Minimax Regret filter for uncertainty Single-Input Single-Output systems: simulation study

José Perea-Arango; Piotr Graczyk; Juan Pablo Fernández Gutiérrez

doi:10.17533/udea.redin.20240412

Autores/as

José Perea-Arango Empresas Públicas de Medellín https://orcid.org/0009-0002-6046-1880
Piotr Graczyk Université d'Angers https://orcid.org/0000-0001-8212-8881
Juan Pablo Fernández Gutiérrez Universidad de Medellín https://orcid.org/0000-0002-0697-0257

DOI:

https://doi.org/10.17533/udea.redin.20240412

Palabras clave:

Enfoque de arrepentimiento minimax, Desconocido pero acotado, Distribución de error desconocida, Optimización de hiperparametro por malla

Resumen

El filtro de Kalman, ampliamente utilizado desde su introducción en 1960, asume ruidos aleatorios gaussianos. Sin embargo, este supuesto puede ser inapropiado en contextos cuyas variables no provienen de una distribución normal, lo que lleva a un desempeño subóptimo del filtro. Los investigadores han propuesto filtros robustos como el filtro minimax para abordar esta limitación, pero estos pueden proporcionar estimaciones demasiado conservadoras. Este trabajo presenta un enfoque novedoso que combina dinámicas desconocidas pero acotadas para el proceso de estado y procesos estocásticos para la ecuación de medidas, junto con un marco de Arrepentimiento Minimax para mejorar la estimación del estado en modelos dinámicos lineales de una dimensión. Evaluamos el método propuesto a través de dos estudios de simulación. El primer estudio utiliza el algoritmo de búsqueda por malla para optimizar el valor del hiperparámetro, mientras que el segundo estudia el desempeño del método propuesto en comparación con métodos convencionales, incluyendo el filtro de Kalman y una versión robusta del filtro RobKF implementada en software R. Los resultados demuestran la superioridad de nuestro algoritmo propuesto.

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Biografía del autor/a

José Perea-Arango, Empresas Públicas de Medellín

Profesional comercial, Departamento de Gas Natural

Piotr Graczyk, Université d'Angers

Departamento de Matemáticas, Facultad de Ciencias

Juan Pablo Fernández Gutiérrez, Universidad de Medellín

Profesor de Ciencias Básicas

Citas

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