Compressed Gaussian Estimation under Low Precision Numerical Representation.

Area of Science:

• Robotics
• Computational Mathematics
• Control Theory

Background:

• High-dimensional Gaussian estimation, crucial for Simultaneous Localization and Mapping (SLAM) and Stochastic Partial Differential Equations (SPDEs), faces computational challenges.
• Existing Generalized Compressed Kalman Filter (GCKF) methods reduce complexity but remain computationally intensive for embedded systems.
• Standard double-precision formats for covariance matrices increase computational load.

Purpose of the Study:

• To propose a computationally efficient Gaussian estimation method for high-dimensional problems.
• To address the computational cost limitations of the Generalized Compressed Kalman Filter (GCKF) on embedded processors.
• To maintain filter stability and accuracy despite using low-precision numerical representations.

Main Methods:

• Implementing a low-precision numerical representation (16-bit integer or 32-bit single-precision) for the global covariance matrix.
• Introducing a Minimal Covariance Inflation (MCI) technique to counteract instability caused by covariance matrix truncation.
• Utilizing simulation-based experiments to evaluate the proposed method's performance.

Main Results:

• The proposed method significantly reduces processing time compared to existing approaches.
• Minimal loss of accuracy was observed despite the use of low-precision formats.
• The Minimal Covariance Inflation (MCI) method effectively ensures filter consistency.

Conclusions:

• The novel Minimal Covariance Inflation (MCI) method offers a computationally efficient solution for Gaussian estimation in high-dimensional systems.
• This approach enables the practical implementation of advanced filters on resource-constrained embedded processors.
• The method balances computational savings with acceptable accuracy for applications like SLAM.