L-1 Norm Position Computation Mitigating Multipath Errors
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Solution Overview
Problem
In urban environments, multipath reflections lead to less accurate and longer time-consuming position estimation of receivers due to signal pathways being affected by buildings, resulting in longer distances between the receiver and transmitters, which degrades the accuracy of positioning solutions.
Innovation Solution
The use of L-1 norm and L-2 norm objective functions in trilateration, along with optimal time bias calculation and altitude estimation, to mitigate multipath errors, where the L-1 norm reduces the impact of large errors and the L-2 norm is used in environments with minimal multipath, and global optimization functions like differential evolution help find the most accurate position.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If trilateration is used to estimate receiver position using signals from geographically-distributed transmitters, then position estimation can be achieved, but multipath reflections in urban environments cause longer signal paths that degrade accuracy and increase computation time
Solution Approach 1:
The patent changes the mathematical parameter used in position computation from conventional least-squares (L-2 norm) to L-1 norm minimization. This parameter change makes the objective function more robust to multipath errors by reducing the influence of large residuals, thereby improving position estimation accuracy in urban environments with multipath reflections while maintaining computational efficiency
Solution Approach 2:
The patent uses multiple candidate position estimates generated from different signal paths and selects the most accurate one by comparing against known transmitter positions and signal characteristics. This copying and comparison approach allows the system to identify and select the direct path signal while rejecting multipath reflections, improving accuracy without significantly increasing computation time
2Reliability
If multipath reflections are present in urban environments, then signal pathways become longer and more complex, but this directly degrades the accuracy of position estimation results
Solution Approach 1:
The patent converts the harmful effect of multipath reflections into a beneficial filtering mechanism. By using L-1 norm minimization, the system exploits the statistical properties of multipath errors to automatically down-weight their influence in the position computation. The harmful multipath signals are transformed from accuracy-degrading factors into manageable noise that the robust objective function naturally rejects
Solution Approach 2:
The patent introduces an intermediary objective function (L-1 norm minimization) that acts as a mediator between the raw signal measurements and the final position estimate. This intermediary computation layer processes the noisy measurements in a way that protects the final result from multipath errors, providing a buffer that isolates the position estimation from the harmful effects of signal reflections
Data Source
AI summary
Estimating an unknown position of a receiver. In some embodiment, trilateration techniques that quantify uncertainty in the estimate of the unknown position are applied. One such technique for estimating a two-dimensional or three-dimensional position of a receiver uses an L-1 norm computation instead of an L-2 norm computation.