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Modifications to the extended Kalman filter and the Jazwinski filter are made and compared with the classical extended Kalman filter in applications to orbit determination using real data. The results show that with the kind of data available today, the application of filtering theories in this field presents many problems.
Results of an experimental study of the effect of discharges in oxygen on the oxide thickness and transmittance of aluminum filters. The studies were performed by exposing the filters to RF discharges and dc glow discharges in oxygen. In all experiments except one in which an aluminum ring was used as the cathode an increase in the transmittance of the filters is noted. It is thus demonstrated that the transmittance of aluminum filters increases on exposure to electrical discharges in oxygen, although it is not certain whether this phenomenon is caused by atomic oxygen.
In this paper a technique is developed for choosing programing forms and bit configurations for digital filters that minimize the quantization errors. The technique applies to digital filters operating in fixed-point arithmetic in either open-loop or closed-loop systems, and is implemented by a digital computer program that is based on a digital simulation of the system. As an output the program gives the programing form required for minimum quantization errors, the total bit configuration required in the filter, and the location of the binary decimal point at each quantizer within the filter.
The development of a cryogenically cooled filter radiometer for use with high altitude balloons is discussed. The radiometer has features which include the options for remote operation of two filter wheels each containing six filters at helium temperature and a cryogenic rotary chopper which may be run at 200 cycles per second or positioned open or closed, and a remotely operable chopped blackbody calibration source. The radiometer contains a ten inch diameter liquid nitrogen cooled Cassegrain telescope with nine individually filtered field stops in the focal plane. The telescope is mounted on a two-axis servo operated gimbal which is used to make sky scans under the control of an onboard programmer.
An onboard navigation system which employed complementary filtering was developed to provide velocity and position information. The inputs to the mix filter included both acceleration inputs, which provided high-frequency position and velocity information, and radar position inputs, which provided the low-frequency position and velocity information. Onboard aircraft instrumentation, including attitude reference gyros and body-mounted accelerometers, was used to provide the acceleration information. An in-flight comparison of signal quality and accuracy showed good agreement between the complementary filtering system and an aided inertial navigation system. Furthermore, the complementary filtering system was proven to be satisfactory in control and display system applications for both automatic and pilot-in-the-loop instrument approaches and landings.
The video inertial pointing (VIP) system is being developed to satisfy the acquisition and pointing requirements of astronomical telescopes. The VIP system uses a single video sensor to provide star position information that can be used to generate three-axis pointing error signals (multi-star processing) and for input to a cathode ray tube (CRT) display of the star field. The pointing error signals are used to update the telescope's gyro stabilization system (gyro filtering). The CRT display facilitates target acquisition and positioning of the telescope by a remote operator. Linearized small angle equations are used for the multistar processing and a consideration of error performance and singularities lead to star pair location restrictions and equation selection criteria. A discrete steady-state Kalman filter which uses the integration of the gyros is developed and analyzed. The filter includes unit time delays representing asynchronous operations of the VIP microprocessor and video sensor. A digital simulation of a typical gyro stabilized gimbal is developed and used to validate the approach to the gyro filtering.
The numerical stability and accuracy of various Kalman filter algorithms are thoroughly studied. Numerical results and conclusions are based on a realistic planetary approach orbit determination study. The case study results of this report highlight the numerical instability of the conventional and stabilized Kalman algorithms. Numerical errors associated with these algorithms can be so large as to obscure important mismodeling effects and thus give misleading estimates of filter accuracy. The positive result of this study is that the Bierman-Thornton U-D covariance factorization algorithm is computationally efficient, with CPU costs that differ negligibly from the conventional Kalman costs. In addition, accuracy of the U-D filter using single-precision arithmetic consistently matches the double-precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity of variations in the a priori statistics.
An optimum image restoration filter is described in which provision is made to constrain the spatial extent of the restoration function, the noise level of the filter output and the rate of falloff of the composite system point-spread away from the origin. Experimental results show that sidelobes on the composite system point-spread function produce ghosts in the restored image near discontinuities in intensity level. By redetermining the filter using a penalty function that is zero over the main lobe of the composite point-spread function of the optimum filter and nonzero where the point-spread function departs from a smoothly decaying function in the sidelobe region, a great reduction in sidelobe level is obtained. Almost no loss in resolving power of the composite system results from this procedure. By iteratively carrying out the same procedure even further reductions in sidelobe level are obtained. Examples of original and iterated restoration functions are shown along with their effects on a test image.
The theoretical and some experimental results of a study aimed at applying CCD filter and transform techniques to the problem of interference excision within communications channels were presented. Adaptive noise (interference) suppression was achieved by the modification of received signals such that they were orthogonal to the recently measured noise field. CCD techniques were examined to develop real-time noise excision processing. They were recursive filters, circulating filter banks, transversal filter banks, an optical implementation of the chirp Z transform, and a CCD analog FFT.
