4.3 Estimation Algorithms
This page is a checklist of estimation methods. Later you can expand each block into short cheat sheets linked to problems and tools.
4.3.1 Linear Estimation Framework
- State-space models with process and measurement noise
- Covariance propagation and error dynamics
- Innovation / residual definition
- Observability and detectability
4.3.2 Batch Least Squares Methods
- Batch estimator formulation and normal equations
- Weighted Least Squares and a priori constraints
- Sensitivity (design) matrix and Jacobians
- Batch covariance estimation and smoothing idea
4.3.3 Sequential (Recursive) Estimation
- Classical Kalman Filter (KF) structure
- Time update (prediction) and measurement update (correction)
- Innovation statistics and consistency checks
- Numerically stable forms (Joseph update, square-root filters)
4.3.4 Extended Kalman Filter (EKF)
- Linearization of nonlinear dynamics and measurements
- Jacobian computation and error-state models
- Iterated EKF concepts
4.3.5 Unscented Kalman Filter (UKF)
- Sigma-point selection and unscented transform
- Prediction and update with sigma points
- Comparison with EKF and attitude (quaternion) UKF use
4.3.6 Nonlinear Least Squares
- Gauss–Newton method
- Levenberg–Marquardt method
- Maximum Likelihood Estimation link
4.3.7 Smoothers
- Fixed-interval smoother (RTS)
- Fixed-lag smoothing
- Use with batch and sequential estimators
4.3.8 Particle Filters
- Sequential Monte Carlo idea
- Importance sampling and resampling
- Non-Gaussian / strongly nonlinear applications
4.3.9 Covariance Analysis & Error Propagation
- Sensitivity matrices and perturbation covariance
- Error budgets and process noise tuning
- Bias estimation and correlation effects
4.3.10 Orbit Determination Algorithms
- State Transition Matrix (STM) in estimation
- Range, range-rate, and Doppler tracking models
- Angle-only and mixed measurement solutions
- Consider covariance and maneuver estimation concepts