Recursive Norm Calculation Rounding Error Correction
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Solution Overview
Problem
Existing noise-cancellation systems do not effectively correct for rounding errors in recursive norm calculations, leading to accumulating errors over time, which affects the accuracy of noise cancellation.
Innovation Solution
A method that recursively calculates the norm using previous values and incorporates a correction algorithm to periodically recalibrate the norm, either by recalculating it entirely or using a hybrid recursive method that runs in parallel to minimize rounding errors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If recursive norm calculation is used to improve computational efficiency, then processing speed increases, but rounding errors accumulate over time reducing accuracy
Solution Approach 1:
The patent implements periodic correction of the recursively calculated norm by comparing it against a reference norm calculated from scratch at predetermined intervals. This periodic intervention resets accumulated rounding errors while maintaining the computational efficiency of recursive calculation during normal operation.
Solution Approach 2:
The system continuously monitors the recursively calculated norm and periodically compares it with a reference norm to detect rounding errors. When discrepancies are detected, the system provides feedback by correcting the recursive norm value, ensuring long-term accuracy while maintaining computational efficiency.
2Measurement precision
If periodic correction of norm is implemented to reduce rounding errors, then accuracy is maintained, but computational overhead increases
Solution Approach 1:
Instead of continuously recalculating the reference norm, the system performs partial corrections at predetermined intervals or when specific conditions are met. This approach maintains sufficient accuracy by correcting rounding errors periodically rather than continuously, reducing unnecessary computational overhead.
Data Source
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AI summary
A noise-cancellation method, comprising the steps of: receiving a value from a noise sensor at a time step; storing the received value in a buffer, the buffer having a length, the buffer further storing a number of additional values, wherein an end value is removed from the buffer to accommodate the received value; providing a previously-computed result, wherein the previously-computed result represents the sum of the square of the values stored in the buffer at a previous time step; adding a square of the received value to the previously-computed result and subtracting a square of the end value from the sum of the received value and the previously computed value in order to yield a newly-computed result and updating a plurality of coefficients of an adaptive filter according to, in part, the value of the newly-computed result.