Bounded Elevation Angle Search for Faster NLS Signal Estimation
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Solution Overview
Problem
The non-linear least squares (NLS) method for determining elevation angles of incoming signals is computationally expensive and relies heavily on a good initial guess, which can be challenging to obtain due to large search spaces and failure to account for physical and environmental constraints.
Innovation Solution
The method employs a bounded linear initial search space and a fixed grid with pre-calculated variables to refine the initial elevation angle pair using NLS iterations, thereby reducing computational burden and improving accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the NLS method is used to determine elevation angles, then measurement precision is improved, but computational resources are excessively consumed
Solution Approach 1:
The patent segments the search space into multiple discrete grid points, transforming the continuous NLS optimization problem into a discrete search problem. This segmentation allows the system to evaluate a finite set of predetermined elevation angle pairs rather than searching through all possible continuous values, significantly reducing computational resources while maintaining measurement precision through the refined grid resolution.
Solution Approach 2:
The patent performs preliminary action by pre-calculating and storing a grid of candidate elevation angle pairs before the actual measurement process. This pre-computed grid serves as a lookup table that guides the NLS method, eliminating the need for extensive real-time calculations and reducing the computational burden during operational use.
2Measurement precision
If a large search space is used to find initial guess, then measurement precision is improved, but loss of time increases
Solution Approach 1:
The search space is segmented into a structured grid of discrete elevation angle pairs, converting an exhaustive continuous search into a targeted discrete evaluation. This segmentation maintains comprehensive coverage of possible solutions while reducing search time by eliminating redundant evaluations of non-candidate values.
Solution Approach 2:
The patent changes the parameter representation from continuous elevation angles to discrete grid-indexed pairs. This parameter transformation allows the system to efficiently navigate the search space using integer indices rather than floating-point calculations, significantly reducing search time while preserving measurement precision through the fine grid resolution.
3Adaptability or versatility
If physical and environmental constraints are not considered, then adaptability is improved, but measurement precision deteriorates
Solution Approach 1:
The patent applies local quality by incorporating physical and environmental constraints into the grid generation process, creating a non-uniform distribution of search points that concentrates computational effort in physically plausible regions. This approach maintains adaptability to different environments while improving measurement precision by focusing the search where actual targets are likely to exist.
Data Source
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AI summary
Described herein is NLS using a bounded linear initial search space and a fixed grid with pre-calculated variables. Specifically, first and second signals with unknown first and second elevation angles, respectively, are received that have been reflected by an object, with the second signal also having been reflected off the ground. A line of second angles is then established as a function of first angles, a sensor height, and a range to the object. The first angles being bound by a function of the sensor height and the range and a function of the sensor height, the range, and the maximum height. A search algorithm is then used to search for an initial elevation angle pair along the line. The initial elevation angle pair may then be fed into a refinement algorithm (e.g., non-linear least squares) to determine the elevation angles associated with the first and second signals.