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NASA NTRS2005

Automatic Certification of Kalman Filters for Reliable Code Generation

AUTOFILTER is a tool for automatically deriving Kalman filter code from high-level declarative specifications of state estimation problems. It can generate code with a range of algorithmic characteristics and for several target platforms. The tool has been designed with reliability of the generated code in mind and is able to automatically certify that the code it generates is free from various error classes. Since documentation is an important part of software assurance, AUTOFILTER can also automatically generate various human-readable documents, containing both design and safety related information. We discuss how these features address software assurance standards such as DO-178B.

Denney, Ewen↗
NASA NTRS1986

Kalman filtering, smoothing and recursive robot arm forward and inverse dynamics

The inverse and forward dynamics problems for multi-link serial manipulators are solved by using recursive techniques from linear filtering and smoothing theory. The pivotal step is to cast the system dynamics and kinematics as a two-point boundary-value problem. Solution of this problem leads to filtering and smoothing techniques identical to the equations of Kalman filtering and Bryson-Frazier fixed time-interval smoothing. The solutions prescribe an inward filtering recursion to compute a sequence of constraint moments and forces followed by an outward recursion to determine a corresponding sequence of angular and linear accelerations. In addition to providing techniques to compute joint accelerations from applied joint moments (and vice versa), the report provides an approach to evaluate recursively the composite multi-link system inertia matrix and its inverse. The report lays the foundation for the potential use of filtering and smoothing techniques in robot inverse and forward dynamics and in robot control design.

Rodriguez, G.↗
NASA NTRS2012

A review of reduced Kalman filters for clock ensembles

This paper reviews the author’s previous work on free-running timescales based on Kalman filters that act upon clock comparisons. The natural Kalman clock ensemble algorithm tends to optimize long-term timescale stability at the expense of short-term stability. By subjecting each postmeasurement error covariance matrix to a non-transparent reduction operation, one obtains corrected clocks with improved short-term stability and little sacrifice of long-term stability. A new result on covariance matrix reduction is also stated.

Greenhall, Charles A.↗
NASA NTRS1994

An Approximate Kalman Filter for Ocean Data Assimilation; An Example with an Idealized Gulf Stream Model

A practical method of data assimilation for use with large, nonlinear, ocean general circulation models is explored. A Kalman filter based on approximations of the state error covariance matrix is presented, employing a reduction of the effective model dimension, the error's asymptotic steady-state limit, and a time-invariant linearization of the dynamic model for the error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. We examine the utility of the approximate filter in assimilating different measurement types using a twin experiment of an idealized Gulf Stream. A nonlinear primitive equation model of an unstable east-west jet is studied with a state dimension exceeding 170,000 elements. Assimilation of various pseudo measurements is examined, including velocity, density, and volume transport at localized arrays, and realistic distributions of satellite altimetry and acoustic tomography observations. Results are compared in terms of their effects on the accuracies of the estimation. The approximate filter is shown to outperform a previous study that used an empirical nudging scheme. The examples demonstrate that useful approximate estimation errors can be computed in a practical manner for general circulation models.

['Kalman↗
NASA NTRS1985

A Kalman filter for a two-dimensional shallow-water model

A two-dimensional Kalman filter is described for data assimilation for making weather forecasts. The filter is regarded as superior to the optimal interpolation method because the filter determines the forecast error covariance matrix exactly instead of using an approximation. A generalized time step is defined which includes expressions for one time step of the forecast model, the error covariance matrix, the gain matrix, and the evolution of the covariance matrix. Subsequent time steps are achieved by quantifying the forecast variables or employing a linear extrapolation from a current variable set, assuming the forecast dynamics are linear. Calculations for the evolution of the error covariance matrix are banded, i.e., are performed only with the elements significantly different from zero. Experimental results are provided from an application of the filter to a shallow-water simulation covering a 6000 x 6000 km grid.

Parrish, D. F.↗
NASA NTRS2002

Kalman Filter Chemical Data Assimilation: A Case Study in January 1992

This paper describes a Kalman filter chemical data assimilation system and its use for analysing a vertical atmospheric profile during January 1992. The vertical profile was at an equivalent PV latitude (phi(sub e)) of 55 deg S and consisted of 21 potential temperature (theta) levels spaced equally in log(theta) between 400 K and 2000 K. This equivalent latitude was chosen as it was well observed during January 1992 by instruments on board the Upper Atmosphere Research Satellite (UARS).

