Parameter Estimation via Residual Thresholding
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Solution Overview
Problem
Existing parameter estimation methods, such as LMeds and RANSAC, face challenges in handling high outlier ratios, requiring excessive calculations and being unsuitable for high-speed applications, with instability due to random sampling and difficulty in setting appropriate thresholds, especially when the outlier error distribution is unknown.
Innovation Solution
A parameter estimation apparatus and method that calculates a threshold for separating outliers and inliers based on statistical information of residuals, using a parameter estimation unit, a threshold setting unit, and a convergence determination unit to iteratively refine the threshold until convergence is reached, ensuring accurate separation and estimation of geometrical parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If random sampling methods (LMeds, RANSAC) are used to handle outliers, then parameter estimation accuracy is improved, but calculation amount increases exponentially and processing speed decreases
Solution Approach 1:
The patent transforms the parameter estimation problem from directly fitting all data points to first identifying inliers through threshold-based separation, then fitting parameters only to inliers. This changes the estimation parameter from a direct fit to a two-stage process involving outlier detection threshold and inlier-only parameter fitting, thereby improving speed while maintaining accuracy
Solution Approach 2:
The patent segments the data points into two distinct groups: inliers and outliers, based on a calculated threshold. This segmentation allows the parameter estimation to focus only on the inlier subset, avoiding the exponential calculation burden of random sampling methods while achieving the same or better accuracy
2Reliability
If random sampling is used to estimate parameters, then outlier handling capability is improved, but stability decreases due to random variation
Solution Approach 1:
The patent employs an iterative process where the algorithm automatically recalculates the threshold and re-estimates parameters using only inliers until convergence is achieved. This self-service mechanism eliminates random variation by systematically refining the solution based on the actual data distribution rather than random sampling
Solution Approach 2:
The patent implements a feedback loop where parameter estimation results are used to recalculate the threshold, which then reclassifies data points as inliers or outliers. This feedback mechanism continues until convergence, ensuring stable and reproducible results that are insensitive to random variation
3Device complexity
If fixed threshold values are used in M-estimation, then calculation complexity is reduced, but adaptability decreases when outlier error distribution is unknown
Solution Approach 1:
The patent transforms the static fixed threshold approach into a dynamic threshold that automatically adapts to the data characteristics. The threshold is calculated based on the residual distribution and iteratively refined, allowing it to adapt to unknown outlier error distributions without increasing calculation complexity
Solution Approach 2:
The algorithm automatically determines the appropriate threshold value by analyzing the residual distribution of the data itself, rather than requiring manual specification or fixed values. This self-service capability enables the system to adapt to different data sets and outlier distributions automatically
Data Source
AI summary
A parameter estimation apparatus 10 is an apparatus for calculating a threshold for separating a plurality of data points into outliers and inliers and estimating a parameter fitting the inliers. The parameter estimation apparatus 10 includes: a parameter estimation unit 13 configured to estimate the parameter by using the plurality of data points as input; a threshold setting unit 14 configured to calculate the threshold based on statistical information of residuals of the data points; and a convergence determination unit 15 configured to determine whether or not convergence of the estimation of the parameter is reached based on the estimated parameter and the calculated threshold, and to cause the parameter estimation unit 13 and the threshold setting unit 14 to each execute processing again if the convergence determination unit 15 determines that convergence is not reached.