 1:
The patent applies preliminary action by pre-establishing a framework for adaptive model order selection. Rather than fitting multiple complete models and comparing them, the system prepares selection criteria and algorithms in advance that enable it to choose the appropriate model order quickly during operation. This reduces the computational complexity of actually implementing multiple models while maintaining the precision benefits of adaptive modeling.
Solution Approach 2:
The system performs self-service by automatically selecting the optimal model order based on inherent signal characteristics without requiring external intervention or complex comparison procedures. The adaptive model order selection mechanism enables the system to self-adjust its modeling complexity to match the actual signal conditions, achieving high precision without the burden of maintaining and managing multiple complete models.
3Measurement precision
If the model order is increased to fit noisy signals better, then the measurement precision improves, but the loss of time for computation increases
Solution Approach 1:
The patent applies dynamics by making the model order adaptive rather than fixed. The system dynamically selects the optimal model order based on the characteristics of the input signal and noise conditions, allowing the modeling parameters to change in response to varying signal conditions. This resolves the contradiction by enabling the system to achieve high measurement precision across different noise levels without requiring a permanently complex multi-model architecture.
Solution Approach 2:
The patent changes the model order parameter adaptively based on signal characteristics and noise levels. By monitoring signal properties and adjusting the model order parameter accordingly, the system achieves optimal frequency estimation accuracy for different operating conditions without maintaining multiple complete models, thus balancing complexity and precision.
Data Source
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AI summary
A method and apparatus for estimating the frequency of a dominant periodic component in an input signal by modelling the input signal using auto-regressive models of several different orders to generate candidate frequencies for the periodic component, generating synthetic sinusoidal signals of each of the candidate frequencies, and calculating the cross-correlation of the synthetic signals with the original signal. The frequency of whichever of the synthetic signals has the highest cross- correlation with the original signal is taken as the estimate of the frequency for the dominant periodic component of the input signal. The method may be applied to any noisy signal which has a suspected periodic component, for example physiological signals such as photoplethysmogram signals, and in the estimation of heart rate and breathing rate from such physiological signals.