Least Squares Signal Transform Estimation
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Solution Overview
Problem
Existing signal processing technologies face challenges in accurately and efficiently computing affine transformations between suspect and reference signals, particularly in digital computing environments, due to errors introduced by discrete signal representation, quantization, and computational complexity, which hinders effective signal detection and recognition applications.
Innovation Solution
A method involving a seed set of candidate geometric transform parameters is used to transform digital watermark signals, determining correlation measures and refining the geometric transformation by updating peak locations, and employing direct least squares techniques to estimate linear transforms and phase shifts, thereby improving correlation between signals.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional signal processing methods are used to compute affine transformations, then the computation can be performed, but errors are introduced due to discrete signal representation and quantization, reducing measurement precision
Solution Approach 1:
The patent applies preliminary action by performing coordinate updates and peak location identification before the final transformation computation. The method iteratively refines transform parameters by updating candidate locations based on peak detection in the suspect signal, thereby pre-correcting for quantization and discretization errors before the final alignment is computed.
Solution Approach 2:
The patent replaces traditional mechanical signal processing approaches with a least-squares optimization framework. Instead of using conventional correlation or matching methods that are sensitive to discrete representation errors, the invention formulates the transformation problem as a least-squares minimization that is more robust to quantization effects and provides statistically optimal estimates of transform parameters.
2Measurement precision
If complex transformation algorithms are used to improve alignment accuracy, then measurement precision improves, but computational complexity and processing time increase
Solution Approach 1:
The patent segments the transformation computation into distinct stages: (1) initial transform estimation, (2) coordinate update based on peak detection, (3) least-squares refinement, and (4) final alignment computation. This segmentation allows each stage to focus on specific aspects of the problem, reducing overall computational complexity while maintaining precision.
Solution Approach 2:
The patent applies partial action by computing transformations only for selected peak locations rather than all possible signal points. The method identifies and processes only the most significant features (peaks) in the suspect signal, thereby achieving accurate alignment with reduced computational effort compared to processing the entire signal.
3Manufacturing precision
If iterative refinement methods are used to improve transformation accuracy, then manufacturing precision improves, but processing time and loss of time increase
Solution Approach 1:
The patent implements feedback through iterative coordinate updates where each iteration uses the results of peak detection to refine the transform parameters, which in turn improves the accuracy of subsequent peak detections. The least-squares optimization provides feedback on the quality of alignment, allowing the algorithm to converge to an optimal solution efficiently.
Solution Approach 2:
The method performs preliminary peak detection and coordinate updates before the final least-squares computation. By pre-identifying significant features and their approximate locations, the algorithm reduces the search space and computational burden of the iterative refinement process, thereby reducing overall processing time.
Data Source
AI summary
Signal processing devices and methods estimate transforms between signals using a least squares technique. From a seed set of transform candidates, a direct least squares method applies a seed transform candidate to a reference signal and then measures correlation between the transformed reference signal and a suspect signal. For each candidate, update coordinates of reference signal features are identified in the suspect signal and provided as input to a least squares method to compute an update to the transform candidate. The method iterates so long as the update of the transform provides a better correlation. At the end of the process, the method identifies a transform or set of top transforms based on a further analysis of correlation, as well as other results.