The performance of Kalman-type, linear, discrete-time filters in the presence of modeling errors is considered. The discussion is limited to stationary performance, and bounds are obtained for the performance index, the mean-squared error of estimates for suboptimal and optimal (Kalman) filters. The computation of these bounds requires information on only the model matrices and the range of errors for these matrices. Consequently, a design can easily compare the performance of a suboptimal filter with that of the optimal filter, when only the range of errors in the elements of the model matrices is available.
A spatial filtered Q-switched laser system is reported that prevents ionization of air in close proximity to the aperture of the spatial filter. A compound lens system having an astigmatic focus is positioned between the laser and the spatial filter for defocusing the light beam emanating from the laser in the vicinity of the aperture of the spatial filter to an intensity below that which produces ionization of air. The preferred construction of the compound lens system as viewed from the laser comprises a cylindrical lens and a pair of positive lenses.
Numerical characteristics of various Kalman filter algorithms are illustrated with a realistic orbit determination study. The case study of this paper highlights the numerical deficiencies of the conventional and stabilized Kalman algorithms. Computational errors associated with these algorithms are found to be so large as to obscure important mismodeling effects and thus cause misleading estimates of filter accuracy. The positive result of this study is that the U-D covariance factorization algorithm has excellent numerical properties and is computationally efficient, having CPU costs that differ negligibly from the conventional Kalman costs. Accuracies of the U-D filter using single precision arithmetic consistently match the double precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity to variations in the a priori statistics.
Numerical characteristics of various Kalman filter algorithms are illustrated with a realistic orbit determination study. The case study of this paper highlights the numerical deficiencies of the conventional and stabilized Kalman algorithms. Computational errors associated with these algorithms are found to be so large as to obscure important mismodeling effects and thus cause misleading estimates of filter accuracy. The positive result of this study is that the U-D covariance factorization algorithm has excellent numerical properties and is computationally efficient, having CPU costs that differ negligibly from the conventional Kalman costs. Accuracies of the U-D filter using single precision arithmetic consistently match the double precision reference results. Numerical stability of the U-D filter is further demonstrated by its insensitivity to variations in the a priori statistics.
Thin, unbacked, aluminum film filters were used on two extreme ultraviolet (XUV) instruments flown on the Apollo Telescope Mount of Skylab by the Naval Research Laboratory to transmit the XUV radiation while blocking the longer wavelength radiation that would saturate the detector. The requirements placed on these filters - large size, resistance to degradation by high acoustic and vibration fields, and low pinhole transmittances - were far more severe than those placed on any filters previously flown. Special techniques were developed for vacuum evaporation of the aluminum, removal of the films from the substrates, supporting the films and mounting them to obtain finished filters, and storing them so that no degradation took place. A description of these techniques will be given.
The digital filtering algorithm of W. D. Little, which employs a large RAM to obtain high speed, is implemented in a simple hardware configuration. The nonrecursive version of this filter is compared to the counting digital filter and found to be competitive for low-order filters up to order 7 (8 coefficients).
An extended Kalman-Bucy filter has been implemented for atmospheric temperature profile retrievals from observations made using the Scanned Microwave Spectrometer (SCAMS) instrument carried on the Nimbus 6 satellite. This filter has the advantage that it requires neither stationary statistics in the underlying processes nor linear production of the observed variables from the variables to be estimated. This extended Kalman-Bucy filter has yielded significant performance improvement relative to multiple regression retrieval methods. A multi-spot extended Kalman-Bucy filter has also been developed in which the temperature profiles at a number of scan angles in a scanning instrument are retrieved simultaneously. These multi-spot retrievals are shown to outperform the single-spot Kalman retrievals.
Sensitivity and roundoff errors can seriously limit the application of recursive digital filters in practice, particularly when the filters have poles near z = + 1. A filter structure, based on digital incremental computers is proposed, which has low sensitivity, good error characteristics, and simple hardware implementation for pole locations close to z = + 1. Expressions for the roundoff errors are derived and compared to those for conventional structures. A design procedure is suggested to implement the new filter structure given the transfer function. Simulation results are presented.
Errors limiting the application of recursive digital filters which have poles near z = +1 are considered, and a filter structure for pole locations close to z = +1 is proposed. The filter structure, based on digital incremental computers, has low sensitivity and good error characteristics for pole locations near z = +1. Expressions for the roundoff error are derived, and errors associated with the proposed structure and a conventional structure are compared. A design procedure is suggested for implementing the new filter structure when the transfer function is given. Simulation results are presented.