Coded Filter for Non-Gaussian Noise in Navigation Systems
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Solution Overview
Problem
Existing navigation systems using Kalman filters struggle with non-Gaussian noise, particularly in dense urban environments where multi-path errors occur, leading to significant positional errors due to the assumption of Gaussian noise and smooth motion, which are not well-modeled by conventional methods like thresholding, Gauss-Markov models, or particle filters.
Innovation Solution
A processor-implemented method that estimates and corrects non-Gaussian noise using a 'coded filter' which combines a standard filter like the Kalman filter with a non-linear estimator, leveraging compressive sensing techniques and error models to provide improved state estimation by determining a basis for compressible noise and applying a minimum l1 estimator with constraints.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Kalman filter is used for state estimation, then computational efficiency is maintained, but accuracy deteriorates in the presence of non-Gaussian noise such as multi-path errors
Solution Approach 1:
The filtering process is segmented into two distinct stages: a prediction stage that uses the system model to predict the next state, and an update stage that incorporates measurements while accounting for non-Gaussian noise characteristics. This segmentation allows each stage to be optimized for its specific function, improving overall accuracy without sacrificing computational efficiency.
Solution Approach 2:
An intermediary weighting mechanism is introduced that dynamically adjusts the influence of measurements versus predictions based on the statistical properties of the noise. This intermediary layer transforms the raw measurements and predictions into a weighted combination that optimally balances accuracy and robustness, allowing the system to adapt to non-Gaussian noise conditions while maintaining computational tractability.
2Productivity
If conventional noise filtering methods are applied, then computational complexity is reduced, but measurement precision deteriorates due to inability to model non-Gaussian errors
Solution Approach 1:
The noise characteristics are modeled using time-varying parameters that capture the non-Gaussian nature of errors such as multi-path effects. By allowing these parameters to change dynamically based on observed error statistics, the system achieves accurate modeling of complex noise patterns without requiring computationally expensive methods like particle filters or neural networks.
3Ease of operation
If Gaussian noise assumption is made, then mathematical tractability is improved, but adaptability to real-world conditions deteriorates
Solution Approach 1:
The noise model transitions from a static Gaussian assumption to a dynamic model that adapts its characteristics based on observed error patterns. The system continuously updates its understanding of noise properties and adjusts its filtering behavior accordingly, maintaining mathematical tractability while becoming adaptable to diverse real-world conditions including multi-path, shadowing, and other non-Gaussian error sources.
Data Source
AI summary
A method and apparatus for estimating and compensating for a broad class of non-Gaussian sensor and process noise. In one example, a coded filter combines a dynamic state estimator (for example, a Kalman filter) and a non-linear estimator to provide approximations of the non-Gaussian process and sensor noise associated with a dynamic system. These approximations are used by the dynamic state estimator to correct sensor measurements or to alter the dynamic model governing evolution of the system state. Examples of coded filters leverage compressive sensing techniques in combination with error models based on concepts of compressibility and the application of efficient convex optimization processes.