Related Experiment Video
Updated: Jan 17, 2026
10:22
Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
Published on: September 7, 2019
8.7K
Uncertainty Quantification of First Fix in a Time-Differenced Carrier Phase Observation Model
Hakim Cherfi1, Julien Lesouple1, Joan Solà2
1Fédération ENAC ISAE-SUPAERO ONERA, Université de Toulouse, 7, Avenue Edouard Belin, 31400 Toulouse, France.
Sensors (Basel, Switzerland)
|September 19, 2025
Summary
Initial position errors in Global Navigation Satellite System (GNSS) odometry significantly impact displacement estimation. This study quantifies these errors in time-differenced carrier phase (TDCP) models, showing a linear relationship between initial position error and displacement error.
Area of Science:
- Geomatics Engineering
- Satellite Navigation Systems
- Signal Processing
Background:
- Time-differenced carrier phase (TDCP) is crucial for precise Global Navigation Satellite System (GNSS) odometry.
- Accurate initial position is a critical assumption in TDCP modeling, often unmet in real-world scenarios.
Purpose of the Study:
- To perform uncertainty quantification of the first fix in TDCP observation models.
- To assess the impact of initial position errors on GNSS-based displacement estimation.
Main Methods:
- Formulated correct and misspecified TDCP models to analyze initial position error effects.
- Derived theoretical frameworks for estimation under misspecified models, including Mean Squared Error (MSE) and Misspecified Cramer-Rao Bound (MCRB).
- Conducted extensive simulations with realistic GNSS geometry to evaluate performance under varying conditions.
Main Results:
- Displacement estimation error is linearly related to the initial position error and the time interval between observations.
- Demonstrated that a 10m initial first-fix error in a 1s TDCP can introduce up to 1.3mm displacement error.
- Quantified the order of magnitude of errors introduced by parameter uncertainties in GNSS solutions.
Conclusions:
- Accurate first-fix estimation is vital for reliable TDCP-based odometry.
- The study provides a quantitative understanding of how initial position uncertainties propagate through TDCP models.
- Findings are essential for improving the robustness and accuracy of GNSS displacement estimation techniques.
More Related Videos
Related Concept Videos
01:10Propagation of Uncertainty from Systematic Error
1.4K
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...
1.4K
00:59Propagation of Uncertainty from Random Error
1.8K
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...
1.8K
01:05Estimation of the Physical Quantities
7.2K
On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...
7.2K
00:59Uncertainty: Overview
1.6K
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.
1.6K
00:54Uncertainty: Confidence Intervals
10.2K
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...
10.2K
03:37Uncertainty in Measurement: Accuracy and Precision
99.9K
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.
99.9K