Direction of Arrival Estimation via Thresholded Householder Transform
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Solution Overview
Problem
Existing methods for estimating the direction of arrival waves, such as radio and acoustic waves, face issues with vain eigenvalue decomposition operations due to low signal-to-noise ratios and small differences in arrival azimuths, leading to incorrect estimations and increased processing load.
Innovation Solution
The apparatus implements Householder transformation operations only if the maximum column norm of the correlation matrix is above a predetermined threshold, and sets a threshold value higher than noise column norms to avoid unnecessary operations, thereby reducing vain decompositions and improving estimation credibility.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If eigenvalue decomposition operation is performed using fixed decimal mode with insufficient word size, then the operation can be completed, but underflow occurs in smaller eigenvalues leading to negative or low-credibility computed eigenvalues
Solution Approach 1:
The patent applies dynamic scaling by computing column norms and comparing them against threshold values to determine whether to continue Householder transformation operations. This dynamic approach adjusts the operation continuation based on real-time numerical stability conditions, preventing underflow while maintaining operation completion.
2Reliability
If Householder transformation operation is repeated to obtain eigenvalues with low credibility, then the eigenvalue decomposition can be completed, but unnecessary operations are loaded on the processing unit
Solution Approach 1:
The patent performs preliminary computation of column norms before continuing with Householder transformation operations. By evaluating the maximum column norm against a threshold in advance, the system determines whether further operations are necessary, avoiding unnecessary computations that would load the processing unit without improving eigenvalue credibility.
3Productivity
If the number of arrival waves is estimated from low-credibility eigenvalues, then an estimation can be obtained, but the estimated number is likely to be incorrect
Solution Approach 1:
The patent implements feedback control by continuously monitoring column norms during the eigenvalue decomposition process and comparing them against threshold values. This feedback mechanism ensures that operations continue only when they contribute to obtaining credible eigenvalues, thereby ensuring accurate estimation of the number of arrival waves while maintaining efficient processing.
Data Source
AI summary
Apparatus and method are disclosed for estimating direction of an arrival wave, such as radio or acoustic waves. A correlation matrix of an arrival wave is computed, and matrices for obtaining eigenvalues and eigenvectors are produced. Column norms of the matrix, which is subject to a Householder transformation, are computed. Whether a maximum value of the column norms is the same as or lower than a predetermined threshold is judged. A Householder transformation of the matrix is performed only if the maximum value of the column norms is determined to be greater than or equal to the threshold, and not when the maximum value of the column norms is less than the threshold. The eigenvectors and the eigenvalues of the correlation matrix are obtained by further implementing the Householder transformation. The number of arrival waves is judged from the number of times the Householder transformation is performed.