Mohinder S. Grewal

Application of Kalman filtering to the calibration and alignment of inertial navigation systems

The development of Kalman filters for the calibration and alignment of complex inertial guidance systems is presented. The attitude error equation is augmented by gyro and accelerometer model parameters. The mechanization of the algorithm involves preprocessing the raw measurements to reduce the computational load. Results for simulated data show that preprocessing has very little effect on the performance of the filter. Other topics discussed include gyro and accelerometer models and a technique for generating parameter excitation trajectories. >

Identification of Parameters in a Freeway Traffic Model

The methodology of discrete time, extended Kalman filtering is applied to the problem of identifying parameters of a macroscopic freeway traffic model. Macroscopic models provide a representation of traffic flow in terms of its gross properties, i.e., volume, density, and speed. The local identifiability of a parameterization of macroscopic model at nominal values of the unknown parameters is checked before any identification is attempted. It is shown that the parameterization is locally identifiable. Two parameters of the model (reaction time and sensitivity to changing density) were identified through the use of this methodology. The data base for studies to date was generated from a microscopic simulation of freeway traffic, which involves following all individual vehicle movements. Techniques for extending the methodology to employ real freeway traffic data, especially as can be obtained from automated surveillance systems, are discussed.

Application of Kalman filtering to gyroless attitude determination and control system for environmental satellites

A highly accurate, gyroless, attitude determination and control system for advanced environmental satellites is developed and validated by analysis and simulation. The features of this approach include an algorithm to determine satellite rates directly from the apparent motion of the stars on the focal plane and an extended square root Kalman filter algorithm to estimate attitude. This system is appropriate for satellites with slowly varying attitude dynamics and high priority accuracy. Missions of this variety are meteorology, Earth resources, communication and surveillance. Appropriate attitude control techniques are reaction wheel and bias momentum system providing three-axis pointing control. The simulation results of the attitude estimation with various noise statistics on the star data are shown. The results of this approach are also compared with the gyro-aided system in accuracy of the attitude estimation process. The results show that the concept presented in the paper does work and that the accuracy would meet a large variety of satellite mission requirements. The major result of this research is the realization of a space-capable stellar attitude determination system which does not require a rate gyro package.

Relationships between identifiability and input selection

This paper points out a relationship between identifiability and input selection for multiparameter systems. Two examples are given to illustrate this relationship.

Kalman Filter Implementation With Improved Numerical Properties

This paper presents a new form of Kalman filter-the sigmaRho filter-useful for operational implementation in applications where stability and throughput requirements stress traditional implementations. The new mechanization has the benefits of square root filters in both promoting stability and reducing dynamic range of propagated terms. State standard deviations and correlation coefficients are propagated rather than covariance square root elements and these physically meaningful statistics are used to adapt the filtering for further ensuring reliable performance. Finally, all propagated variables can be scaled to predictable dynamic range so that fixed point procedures can be implemented for embedded applications. A sample problem from communications signal processing is presented that includes nonlinear state dynamics, extreme time-variation, and extreme range of system eigenvalues. The sigmaRho implementation is successfully applied at sample rates approaching 100 MHz to decode binary digital data from a 1.5-GHz carrier.

An introduction to the kalman filter

This is a list of errors in the book Optimal State Estimation, John Wiley & Sons, 2006. The main web site for the book is at http://academic.csuohio.edu/simond/estimation. My email address is listed on my home page at http://academic.csuohio.edu/simond. I enthusiastically welcome feedback, comments, suggestions for improvements, and corrections. I also gratefully acknowledge those who have pointed out many of the errata that are documented here: Ali Javadi, Juan Luque, Ibrahim Abdel Hameed, Rick Rarick, Memo Ergezer, David Schwartz, Jeff Gove, Kevin Sharp, Stephan Busch, Yeoh WeeSoon, Michael Haralambous, Ville Kyrki, George Dontas, Felix Monasterio-Huelin, Cagdas Ozgenc, Cheng Zhong, Ning Lei, Roberto Rigamonti, Vincent Sircoulomb, Sami Fadali, Max Medvetsky, Jonathan How, Ismar Masic, Arthur Menikoff, Nedzad Arnautovic, Gabriel Zigelboim, Antje Westenberger, Laurent de Vito, Warner Losh, HunCheol Im, Martin Grossman, Christof Voemel, Bill Jordan, Bruno Stratmann, Philipp Warode, John McFarland, and James Tursa.In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation. The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error. The filter is very powerful in several aspects: it supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modeled system is unknown. The purpose of this paper is to provide a practical introduction to the discrete Kalman filter. This introduction includes a description and some discussion of the basic discrete Kalman filter, a derivation, description and some discussion of the extended Kalman filter, and a relatively simple (tangible) example with real numbers & results.

Optimal selection of trajectories for parameter estimation in dynamical systems

In this paper, an optimal path of trajectory for inertial platform motion relative to the earth will be designed. The time dependent motion, (i.e., vertical and level mobility rates), must be designed to excite all the parameters of the system, i.e., gyro and accelerometer parameters. The criterion used for optimization is the maximization of the determinant of the observability matrix. An application of this technique to two and three parameters of an accelerometer is shown. The computer results for a four accelerometer parameters case is also given.

Kalman Filters and Observers

The sections in this article are 1 White Noise 2 Linear Estimation 3 The Linear Optimal Estimator In Discrete Time (Kalman Filter) 4 The Continuous-Time Optimal Estimator (Kalman-Bucy Filter) 5 Nonlinear Estimation 6 The Matrix Riccati Differential Equation 7 Controllers, Observers, And The Separation Principle 8 Implementation Methods

A computational method for evaluating the identifiability of linear parameterized dynamical systems

The computational method developed in this short paper allows the user a simple direct method of determining the identifiability of a linear parameterized system under the following assumptions: The nominal values of the parameters are available and the state matrices are linear functions of the unknown parameters. The development analysis necessary to implement the computational method with examples is presented.