Kalman filtering with censored measurements
Kostas Loumponias1, George Tsaklidis1
1Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, Greece.
Journal of Applied Statistics
|June 16, 2022
Summary
This study introduces a Kalman filtering method for censored data using the Tobit model. The new Bayesian algorithm effectively estimates hidden states, outperforming existing methods in accuracy and computational cost.
Area of Science:
- Statistics
- Signal Processing
- Control Systems
Background:
- Kalman filtering is essential for state estimation in dynamic systems.
- Censored measurements, common in real-world data, pose challenges for standard filtering techniques.
- The Tobit model of Type I is a statistical approach for handling censored data.
Purpose of the Study:
- To develop a novel Kalman filtering algorithm for systems with censored measurements.
- To provide Bayesian estimates for multidimensional hidden state vectors in the presence of censored data.
- To evaluate the performance of the proposed algorithm against existing filtering methods.
Main Methods:
- The study employs a recursive Kalman filtering-type algorithm.
- Bayesian estimation is used for state vectors under a Type I Tobit model.
- The algorithm handles one-dimensional censored measurements with two limits and multidimensional state vectors.
Main Results:
- The proposed algorithm effectively provides Bayesian estimates for state vectors.
- Experimental results demonstrate the algorithm's effectiveness and applicability.
- The new method shows superior performance in minimizing Root Mean Square Error (RMSE) and computational cost.
Conclusions:
- The developed Kalman filtering approach is effective for systems with censored measurements.
- The algorithm offers significant improvements in accuracy and computational efficiency.
- This method is applicable to both synthetic and real-world datasets.
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