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Information Formulation of the UDU Kalman Filter.

Christopher D'Souza1, Renato Zanetti2

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Summary

A novel information formulation enhances the Kalman filter using UDU factorization for improved numerical stability. This new method allows vector measurements, overcoming limitations of scalar processing in the classic UDU factorization.

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Area of Science:

  • Control Theory
  • Signal Processing
  • Numerical Analysis

Background:

  • The Kalman filter is a widely used algorithm for state estimation in dynamic systems.
  • Numerical stability is crucial for reliable performance, especially in complex applications.
  • Existing UDU factorization methods for Kalman filters offer stability but have limitations in measurement processing.

Purpose of the Study:

  • To introduce a new information formulation of the Kalman filter.
  • To extend the numerically stable UDU factorization technique to the information filter.
  • To enable vector measurement processing in the information filter.

Main Methods:

  • Parameterizing the information matrix using the UDU factorization (upper triangular, diagonal, transpose).
  • Developing an algorithm for the information filter based on this UDU parameterization.
  • Comparing the new method's capabilities with the classic UDU factorization for Kalman filters.

Main Results:

  • The proposed information formulation maintains numerical stability.
  • The new algorithm successfully processes measurements as vectors.
  • This overcomes the scalar measurement processing limitation of the classic UDU factorization.

Conclusions:

  • The UDU factorization of the information filter offers enhanced numerical stability and flexibility.
  • Vector measurement processing capability makes the new algorithm more versatile for various applications.
  • This work represents a significant advancement in information filter algorithms.