Kalman Filters

Sigma-Point Kalman Filter & Stabilization Research:

• Introduction to the Kalman filter (Greg Welch & Gary Bishop)
• Unscented Kalman filter for Nonlinear Estimation (van der Merwe & Wan)
• Comparison of the Extended and Sigma-Point Kalman Filters on Inertial Sensor Bias Estimation through Tight Integration of GPS and INS (Wang & Rios)
• Sigma-point Kalman Filtering for Integrated Navigation (van der Merwe & Wan)
• Sigma-point Kalman Filters for Nonlinear Estimation & Sensor Fusion - Applications to Integrated Navigation (van der Merwe & Wan)
• Sigma-point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models (van der Merwe & Wan)
• Sigma-point Kalman Filtering for Integrated GPS & Inertial Navigation (Crassidis)
• Sigma-point Gaussian Sum Filter Design Using Square Root Unscented Filters (Simandl & Dunik)
• Unscented Kalman Filter Tutorial (Terejanu)
• Sigma-point Kalman Filters for GPS Navigation with Integrity in Aviation (Greer, et-al)
• Sigma-point Kalman Filtering for Tightly Coupled GPS/INS Integration (Li, Rizos, et-al)
• Comparison of Kalman Filter Estimation Approaches for State-Space Models with Nonlinear Measurements (Orderud)
• Highly Efficient Sigma Point Filter for Spacecraft Attitude & Rate Estimation (Fan & You, html)

"Incorporates the Geometric Simplex sigma point set into the Marginal SPKF framework, thus producing a nonlinear SPKF estimator for attitude estimation, aka the Marginal Geometric Sigma Point Kalman Filter (MGSPKF)."

• A New Extension of the Kalman Filter to Nonlinear Systems (Julier & Uhlmann)
• A New Approach for Filtering Nonlinear Systems (Uhlmann & Durrant-Whyte)
• Airborne Attitude Estimation Using a Kalman Filter (Marmion) 

"The Kalman filter is really precise in steady conditions; but reacts strongly to inertial forces. The integration model drifts in steady conditions, but does not react strongly to inertial forces. Thus, I had the idea to combine both models, depending on motion conditions: steady-state or not.  But then I blew it by writing this paper as if I were writing a screenplay for another reality show - and Lew Payne hates reality shows.  Also a continuous-time (blended) model would be better, rather than an 'or' model as you've done.  In fact, I believe I've seen such a model out there somewhere, in another research paper."

• Comparative Study of UKF/EKF in VTOL UAV (Fiorenzani, et-al)

"The UKF has a faster convergence with respect to the EKF, but after a settling time the performance becomes identical" ... "If initial estimation error is very large, and the initial covariance is inappropriate, the EKF diverges while the UKF converges.  The divergence at attitude angle brings with it the divergence of all other state variables."

• The Scaled Unscented Transformation (Simon J. Julier)
• Novel Simplex Unscented Transform & Filter (Wan-Chun Li, et-al)
• Forearm Controller & Tactile Display (David Sachs)
• Unscented Kalman Filter Tutorial (Terejanu)
• Single 7-State Discrete Time EKF for MAV's (Malik/Riaz)
• Triangular Covariance Factorizations for Kalman Filtering (Thornton)

"Square-root unscented Kalman filter with code in C++ and step-by-step explanation of math. Uses rank-one updates to the filter covariance so as to reduce the matrix math down to a scalar division, aka U-D decomposition."

• Kalman Filtering (Dan Simon Article)
• State Estimation for Micro Air Vehicles (Randall Beard)
• Improved State Estimation for Miniature Air Vehicles (Eldredge)

"Three-state state estimation scheme; pitch and roll, estimated heading, and position estimate which includes wind speed and direction." 

Kalman Filter Code:

• Matlab Kalman filter library, including sigma-point (van der Merwe contribution)
• Jonathan Brandmeyer's C++ Extended Kalman Code
• MatLab Central Kalman Filter Code (various)
• EKF/UKF Toolbox for Matlab (COSY)
• Kfilter C++ Extended Kalman Filter Library (sourceforge)
• Kalman Filtering of IMU data (tutorial)
• eNotes Kalman Filter Tutorial
• U-D Kalman Filter Fortran Code
• 5DOF Kalman Filtered IMU Code
• MRPT Project 6D-SLAM Kalman step-by-step (including U-D decomposition)
• BAYES++ Bayesian Filtering Classes
• Memsense Kalman Filter Library (in C++)
• Orocos Bayesian Filtering Library
• Andrew Straw's Python Kalman filter
• Adrian Boeing's Kalman filter explanation
• Tutorial on Filtering, Restoration & State Estimation (with source)

Other Stabilization Methods:

• DCM IMU Theory Papers (Mahony, Premineli)
• Adaptive Control of MAVs (Matthews)
• Coupled Non-Linear State Estimation and Control + seminar (Sung Han Cha)
• Coupled Estimation & Control Analysis for Attitude Stabilization + seminar (Sung Han Cha)
• Attitude Estimation - Comparison of Various Methods (GluonPilot)

"This paper proposes a coupled nonlinear attitude estimation and control design... Attitude estimation is based on a nonlinear complementary filter expressed on the rotation group.  The attitude control algorithm is based on a nonlinear Lyapunov function analysis derived directly in terms of the rigid-body attitude dynamics.  The interaction terms are bounded in terms of estimation and control errors and the full coupled system is show to be almost globally stable."

• Real-Time Attitude & Position Estimation for Small UAVs (Kingston/Beard)

"In connection with an extended Kalman filter attitude estimation scheme, a novel method for dealing with latency in real-time is presented using a distributed-in-time architecture."  Lew: This also uses an interesting cascaded INS concept.

Control Theory:

• OpenPilot PID controller mapping to pitch, roll and yaw
• PID Without a PhD (Tim Wescott)
• PID controller tuning (including relay tuning) 
• Sensor Performance Improvement Using Allan Variance Analysis (pdf)