Elevation Angle NLS Refinement Using Bounded Grid Search
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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 prone to failure due to large search spaces and environmental constraints, especially in crowded environments, requiring significant computational resources.
Innovation Solution
Implementing a bounded linear initial search space and a fixed grid with pre-calculated variables, utilizing physics and environmental constraints to reduce the search space and simplify computations through a greedy search and NLS iterations with pre-calculated variables.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the NLS method is used to determine elevation angles with good initial guess techniques, then measurement precision is improved, but device complexity increases due to large search spaces and multiple iterations
Solution Approach 1:
The patent segments the elevation angle search space into discrete grid points, transforming the continuous optimization problem into a discrete search problem. This segmentation allows the system to evaluate predefined grid points rather than performing exhaustive continuous searches, reducing computational complexity while maintaining measurement precision through systematic grid-based evaluation.
Solution Approach 2:
The patent applies preliminary action by establishing physical and environmental constraints before the NLS optimization process. By pre-defining the search space boundaries based on known physical constraints (such as maximum elevation angles, ground plane geometry, and sensor mounting height), the system reduces the initial search space, making subsequent NLS iterations more efficient and less computationally intensive.
2Measurement precision
If multiple iterations of the NLS method are performed in crowded environments, then measurement precision is improved, but productivity decreases due to computational expense
Solution Approach 1:
The patent extracts and removes computationally expensive matrix operations from the iterative NLS process by pre-calculating the geometric relationship between sensor positions and grid points. By extracting the essential geometric information into a pre-computed grid structure, the system eliminates redundant calculations during real-time processing, significantly improving productivity while maintaining the precision benefits of NLS refinement.
Solution Approach 2:
The patent changes the parameter representation from continuous angle values to discrete grid point indices. This parameter transformation allows the system to work with integer indices rather than continuous floating-point angles during the search phase, reducing computational burden. The NLS method then refines these discrete parameters back to continuous angle values, maintaining precision while improving processing speed.
3Adaptability or versatility
If a large search space is used for initial guess generation, then adaptability is improved, but ease of operation deteriorates due to computational burden
Solution Approach 1:
The patent applies preliminary action by pre-defining the search space boundaries based on known physical constraints (such as maximum elevation angles, ground plane geometry, and sensor mounting height). This preliminary constraint application reduces the effective search space from a large, unbounded region to a manageable, physically-relevant subset, making the system easier to operate while maintaining adaptability to different environmental conditions through configurable constraint parameters.
Data Source
AI summary
Described herein is NLS using a bounded linear initial search space and a fixed grid with pre-calculated variables. An initial first elevation angle corresponding to a direct reflection from an object and an initial second elevation angle corresponding to a multi-path reflection from the object are received along with a grid comprising pre-calculated variables for each of a plurality of grid points. The initial elevation angle pair is then refined by, for a plurality of iterations, determining a closest grid point to a current elevation angle pair and performing a non-linear least squares iteration on the closest grid point using the pre-calculated variables for the closest grid point to determine a next elevation angle pair. When the iterations have converged, a height of the object is calculated based on a final elevation angle pair.