Lary, D. J.↗
NASA NTRS1995

A steady-state Kalman filter for assimilating data from a single polar orbiting satellite

A steady-state scheme for data assimilation in the context of a single, short period (relative to a day), sun-synchronous, polar-orbiting satellite is examined. If the satellite takes observations continuously, the gains, which are the weights for blending observations and predictions together, are steady in time. For a linear system forced by random noise, the optimal steady-state gains (Wiener gains) are equivalent to those of a Kalman filter. Computing the Kalman gains increases the computational cost of the model by a large factor, but computing the Wiener gains does not. The latter are computed by iteration using prior estimates of the gains to assimilate simulated observations of one run of the model, termed 'truth' into another run termed 'prediction'. At each stage, the prediction errors form the basis for the next estimate of the gains. Steady state is achieved after three or four iterations. Further simplification is achieved by making the gains depend on longitudinal distance from the observation point, not on absolute longitude. For a single-layer primitive equation model, the scheme works well even if only the mass field is observed but not the velocity field. Although the scheme was developed for Mars Observer, it should be applicable to data retrieved from Earth atmosphere satellites, for example, UARS.

Banfield, Don↗
NASA NTRS1987

Kalman filtering, smoothing, and recursive robot arm forward and inverse dynamics

The recursive difference equations of Kalman filtering and Bryson-Frazier fixed time-interval smoothing, arising in the state estimation theory for linear state space systems, are used here to solve problems of serial manipulator inverse and forward dynamics. The configuration analyzed is that of a joint connected N-link serial manipulator attached to an immobile base. The equivalence between the filtering and smoothing techniques from state estimation theory and recursive robot dynamics methods is demonstrated. Several areas for future research are suggested.

Rodriguez, Guillermo↗
NASA NTRS2004

Data assimilation of ground GPG total electron content into a physics-based ionosheric model by use of the Kalman filter

A three-dimensional (3-D) Global Assimilative Ionospheric Model (GAIM) is currently being developed by a joint University of Southern California and Jet Propulsion Laboratory (JPL) team. To estimate the electron density on a global grid, GAIM uses a first-principles ionospheric physics model and the Kalman filter as one of its possible estimation techniques.

ionosphere forecast data assimilation Kalman filte↗
NASA NTRS1988

An extended Kalman filter based automatic frequency control loop

An Automatic Frequency Control (AFC) loop based on an Extended Kalman Filter (EKF) is introduced and analyzed in detail. The scheme involves an EKF which operates on a modified set of data in order to track the frequency of the incoming signal. The algorithm can also be viewed as a modification to the well known cross-product AFC loop. A low carrier-to-noise ratio (CNR), high-dynamic environment is used to test the algorithm and the probability of loss-of-lock is assessed via computer simulations. The scheme is best suited for scenarios in which the frequency error variance can be compromised to achieve a very low operating CNR threshold. This technique can easily be incorporated in the Advanced Receiver (ARX), requiring minimum software modifications.

Hinedi, S.↗
NASA NTRS1989

Extended Kalman filter for attitude estimation of the earth radiation budget satellite

The design and testing of an Extended Kalman Filter (EKF) for ground attitude determination, misalignment estimation and sensor calibration of the Earth Radiation Budget Satellite (ERBS) are described. Attitude is represented by the quaternion of rotation and the attitude estimation error is defined as an additive error. Quaternion normalization is used for increasing the convergence rate and for minimizing the need for filter tuning. The development of the filter dynamic model, the gyro error model and the measurement models of the Sun sensors, the IR horizon scanner and the magnetometers which are used to generate vector measurements are also presented. The filter is applied to real data transmitted by ERBS sensors. Results are presented and analyzed and the EKF advantages as well as sensitivities are discussed. On the whole the filter meets the expected synergism, accuracy and robustness.

Deutschmann, Julie↗
NASA NTRS1990

Comparison and testing of extended Kalman filters for attitude estimation of the Earth radiation budget satellite

The testing and comparison of two Extended Kalman Filters (EKFs) developed for the Earth Radiation Budget Satellite (ERBS) is described. One EKF updates the attitude quaternion using a four component additive error quaternion. This technique is compared to that of a second EKF, which uses a multiplicative error quaternion. A brief development of the multiplicative algorithm is included. The mathematical development of the additive EKF was presented in the 1989 Flight Mechanics/Estimation Theory Symposium along with some preliminary testing results using real spacecraft data. A summary of the additive EKF algorithm is included. The convergence properties, singularity problems, and normalization techniques of the two filters are addressed. Both filters are also compared to those from the ERBS operational ground support software, which uses a batch differential correction algorithm to estimate attitude and gyro biases. Sensitivity studies are performed on the estimation of sensor calibration states. The potential application of the EKF for real time and non-real time ground attitude determination and sensor calibration for future missions such as the Gamma Ray Observatory (GRO) and the Small Explorer Mission (SMEX) is also presented.

