Linear estimation for discrete-time periodic systems with unknown measurement input and missing measurements

Area of Science:

• Control systems engineering
• Signal processing
• Estimation theory

Background:

• Periodic systems are common in various applications but pose challenges for state estimation.
• Unknown measurement inputs and missing data degrade estimation accuracy.
• Existing methods may not adequately handle the complexities of periodic systems with data uncertainties.

Purpose of the Study:

• To develop an effective estimation strategy for periodic systems with unknown measurement input and missing data.
• To establish a performance criterion based on the Cesaro limit of the mean square error.
• To design a periodic unbiased estimator using advanced mathematical techniques.

Main Methods:

• Utilizing minimum variance unbiased estimation (MVUE).
• Modeling missing measurements using a Bernoulli process.
• Designing the estimator gain via solutions to Lyapunov and Riccati equations.

Main Results:

• A periodic unbiased estimator was successfully obtained.
• The estimator gain is derived from unique periodic solutions of associated matrix equations.
• A numerical example demonstrated the efficacy of the developed estimation approach.

Conclusions:

• The proposed estimation technique effectively handles periodic systems with unknown inputs and missing measurements.
• The method provides a robust solution for improving signal estimation quality under data uncertainties.
• The approach is validated by a numerical example, confirming its practical applicability.