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Airplane identification, equation error method, maximum likelihood method, parameter estimation in frequency domain, extended Kalman filter, aircraft equations of motion, aerodynamic model equations, criteria for the selection of a parsimonious model, and online aircraft identification are addressed.
Adaptive control techniques are studied for their future application to the control of large space structures, where uncertain or changing parameters may destabilize standard control system designs. The approach used is to examine an extended Kalman filter estimator, in which the state vector is augmented with the unknown parameters. The associated Riccatti equation is linearized about the case of exact knowledge of the parameters. By assuming that parameter variations occur slowly, the filter complexity is reduced further yet. Simulations on a two degree-of-freedom oscillator demonstrate the parameter-tracking capability of the filter, and an implementation on the JPL Flexible Beam Facility using an incorrect model shows the adaptive filter/optimal control to be stable where a standard Kalman filter/optimal control design is unstable.
An algorithm for processing flight-test data to provide state estimates and instrument calibrations for aerodynamic or hydrodynamic system identification by the equation error estimation method is developed and demonstrated on synthesized data. The extended-Kalman-filter algorithm employs a locally level, north-pointing frame of reference, accounts for rotating ellipsoidal earth effects, and estimates sensor bias, scale factors, wind components, and process noise levels by maximum-likelihood parameters. The method is found to be most effective with navigation quality inertial input data. The algorithm is applied to data from a six-degree-of-freedom F-4 aircraft simulation and shown to produce state estimates in good agreement with the simulation values.
The mathematical developments and their computer program implementation for the Space Shuttle propulsion parameter estimation project are summarized. The estimation approach chosen is the extended Kalman filtering with a modified Bryson-Frazier smoother. Its use here is motivated by the objective of obtaining better estimates than those available from filtering and to eliminate the lag associated with filtering. The estimation technique uses as the dynamical process the six degree equations-of-motion resulting in twelve state vector elements. In addition to these are mass and solid propellant burn depth as the ""system'' state elements. The ""parameter'' state elements can include aerodynamic coefficient, inertia, center-of-gravity, atmospheric wind, etc. deviations from referenced values. Propulsion parameter state elements have been included not as options just discussed but as the main parameter states to be estimated. The mathematical developments were completed for all these parameters. Since the systems dynamics and measurement processes are non-linear functions of the states, the mathematical developments are taken up almost entirely by the linearization of these equations as required by the estimation algorithms.
A computational algorithm for the identification of biases in discrete-time, nonlinear, stochastic systems is derived by extending the separate bias estimation results for linear systems to the extended Kalman filter formulation. The merits of the approach are illustrated by identifying instrument biases using a terminal configured vehicle simulation.
A computational algorithm for the identification of input and output biases in discrete-time nonlinear stochastic systems is derived by extending the separate bias estimation results for linear systems to the extended Kalman filter formulation. The merits of the approach are illustrated by identifying instrument biases using a terminal configured vehicle simulation.
This investigation considers the problem of autonomous satellite navigation using the NAVSTAR Global Positioning System (GPS). The major topics covered include the design, implementation, and validation of onboard navigation filter algorithms by means of computer simulations. The primary errors that the navigation filter design must minimize are computational effects and modeling inaccuracies due to limited capability of the onboard computer. The minimization of the effect of these errors is attained by applying the sequential extended Kalman filter using a factored covariance implementation with Q-matrix or dynamical model compensations. Peformance evaluation of the navigation filter design is carried out using both the CDC Cyber 170/750 computer and the PDP-11/60 computer. The results are obtained assuming the Phase I GPS constellation, consisting of six satellites, and a Landsat-D type spacecraft as the model for the user satellite orbit.
In a previous paper Schaechter proposes using an extended Kalman filter to estimate adaptively the (slowly varying) frequencies and damping ratios of a large space structure. The time varying gains for estimating the frequencies and damping ratios can be determined in closed form so it is not necessary to integrate the matrix Riccati equations. After certain approximations, the time varying adaptive gain can be written as the product of a constant matrix times a matrix derived from the components of the estimated state vector. This is an important savings of computer resources and allows the adaptive filter to be implemented with approximately the same effort as the nonadaptive filter. The success of this new approach for adaptive filtering was demonstrated using synthetic data from a two mode system.
The modifications to the design of a fault inferring nonlinear detection system (FINDS) algorithm to accommodate flight computer constraints and the resulting impact on the algorithm performance are summarized. An overview of the flight data-driven FINDS algorithm is presented. This is followed by a brief analysis of the effects of modifications to the algorithm on program size and execution speed. Significant improvements in estimation performance for the aircraft states and normal operating sensor biases, which have resulted from improved noise design parameters and a new steady-state wind model, are documented. The aircraft state and sensor bias estimation performances of the algorithm's extended Kalman filter are presented as a function of update frequency of the piecewise constant filter gains. The results of a new detection system strategy and failure detection performance, as a function of gain update frequency, are also presented.
