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Recursive Batch Smoother with Multiple Linearization for One Class of Nonlinear Estimation Problems: Application for

Oleg Stepanov1, Alexey Isaev1, Elena Dranitsyna1

  • 1Faculty of Control Systems and Robotic, ITMO University, 197101 St. Petersburg, Russia.

Sensors (Basel, Switzerland)
|December 31, 2025
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Summary
This summary is machine-generated.

Two novel algorithms, Recursive Iterative Batch Linearized Smoother (RI-BLS) and Recursive Iterative Batch Multiple Linearized Smoother (RI-BMLS), efficiently solve complex nonlinear filtering problems in navigation systems. These methods offer significant computational advantages over existing techniques.

Keywords:
Bayesian approachbatch algorithmextended kalman filterfilteriterative algorithmmap-aided navigationmultiple linearizationmultisensor navigation data fusionnonrecursive schemeparticle filtersrecursive schemesmother

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Area of Science:

  • Navigation systems engineering
  • Nonlinear estimation theory
  • Computational mathematics

Background:

  • Data fusion from multiple navigation sensors presents nonlinear filtering challenges.
  • Posterior probability density functions (PDFs) evolve from multi-extremal to single-extremal with accumulating measurements.
  • Sequential Monte Carlo methods offer potential accuracy but are computationally intensive for real-time applications.
  • Traditional recursive algorithms like the extended Kalman filter are often inoperable for these problems.

Purpose of the Study:

  • To develop computationally efficient algorithms for nonlinear filtering in navigation systems.
  • To address the limitations of existing methods, including sequential Monte Carlo and traditional recursive filters.
  • To propose novel solutions that overcome the drawbacks of current approaches.

Main Methods:

  • Development of a Recursive Iterative Batch Linearized Smoother (RI-BLS) that processes all accumulated measurements iteratively using a recursive procedure.
  • Introduction of a Recursive Iterative Batch Multiple Linearized Smoother (RI-BMLS) utilizing a parallel set of RI-BLS algorithms.
  • Validation through a methodological example and a map-aided navigation problem.

Main Results:

  • The proposed RI-BLS and RI-BMLS algorithms effectively solve the considered class of nonlinear filtering problems.
  • RI-BLS demonstrates over 15-fold computational simplicity compared to particle filters.
  • RI-BMLS shows over 20-fold computational simplicity compared to particle filters, with comparable estimation accuracy.

Conclusions:

  • RI-BLS and RI-BMLS provide efficient and accurate solutions for nonlinear filtering in navigation systems, particularly for data fusion.
  • These algorithms overcome the computational complexity and inoperability issues associated with existing methods.
  • The proposed methods offer a practical alternative for real-time navigation system implementations.