Lew Payne's Technical Blog

Welcome to my technical blog. I created this blog to facilitate my ongoing research, by giving me a place to store useful research data. It also allows me to comment on various items as I work through their various implementations and determine suitability for my particular projects. Initially, my research was into Kalman filters; hence that is where the bulk of my commentary is located.

This blog is updated regularly, each time I run into something that is useful or substantive. While its format might not be ideal (since it grew to be more than anticipated), keep in mind that its main purpose is to allow me easy access to information that would otherwise be a pain to retrieve (not to mention difficult to integrate my comments into).

Major Categories

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)."

"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."

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

Kalman Filter Code:

Other Stabilization Methods:
"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."
"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:

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