Nonlinear filtering techniques are applied to spacecraft attitude estimation using quaternion parameterization for the attitude kinematics. By replacing the angular velocity vector by the gyro output vector, a state dependent noise vector is introduced in the seven-dimensional system equations. The resulting conditional probability density function from the Ito differential rule is governed by the Fokker Planck partial differential equation which is approximated by the second order mean and covariance differential equations. In order to minimize computer loading, the covariance propagation is carried out in six-dimensional state space using a matrix transformation. The star tracker data is used to update the covariance matrix in the seven-dimensional space. The algorithm is simulated for an earth pointing spacecraft mission, using Monte Carlo samples of gyro and star measurements. The performance of the second order filter is compared with the extended Kalman Filter through several simulation runs and drift rates have been identified.
This paper summarizes the modifications made to the design of a fault inferring nonlinear detection system (FINDS) algorithm to accommodate flight computer constraints and the resulting impact on the algorithm performance. An overview of the flight data-driven FINDS algorithm is presented. This is followed by a brief analysis of the effects of modifications to the algorithm on program size and execution speed. Significant improvements in estimation performance for the aircraft states and normal operating sensor biases, which have resulted from improved noise design parameters and a new steady-state wind model, are documented. The aircraft state and sensor bias estimation performances of the algorithm's extended Kalman filter are presented as a function of update frequency of the piecewise constant filter gains. The results of a new detection system strategy and failure detection performance, as a function of an update frequency, are also presented.
Real-time flutter prediction including close modes can be effectively estimated from turbulence or on-board excitation with an Extended Kalman Filter (EKF) approach. A physically based model form enables prediction of the damping rate as well as damping, giving a time to instability estimate with its variance. The approach is recursive and can operate asynchronously to drop data outliers and hence is quite robust. Its speed is reasonable for on-line application but can also be used effectively as an off-line analysis tool for application to any modal testing situation.
A new methodology is described for the design of nonlinear dynamic controllers for nonlinear multivariable systems providing guarantees of closed-loop stability, performance, and robustness. The methodology is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate inverse operator for the plant. A major feature of the methodology is a unification of both the state-space and input-output formulations. In addition, new results on stability theory, nonlinear state estimation, and optimal nonlinear regulator theory are presented, including the guaranteed global properties of the extended Kalman filter and optimal nonlinear regulators.
The filtering of the satellite range and range-rate measurements from single channel sequential Global Positioning System receivers is usually done with an extended Kalman filter which has state variables defined in terms of an orthogonal navigation reference frame. An attractive suboptimal alternative is range-domain filtering, in which the individual satellite measurements are filtered separately before they are combined for the navigation solution. The main advantages of range-domain filtering are decreased processing and storage requirements and simplified tuning. Several range filter mechanization alternatives are presented, along with an innovative approach for combining the filtered range-domain quantities to determine the navigation state estimate. In addition, a method is outlined for incorporating measurements from auxiliary sensors such as altimeters into the navigation state estimation scheme similarly to the satellite measurements. A method is also described for incorporating inertial measurements into the navigation state estimator as a process driver.
A dynamic force sensing method is proposed for a robot manipulator. A 6-axis wrist force sensor which is commonly used for robot force sensing does not take the direct measurement of the force and moment applied to an end effector externally from the environment of the manipulator, but takes the resultant of the gravity, the inertial force and moment on the end effector, and the external force and moment. The separation of gravitational and inertial force and moment from the measurement of the force sensor is crucial to achieving dynamically accurate force sensing and fast manipulator motion under force feedback control. A mathematical model is derived for the force sensing process and the separation of the force and moment as a nonlinear optimal state estimation problem formulated. Then an approximate solution is given using extended Kalman filtering techniques.
An optimal estimation scheme is presented, which determines the satellite attitude using the gyro readings and the star tracker measurements of a commonly used satellite attitude measuring unit. The scheme is mainly based on the exponential Fourier densities that have the desirable closure property under conditioning. By updating a finite and fixed number of parameters, the conditional probability density, which is an exponential Fourier density, is recursively determined. Simulation results indicate that the scheme is more accurate and robust than extended Kalman filtering. It is believed that this approach is applicable to many other attitude measuring units. As no linearization and approximation are necessary in the approach, it is ideal for systems involving high levels of randomness and/or low levels of observability and systems for which accuracy is of overriding importance.
Based on a Taylor series expansion, an easily-computed approximation to the Cartesian state transition matrix is presented for a general velocity-independent force field. Suitable for the short time intervals encountered in onboard navigation applications of the extended Kalman filter, it provides approximately five decimal digits of accuracy for earth orbiting spacecraft with update intervals of one minute, and better accuracy for shorter intervals.
The objectives and accomplishments of the two-and-a-half year effort to describe how returns from on-board Doppler radar are to be used to detect the presence of a wind shear are reported. The problem is modeled as one of first passage in terms of state variables, the state estimates are generated by a bank of extended Kalman filters working in parallel, and the decision strategy involves the use of a voting algorithm for a series of likelihood ratio tests. The performance issue for filtering is addressed in terms of error-covariance reduction and filter divergence, and the performance issue for detection is addressed in terms of using a probability measure transformation to derive theoretical expressions for the error probabilities of a false alarm and a miss.