A Two-Dimensional Frequency Estimation Algorithm with Automatic Pairing of Cross-Dimensional Estimation Results

This paper introduces a two-dimensional frequency estimation algorithm capable of automatically pairing estimation results across different dimensions. The implementation begins by transforming the 2D frequency estimation problem into two generalized eigenvalue problems formulated through matrix pencils. Through eigenanalysis, the algorithm computes the common eigenvectors of both matrix pencils, which then serves as the foundation for simultaneously extracting eigenvalues from both matrix structures. The estimation accuracy of this algorithm is comparable to existing methods, while successfully addressing the persistent pairing problem common to current approaches. From an application perspective, this algorithm finds utility across multiple domains. In medical applications, for instance, patient diagnostic results can be converted into feature matrices, where this algorithm performs automatic pairing to yield more precise medical diagnoses. In financial applications, security trading data can be similarly transformed into feature matrices, with the algorithm enabling accurate pairing for improved investment strategies. In summary, this algorithm provides a novel approach to automatic estimation result pairing, offering new methodologies and tools for data processing and analysis across various domains. The core implementation involves matrix pencil operations and joint eigenvector computation, providing a robust framework for cross-dimensional frequency estimation tasks.