State Estimation in Practice: Kalman, H-Infinity, and Nonlinear Filtering for Robotics, Aerospace, and Autonomous Systems - with Python

State Estimation in Practice is a graduate-level, code-first treatment of optimal filtering for engineers who need to implement, tune, and defend a working estimator - not just recognize its equations. Across sixteen chapters it derives the discrete and continuous Kalman filter, the extended and unscented Kalman filter, particle filters, and H-infinity and mixed Kalman/H-infinity robust filtering from first principles, then hand-rolls every one of them in short, runnable Python so the derivation on the page and the algorithm on the screen are the same object.

WHAT'S INSIDE THIS BOOK

• State-Space Foundations and Observability - Discrete and continuous state-space models, Van Loan exact discretization, and the observability/controllability rank tests that determine whether a sensor suite can estimate the state you actually want.
• Probability and Random Processes for Estimation - The multivariate Gaussian, the Chapman-Kolmogorov equation, and Gauss-Markov noise models built up to the exact Bayesian recursion every filter in the book runs on.
• Least Squares and the Cramér-Rao Bound - Batch and weighted least squares, the Gauss-Markov BLUE theorem, and recursive least squares, closing with the Cramér-Rao lower bound as the hard limit on estimator accuracy.
• The Discrete-Time Kalman Filter, Fully Derived - An orthogonality-principle derivation of the Kalman gain across 5 worked examples, plus the Joseph-form covariance update and the innovation whiteness test.
• Numerical Robustness and Filter Tuning - Information filters, square-root and UD factorization, sequential scalar measurement processing, and the NEES/NIS statistics that catch a diverging filter before it fails in the field.
• Correlated Noise, Colored Noise, and Constraints - Cross-correlation-corrected Kalman gains, shaping filters for colored process noise, and projection-based constrained filtering for states with known physical bounds.
• The Continuous and Continuous-Discrete Kalman Filter - The Kalman-Bucy filter, the continuous Riccati differential equation, and the algebraic Riccati equation as its steady-state fixed point.
• Fixed-Interval, Fixed-Lag, and Fixed-Point Smoothing - The Rauch-Tung-Striebel smoother, derived and proven to dominate the forward filter, across 12 worked problems with full solutions.
• The Extended Kalman Filter and Its Failure Modes - Jacobian linearization, iterated EKF re-linearization, and a bearings-only tracking example showing exactly how and why an EKF diverges.
• The Unscented Kalman Filter - Sigma-point generation from the unscented transform, scaling-parameter tuning, and a head-to-head UKF-versus-EKF accuracy comparison on a strongly nonlinear system.
• Particle Filters and Sequential Monte Carlo - Importance sampling, systematic resampling, effective-sample-size monitoring, and a multimodal tracking example where a Gaussian filter provably fails.
• H-Infinity and Mixed Kalman/H-Infinity Robust Filtering - The H-infinity Riccati recursion derived from a minimax cost functional across 4 worked examples in navigation, spacecraft attitude, and wind-gust rejection.
• Adaptive and Interacting Multiple Model Filtering - Sage-Husa recursive noise-covariance estimation and interacting multiple model (IMM) filtering for a maneuvering target switching motion models.
• Sensor Fusion for Inertial Navigation - Loosely- and tightly-coupled GNSS/INS architectures, the error-state Kalman filter, and IMU bias and random-walk error models for a full INS/GPS fusion example.
• SLAM and Multi-Target Tracking for Robotics - EKF- and UKF-SLAM landmark estimation, nearest-neighbor and JPDA data association, and a simulated autonomous-vehicle pipeline fusing lidar, radar, and camera tracks.
• Three Fully Worked Capstones