Single-Epoch GNSS Protection Level Using Non-Gaussian Error Models
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Solution Overview
Problem
Existing GNSS positioning systems face challenges in accurately determining a protection level due to non-independent observables, leading to difficulties in modeling error distributions and providing reliable position estimates.
Innovation Solution
A method and apparatus that utilize a single epoch of GNSS measurements, specifying a prior probability density, system model, and non-Gaussian residual error probability density model to determine a protection level by integrating a posterior probability density, while excluding or de-weighting outliers using MCMC or importance sampling.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional methods model errors of GNSS observables to determine protection levels, then reliability of position estimates can be improved, but when observables are not independent, the complexity of error modeling increases significantly
Solution Approach 1:
The patent segments the joint error distribution modeling into individual observable error distributions. Instead of modeling the complex joint distribution of multiple observables, the method models each observable's error distribution separately using non-Gaussian probability density functions, then combines these individual models to determine protection levels. This segmentation avoids the complexity of modeling correlations between observables while maintaining reliability.
2Measurement precision
If multiple epochs of GNSS data are used to improve position estimate reliability, then accuracy can be enhanced, but latency and processing time increase
Solution Approach 1:
The patent performs preliminary action by pre-determining the non-Gaussian probability density function parameters for each observable error distribution before processing the actual position estimation. By having these error models ready in advance, the system can quickly determine protection levels using a single epoch of data without needing to collect and process multiple epochs, thus reducing latency while maintaining accuracy through the sophisticated error modeling.
3Reliability
If non-Gaussian error distributions are modeled for each observable, then tail probability densities can be captured accurately, but computational complexity increases
Solution Approach 1:
The patent applies parameter changes by using non-Gaussian probability density functions (such as Student's t-distribution or other heavy-tailed distributions) to model observable errors instead of traditional Gaussian distributions. These non-Gaussian models have parameters that can capture the characteristics of tail probability densities more accurately, allowing the system to account for rare but significant errors while maintaining computational feasibility through efficient numerical integration methods.
Data Source
AI summary
A method for determining a protection level of a position estimate using a single epoch of GNSS measurements, the method includes: specifying a prior probability density P(x) of a state x; specifying a system model h(x) that relates the state x to observables z of the measurements; quantifying quality metrics q associated with the measurements; specifying a non-Gaussian residual error probability density model ƒ(r|θ, q) and fitting model parameters θ using a set of experimental data; and defining a posterior probability density P(x|z, q, θ); estimating the state x; and computing the protection level by integrating the posterior probability density P(x|z, q, θ) over the state x.