Deutschmann, Julie↗
NASA NTRS1990

Extended Kalman Filter for attitude estimation of the Earth Radiation Budget Satellite

The design and testing of an Extended Kalman Filter (EKF) for ground attitude determination, misalignment estimation and sensor calibration of the Earth Radiation Budget Satellite (ERBS) are described. Attitude is represented by the quaternion of rotation and the attitude estimation error is defined as an additive error. Quaternion normalization is used for increasing the convergence rate and for minimizing the need for filter tuning. The development of the filter dynamic model, the gyro error model and the measurement models of the sun sensors, the IR horizon scanner and the magnetometers which are used to generate vector measurements are also presented. The filter is applied to real data transmitted by ERBS sensors. Results are presented and analyzed and the EKF advantages as well as sensitivities are discussed. On the whole the filter meets the expected synergism, accuracy and robustness.

Deutschmann, Julie↗
NASA NTRS2005

Application of a Constant Gain Extended Kalman Filter for In-Flight Estimation of Aircraft Engine Performance Parameters

An approach based on the Constant Gain Extended Kalman Filter (CGEKF) technique is investigated for the in-flight estimation of non-measurable performance parameters of aircraft engines. Performance parameters, such as thrust and stall margins, provide crucial information for operating an aircraft engine in a safe and efficient manner, but they cannot be directly measured during flight. A technique to accurately estimate these parameters is, therefore, essential for further enhancement of engine operation. In this paper, a CGEKF is developed by combining an on-board engine model and a single Kalman gain matrix. In order to make the on-board engine model adaptive to the real engine s performance variations due to degradation or anomalies, the CGEKF is designed with the ability to adjust its performance through the adjustment of artificial parameters called tuning parameters. With this design approach, the CGEKF can maintain accurate estimation performance when it is applied to aircraft engines at offnominal conditions. The performance of the CGEKF is evaluated in a simulation environment using numerous component degradation and fault scenarios at multiple operating conditions.

Kobayashi, Takahisa↗
NASA NTRS1980

Estimation of Kalman filter model parameters from an ensemble of tests

A methodology for estimating initial mean and covariance parameters in a Kalman filter model from an ensemble of nonidentical tests is presented. In addition, the problem of estimating time constants and process noise levels is addressed. Practical problems such as developing and validating inertial instrument error models from laboratory test data or developing error models of individual phases of a test are generally considered.

Gibbs, B. P.↗
NASA NTRS1981

Real time estimation of the heaving and pitching motions of a ship, using a Kalman filter

In the present study the estimation of the heave and pitch motion of a ship is considered, using Kalman filtering techniques. A significant part of the study is devoted to constructing appropriate models for the sea and the ship. The governing equations are obtained from hydrodynamic considerations in the form of linear differential equations with frequency dependent coefficients. In addition, nonminimum phase characteristics are obtained due to the spatial integration of the water wave forces. The resulting transfer matrix function is irrational and nonminimum phase. The conditions for a finite-dimensional approximation are considered and the impact of the various parameters is assessed. A numerical application is considered for a DD-963 destroyer.

Triantafyllou, M.↗
NASA NTRS2004

Using an Extended Kalman Filter Learning Algorithm for Feed-Forward Neural Networks to Describe Tracer Correlations

In this study a new extended Kalman filter (EKF) learning algorithm for feed-forward neural networks (FFN) is used. With the EKF approach, the training of the FFN can be seen as state estimation for a non-linear stationary process. The EKF method gives excellent convergence performances provided that there is enough computer core memory and that the machine precision is high. Neural networks are ideally suited to describe the spatial and temporal dependence of tracer-tracer correlations. The neural network performs well even in regions where the correlations are less compact and normally a family of correlation curves would be required. For example, the CH4-N2O correlation can be well described using a neural network trained with the latitude, pressure, time of year, and CH4 volume mixing ratio (v.m.r.). The neural network was able to reproduce the CH4-N2O correlation with a correlation coefficient between simulated and training values of 0.9997. The neural network Fortran code used is available for download.

Lary, David J.↗