Continuous Basis Projection Kalman Filter for Time-Varying Signal Adaptation
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Solution Overview
Problem
Standard Kalman filtering techniques are inadequate for time-varying systems, as they fail to adapt to changes in the data-generating process, leading to poor performance in processing signals from non-invasive blood monitoring and EEG systems.
Innovation Solution
The implementation of continuous basis projection Kalman filtering, which allows for a time-varying loading to be applied to a sparse set of basis functions, enabling dynamic representation of coherent structures in signals. This approach combines Fourier transforms and Kalman filtering to process and predict signals from time-varying systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If standard Kalman filtering is used, then the filtering process is simple and computationally efficient, but it cannot adapt to time-varying systems leading to poor performance
Solution Approach 1:
The patent applies dynamics by making the basis functions time-varying and adaptive. The continuous basis projection Kalman filter uses a set of basis functions that can dynamically adjust to capture time-varying structures in the signal, allowing the filter to adapt to changing system characteristics while maintaining the computational framework of Kalman filtering
Solution Approach 2:
The patent changes parameters by introducing time-varying basis functions and projection coefficients that adapt to the underlying data-generating process. The continuous basis projection allows the filter to modify its representation of the signal over time, capturing evolving patterns without requiring a complete redesign of the filtering algorithm
2Measurement precision
If continuous basis projection Kalman filtering is implemented, then adaptability to time-varying systems is improved, but computational complexity increases
Solution Approach 1:
The patent uses a sparse set of basis functions rather than a complete basis representation. By selecting only the most relevant basis functions and using continuous projection to update their coefficients, the method achieves high estimation precision with reduced computational effort compared to processing the full signal spectrum
3Loss of information
If Fourier transform is applied to sections of signal data, then frequency domain information is extracted, but processing time increases
Solution Approach 1:
The patent performs Fourier transforms on sections of signal data to pre-extract frequency domain information and identify relevant basis functions. This preliminary analysis allows subsequent Kalman filtering operations to work with a reduced set of meaningful components, reducing the computational burden of real-time processing
Solution Approach 2:
The patent divides the signal into sections or segments for Fourier transform processing. By analyzing smaller segments rather than the entire signal at once, the method efficiently extracts frequency domain information while minimizing processing time, and then uses Kalman filtering to integrate these segment results
Data Source
AI summary
Systems and methods for processing signals from a non-invasive blood analyte measurement system. In some such methods, signal data may be received from a non-invasive blood monitor. The signal data may comprise frequency data corresponding to a heart rate pulse of a user of the non-invasive blood monitor. A Fourier transform of one or more sections of the signal data may be performed. A subset of modes from the Fourier transform may be selected and data from the Fourier transform may be used to initialize an adaptive, linear signal model. Kalman filtering may then be applied to the linear signal model to update the linear signal model by propagating the subset of modes and processing a dynamic projection of the signal data onto the subset of modes.