- Description: Fundamentals of estimation theory and sequential filtering, traditional concepts and recent advances in estimation, and applications to dynamic systems in engineering. Emphasis on mathematical modeling of physical problems.
- Goal: To provide traditional concepts and recent advances in estimation related to modern dynamic systems found in engineering disciplines; least squares estimation, state estimation, nonlinear filtering, aircraft position and velocity tracking, attitude determination of spacecraft vehicles, gyro bias estimation and calibration.
- Contents:
- Linear and Nonlinear Least Square Estimation
- Gaussian Least Square Differential Correction
- Elements of Linear Algebra for Least Squares
- Probability Concepts in Least Squares Estimation
- Elements of Probability Theory
- Functions of One Random Variable
- Vector Functions of n Random Variables
- Propagation of Moments through Linear and Nonlinear Models
- Monte Carlo Methods
- Minimal Variance Estimation
- Maximum Likelihood Estimation
- Differential Equation Models
- Batch and Sequential Estimation of Dynamical Systems
- Extended Kalman Filter
- Theoretical vs Artistic Aspects of Filter Tuning
- Recommended Textbooks:
- Optimal Estimation of Dynamic Systems by John Crassidis and John Junkins, Publisher: Chapman and Hall/CRC, 2nd Edition, 2011, ISBN 9781439839850. http://www.crcpress.com/product/isbn/9781439839850
- Learning Outcomes:
- Formulate estimation theories of algebraic systems and implement these algorithms to solve engineering problems.
- Apply the concepts of probability in least square estimation for linear and nonlinear systems in discrete and continues time.
- Understand the rigorous, detailed treatments of least squares and Kalman filtering.
- Derive estimation techniques to solve nonlinear
filtering problems. - Apply the estimation theories to actual dynamic systems.
- Topical Outline:
- Introduction to Estimation: Mathematical Background, Parameter Optimization (L1-L2)
- Estimation of Algebraic Systems (L3-L8)
- Linear Least Square Approximation
- Batch
- Sequential
- Curve Fitting vs Estimation
- Basis Functions
- Gramm-Schmidt Process for Orthogonalization
- Nonlinear Least Square Estimation
- Nonlinear Programming Approaches
- Gaussian Least Square Differential Correction
- Other Nonlinear LS Topics
- Elements of Linear Algebra for Least Squares
- Matrix Decompositions
- Applications
- Linear Least Square Approximation
- Probability Concepts in Least Squares Estimation (L9-L14)
- Elements of Probability Theory
- Functions of One Random Variable
- Vector Functions of n Random Variables
- Density Functions
- Discrete vs Continuous
- Moments/Expectation Operator
- Mean, Variance, —
- Propagation of Moments through Linear and Nonlinear Models
- Monte Carlo Methods
- Minimal Variance Estimation
- Maximum Likelihood Estimation
- Other Topics
- Applications
- Elements of Probability Theory
- Estimation of Dynamical Systems (L15-L22)
- Differential Equation Models
- Linear Systems
- Continuous vs Discrete Time
- Non-Linear Systems
- Linearization about a trajectory
- Stability of Dynamical Systems
- Linear Systems
- Batch Estimation of Dynamical Systems
- Gaussian Least Square Differential Correction
- Sequential Estimation of Dynamical Systems
- Extended Kalman Filter
- Continuous Time
- Discrete Time
- Extended Kalman Filter
- Theoretical vs Artistic Aspects of Filter Tuning
- In Theory, there is no difference between theory and practice, but In Practice, there is. J
- Other Topics
- Applications
- Differential Equation Models
