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<p>Two schemes of suboptimal estimation algorithms designed with the use of the Bayesian approach and based on the linearization of state vector functions and measurement model are compared. One of these schemes, in which the estimate is calculated recursively with respect to measurements, is traditional, and the other one, nonrecursive, involves the use of a full set of all available measurements. It is shown that when solving a special class of problems in which the posteriori density has a complex multi-extremal character at the initial moments of time, but over time it becomes close to the Gaussian one, algorithms designed with the use of a nonrecursive scheme can be effective, in contrast to traditional recursive algorithms using a Gaussian approximation of the posteriori density at each step. Advantages of the nonrecursive algorithms are discussed and illustrated, first, on a simple methodological example and then by solving a practical navigation problem for a group of autonomous underwater vehicles (AUVs).</p>

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Comparative analysis of recursive and nonrecursive linearization-based estimation algorithms

  • 期刊论文

  • 发表日期：

    2025年2月6日

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  • Alexey Isaev,
  • Oleg Stepanov,
  • Yulia Litvinenko

摘要

Two schemes of suboptimal estimation algorithms designed with the use of the Bayesian approach and based on the linearization of state vector functions and measurement model are compared. One of these schemes, in which the estimate is calculated recursively with respect to measurements, is traditional, and the other one, nonrecursive, involves the use of a full set of all available measurements. It is shown that when solving a special class of problems in which the posteriori density has a complex multi-extremal character at the initial moments of time, but over time it becomes close to the Gaussian one, algorithms designed with the use of a nonrecursive scheme can be effective, in contrast to traditional recursive algorithms using a Gaussian approximation of the posteriori density at each step. Advantages of the nonrecursive algorithms are discussed and illustrated, first, on a simple methodological example and then by solving a practical navigation problem for a group of autonomous underwater vehicles (AUVs).