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Bayesian Cramér-Rao Lower Bounds for Prediction and Smoothing of Nonlinear TASD Systems.
Xianqing Li1, Zhansheng Duan1, Qi Tang1
1Center for Information Engineering Science Research, School of Automation Science and Engineering, Xi'an Jiaotong University, Xi'an 710049, China.
Sensors (Basel, Switzerland)
|July 9, 2022
Summary
This study introduces recursive Bayesian Cramér-Rao lower bounds (BCRLBs) for nonlinear systems with two-adjacent-states dependent (TASD) measurements. The findings are validated through radar target tracking examples, improving state estimation performance.
Area of Science:
- Control Systems Engineering
- Signal Processing
- Estimation Theory
Background:
- State estimation for nonlinear systems is crucial.
- Existing Bayesian Cramér-Rao lower bound (BCRLB) methods primarily address systems with direct current state measurements.
- Many real-world nonlinear systems exhibit two-adjacent-states dependent (TASD) measurements, where current measurements depend on both current and previous states, necessitating new evaluation methods.
Purpose of the Study:
- To develop novel recursive Bayesian Cramér-Rao lower bounds (BCRLBs) for state prediction and smoothing in nonlinear systems with TASD measurements.
- To compare the performance bounds of TASD systems against traditional nonlinear regular systems.
- To analyze specific TASD system cases involving autocorrelated or cross-correlated measurement and process noises.
Main Methods:
- Development of recursive BCRLBs tailored for nonlinear systems with TASD measurements.
- Comparative analysis of BCRLBs between TASD and nonlinear regular systems.
- Derivation of BCRLBs for specialized TASD systems with correlated noises.
- Validation using simulation examples in radar target tracking.
Main Results:
- The study successfully derived recursive BCRLBs for nonlinear systems with TASD measurements, applicable to both prediction and smoothing.
- A quantitative comparison highlighted differences between TASD and nonlinear regular system performance bounds.
- Specific results were presented for TASD systems with autocorrelated or cross-correlated noises.
- Illustrative examples demonstrated the practical effectiveness of the proposed BCRLBs in radar target tracking scenarios.
Conclusions:
- The developed recursive BCRLBs provide a robust framework for evaluating state estimators in nonlinear systems with TASD measurements.
- The findings offer valuable insights into the performance limitations and characteristics of TASD systems compared to regular systems.
- The proposed methods are effective and applicable to complex systems like radar target tracking.
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