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Uncertainty: Overview00:59

Uncertainty: Overview

1.5K
In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
1.6K
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
10.0K
Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

1.2K
The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this...
1.2K
The Uncertainty Principle04:08

The Uncertainty Principle

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Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
31.2K
Uncertainty in Measurement: Accuracy and Precision03:37

Uncertainty in Measurement: Accuracy and Precision

99.2K
Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value. 
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Related Experiment Video

Updated: Jan 6, 2026

Evaluation of an Exclusive Spur Dike U-Turn Design with Radar-Collected Data and Simulation
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Evaluation of an Exclusive Spur Dike U-Turn Design with Radar-Collected Data and Simulation

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Uncertainty Quantification for Space Situational Awareness and Traffic Management.

Samuel Hilton1, Federico Cairola2, Alessandro Gardi3

  • 1School of Engineering, Bundoora, RMIT University, Bundoora, VIC 3083, Australia. sam.hilton@rmit.edu.au.

Sensors (Basel, Switzerland)
|October 12, 2019
PubMed
Summary

This study introduces a sensor-based method for on-orbit position uncertainty, crucial for space situational awareness and collision avoidance of resident space objects (RSO). It quantifies RSO tracking errors to enhance space traffic management.

Keywords:
Cognitive Human-Machine InteractionCovariance RealismCyber-Physical SystemsGauss–Helmert MethodRadar PerformanceResident Space ObjectSpace Situational AwarenessSpace Traffic ManagementSpace-Based SurveillanceUncertainty Quantification

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Area of Science:

  • Space Surveillance and Situational Awareness
  • Astrodynamics and Orbital Mechanics
  • Data Fusion and Uncertainty Quantification

Background:

  • Accurate on-orbit position estimation is critical for space situational awareness (SSA) and collision avoidance.
  • Current methods for quantifying position uncertainty may not fully capture the complexities of sensor data and RSO dynamics.
  • Evolving SSA architectures demand robust methods for representing and managing space object positional uncertainties.

Purpose of the Study:

  • To develop a sensor-orientated approach for generating and quantifying on-orbit position uncertainty for Resident Space Objects (RSO).
  • To establish a mathematical framework supporting separation assurance and collision avoidance.
  • To represent navigation and tracking errors as uncertainty volumes, detailing size, shape, and orientation.

Main Methods:

  • Development of a mathematical framework utilizing least squares formulation.
  • Exploitation of real-time navigation measurements and tracking observables.
  • Generation of uncertainty volumes to characterize positional errors.

Main Results:

  • A validated methodology for on-orbit position uncertainty generation and quantification.
  • Demonstration of the method's capability to support separation assurance and collision avoidance.
  • Analysis of sensor performance impact on Gaussian assumptions for uncertainty representation.

Conclusions:

  • The proposed sensor-orientated approach provides a sound methodology for RSO position uncertainty.
  • Accurate uncertainty quantification is vital for the evolution of SSA and Space Traffic Management (STM).
  • Implications for cyber-physical architectures and cognitive human-machine systems in SSA were explored.