Grid-Shift Acoustic Source Localization via Sparse Optimization
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Solution Overview
Problem
Conventional compressed sensing techniques for acoustic source localization fail when grid points do not coincide with actual source locations, leading to energy leakage and errors in sparse solutions, and increasing grid size violates the restricted isometry property.
Innovation Solution
A wideband joint acoustic source localization approach using an orthogonal matching pursuit-based grid-shift procedure, where a shifted grid structure is constructed across the acoustic scene, allowing each source to be located close to a grid point in at least one of the shifted grids, and combining sparse solutions to estimate source locations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the grid size is increased to improve source location coverage, then the localization accuracy improves, but the restricted isometry property is violated
Solution Approach 1:
The acoustic scene is segmented into multiple shifted grids, each providing a different spatial sampling perspective. By dividing the localization problem into multiple grid-based subproblems with different offsets, the method achieves better coverage without requiring a single overly-dense grid that would violate the restricted isometry property.
Solution Approach 2:
The method introduces an additional dimension by creating multiple grids with different spatial offsets rather than simply increasing the density of a single grid. This dimensional approach allows the system to achieve comprehensive coverage through the combination of multiple coarser grids, maintaining the restricted isometry property while improving localization accuracy.
2Productivity
If grid points are assumed to coincide with actual source locations, then the sparse recovery problem can be solved efficiently, but energy leakage occurs when sources are off-grid
Solution Approach 1:
The method dynamically adjusts the grid structure by applying multiple spatial shifts to create a family of grids. This dynamic approach allows the system to adapt to off-grid source locations by ensuring that at least one shifted grid will have points close to the actual sources, thereby reducing energy leakage while maintaining computational efficiency through sparse recovery.
Solution Approach 2:
The method changes the spatial parameters of the grid by applying different offset vectors to create multiple shifted grids. This parameter transformation allows the system to cover off-grid source locations effectively, as the union of multiple shifted grids provides comprehensive spatial coverage without requiring a single fine-grained grid.
3Measurement precision
If a single fine-grained grid is used to cover all possible source locations, then localization precision improves, but computational complexity increases
Solution Approach 1:
Instead of using a single fine-grained grid, the method segments the spatial coverage task across multiple coarser grids with different offsets. Each grid operates at a lower resolution, but their combination achieves the precision of a fine-grained grid while reducing the computational burden of processing each individual grid.
Solution Approach 2:
The method merges the results from multiple shifted grids to achieve high-precision localization. By combining the sparse solutions from several coarser grids with different spatial offsets, the system attains the localization precision that would otherwise require a single computationally-expensive fine-grained grid.
Data Source
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AI summary
Techniques of source localization and acquisition involve a wideband joint acoustic source localization and acquisition approach in light of sparse optimization framework based on an orthogonal matching pursuit-based grid-shift procedure. Along these lines, a specific grid structure is constructed with the same number of grid points as compared to the on-grid case, but which is "shifted" across the acoustic scene. More specifically, it is expected that each source will be located close to a grid point in at least one of the set of shifted grids. The sparse solutions corresponding to the set of shifted grids are combined to obtain the source location estimates. The estimated source positions are used as side information to obtain the original source signals.