Extended Kalman Filter - Advanced Techniques in Dynamic State Estimation for Robotic Systems

Fouad Sabry

Summary

1: Extended Kalman filter: Introduces the extended Kalman filter (EKF), a core tool in nonlinear estimation.

2: Bra–ket notation: Explains the mathematical foundation, focusing on the structure of quantumlike systems.

3: Curvature: Discusses the concept of curvature and its influence on the performance of nonlinear filters.

4: Maximum likelihood estimation: Details the statistical approach used for estimating parameters with the highest likelihood.

5: Kalman filter: Provides an indepth exploration of the Kalman filter, the basis for many state estimation techniques.

6: Covariance matrix: Describes the covariance matrix and its role in quantifying uncertainty in filtering.

7: Propagation of uncertainty: Explores how uncertainty propagates over time and affects filtering accuracy.

8: Levenberg–Marquardt algorithm: Introduces this algorithm, which optimizes nonlinear least squares problems.

9: Confidence region: Explains the statistical region that quantifies the precision of parameter estimates.

10: Nonlinear regression: Focuses on methods for fitting nonlinear models to data using optimization techniques.

11: Estimation theory: Provides the theory behind estimation, essential for understanding filter design and analysis.

12: Generalized least squares: Discusses the generalized approach for solving regression problems in the presence of heteroscedasticity.

13: Von Mises–Fisher distribution: Introduces this probability distribution useful for directional data in high dimensions.

14: Ensemble Kalman filter: Explores a variation of the Kalman filter suitable for largescale nonlinear systems.

15: Filtering problem (stochastic processes): Details how filtering can be applied to random processes in dynamic systems.

16: GPS/INS: Describes the integration of GPS and inertial navigation systems for precise navigation and estimation.

17: Linear least squares: Covers the least squares method for solving linear regression problems.

18: Symmetrypreserving filter: Introduces filters designed to preserve symmetry in systems, important in robotics.

19: Invariant extended Kalman filter: Explains a variation of EKF that maintains invariance in nonlinear systems.

20: Unscented transform: Discusses the unscented transform, a technique for improving state estimation in nonlinear models.

21: SAMV (algorithm): Introduces the SAMV algorithm for robust estimation in uncertain environments.

Available since: 12/13/2024.

Print length: 407 pages.

Science & Technology

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