GNSS Carrier Phase Processing via Posterior Density Mode Identification
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Solution Overview
Problem
Existing GNSS positioning techniques face challenges in accurately modeling error probability density functions, leading to potential unduly high or low confidence in state information, and difficulties in efficiently integrating posterior probability densities due to integer ambiguities in carrier phase measurements.
Innovation Solution
The method involves defining a state vector and obtaining a posterior probability density based on non-Gaussian residual error models for GNSS measurements. A search is performed to identify modes of the posterior probability density by transforming it into a mixture model, allowing for more targeted random sampling and improved numerical integration.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If non-Gaussian residual error models are used to model error probability density functions, then measurement precision and reliability of state information improve, but device complexity and computational burden increase
Solution Approach 1:
The patent transforms the complex non-Gaussian error modeling problem by changing parameters - specifically transforming the posterior probability density into a mixture model with identifiable components. This allows the system to maintain high measurement precision through non-Gaussian models while reducing computational complexity through the structured mixture model representation.
Solution Approach 2:
The patent segments the complex posterior probability density into multiple mixture components, each representing a distinct mode or cluster. This segmentation allows for more efficient computation by handling each component separately rather than dealing with the entire complex distribution at once, thus reducing device complexity while maintaining accuracy.
2Reliability
If posterior probability density is integrated to compute protection levels, then reliability of error bounds improves, but productivity and computational efficiency decrease
Solution Approach 1:
The patent performs preliminary action by transforming the posterior probability density into a mixture model before integration. This pre-transformation identifies the modes and structures of the distribution, allowing for more efficient numerical integration techniques to be applied subsequently, thus maintaining reliability while improving computational efficiency.
Solution Approach 2:
By changing the parameterization of the probability density from a complex non-Gaussian form to a mixture model with identifiable components, the patent enables more efficient computation of protection levels through targeted sampling and integration methods, improving productivity without sacrificing reliability.
3Measurement precision
If modes of posterior probability density are explicitly identified, then measurement precision and inference accuracy improve, but device complexity increases
Solution Approach 1:
The patent segments the posterior probability density into distinct modes or clusters through mixture model decomposition. This segmentation makes the identification of modes more tractable by breaking down the complex density into simpler, identifiable components, thus improving inference accuracy while managing device complexity.
Solution Approach 2:
The patent changes the parameters and representation of the probability density to a mixture model form, which has identifiable components and modes. This parameter transformation makes mode identification more straightforward and less computationally intensive, improving measurement precision without excessively increasing device complexity.
Data Source
AI summary
A method and apparatus are disclosed for processing GNSS measurements. The GNSS measurements include carrier phase measurements. A state vector is defined, comprising state variables. A posterior probability density for the state vector is obtained, which is based on non-Gaussian residual error models for the GNSS measurements. A search of the posterior probability density is performed, to identify a set of modes of the probability density. State information is inferred based on the posterior probability density, using the identified set of modes. The search comprises transforming the posterior probability density into a mixture model comprising a plurality of mixture components, wherein each mixture component is a multivariate distribution.