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SLAM Graph Loop Closure Mahalanobis Distance & Outlier Rejection Calculator

Easily calculate and compute slam graph loop closure mahalanobis distance & outlier rejection calculator with accurate equations, live formulas, and expert guidance.

Calculated Result
1.75 D_M

Mahalanobis Distance

Mahalanobis Distance

1.75 D_M

Mahalanobis Distance

1.75

Squared Mahalanobis Distance

3.06

Chi Squared Critical Threshold95

7.815

Chi Squared Critical Threshold99

11.345

1.75 — D_M

Calculation Breakdown

  1. Applied FormulaApplies the Mahalanobis distance chi-squared gating test to validate candidate loop closures and reject perceptual aliasing outliers in pose-graph SLAM.D_M^2 = \mathbf{e}^T \mathbf{\Sigma}^{-1} \mathbf{e} = \frac{\Delta x^2}{\sigma_x^2} + \frac{\Delta y^2}{\sigma_y^2} + \frac{\Delta\theta^2}{\sigma_\theta^2}

SLAM Mahalanobis Outlier Test Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.00.40.91.31.8Mahalanobis Distance

What Is the SLAM Graph Loop Closure Mahalanobis Distance & Outlier Rejection Calculator?

This tool computes slam graph loop closure mahalanobis distance & outlier rejection calculator with high precision arithmetic.

How Does the SLAM Graph Loop Closure Mahalanobis Distance & Outlier Rejection Calculator Work?

Applies the Mahalanobis distance chi-squared gating test to validate candidate loop closures and reject perceptual aliasing outliers in pose-graph SLAM.

SLAM Graph Loop Closure Mahalanobis Distance & Outlier Rejection Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

DM2=eTΣ−1e=Δx2σx2+Δy2σy2+Δθ2σθ2D_M^2 = \mathbf{e}^T \mathbf{\Sigma}^{-1} \mathbf{e} = \frac{\Delta x^2}{\sigma_x^2} + \frac{\Delta y^2}{\sigma_y^2} + \frac{\Delta\theta^2}{\sigma_\theta^2}

Applies the Mahalanobis distance chi-squared gating test to validate candidate loop closures and reject perceptual aliasing outliers in pose-graph SLAM.

How to Use the SLAM Graph Loop Closure Mahalanobis Distance & Outlier Rejection Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

SLAM Graph Loop Closure Mahalanobis Distance & Outlier Rejection Calculator Example

Input Values:

residualErrorXMeters:0.24
residualErrorYMeters:0.18
residualErrorYawRad:0.045
varianceX:0.04
varianceY:0.04
varianceYaw:0.0025
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required D_M.

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

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