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Analysis of the bit-level operations involved in the convolutions realizing recursive digital filters leads to hardware designs of such filters based on the operation of counting. Various designs realizing both the canonic and 'direct' forms are presented with particular emphasis on low-cost low-speed high-flexibility machines.
This paper presents the derivation of the recursive algorithms necessary for real-time digital detection of M-ary known signals that are subject to independent multiplicative and additive Gaussian noises. The motivating application is minimum probability of error detection of digital data-link messages aboard civil aircraft in the earth reflection multipath environment. For each known signal, the detector contains one Kalman filter and one probability computer. The filters estimate the multipath disturbance. The estimates and the received signal drive the probability computers. Outputs of all the computers are compared in amplitude to give the signal decision. The practicality and usefulness of the detector are extensively discussed.
The problem of identifying constant and variable parameters in multi-input, multi-output, linear and nonlinear systems is considered, using the maximum likelihood approach. An iterative algorithm, leading to recursive identification and tracking of the unknown parameters and the noise covariance matrix, is developed. Agile tracking, and accurate and unbiased identified parameters are obtained. Necessary conditions for a globally, asymptotically stable identification process are provided; the conditions proved to be useful and efficient. Among different cases studied, the stability derivatives of an aircraft were identified and some of the results are shown as examples.
Attitude estimation of earth orbiting satellites (including Large Space Telescope) subjected to environmental disturbances and noises was investigated. Modern control and estimation theory is used as a tool to design an efficient estimator for attitude estimation. Decomposed linear recursive filters for both continuous-time systems and discrete-time systems are derived. By using this accurate estimation of the attitude of spacecrafts, state variable feedback controller may be designed to achieve (or satisfy) high requirements of system performance.
In this recursive method proposed, the gain matrix for the Kalman filter and the convariance of the state vector are computed not via the Riccati equation, but from certain other equations. These differential equations are of Chandrasekhar-type. The 'invariant imbedding' idea resulted in the reduction of the basic boundary value problem of transport theory to an equivalent initial value system, a significant computational advance. Initial value experience showed that there is some computational savings in the method and the loss of positive definiteness of the covariance matrix is less vulnerable.
Implementation of the recursive maximum likelihood proportion estimator is described. A user's guide to programs as they currently exist on the IBM 360/67 at LARS, Purdue is included, and test results on LANDSAT data are described. On Hill County data, the algorithm yields results comparable to the standard maximum likelihood proportion estimator.
A recursive algorithm was designed to invert large, dense, symmetric, positive definite matrices using small amounts of computer core, i.e., a small fraction of the core needed to store the complete matrix. The described algorithm is a generalized Gaussian elimination technique. Other algorithms are also discussed for the Cholesky decomposition and step inversion techniques. The purpose of the inversion algorithm is to solve large linear systems of normal equations generated by working geodetic problems. The algorithm was incorporated into a computer program called SOLVE. In the past the SOLVE program has been used in obtaining solutions published as the Goddard earth models.
The problem of designing recursive digital filters can be reduced to polynomial approximation on a finite interval. The procedure to demonstrate this equivalence described in a recent paper yielded filters with multiple poles. An alternative method is described which avoids this restriction.
Time-domain methods for the design of recursive digital filters using a squared error criterion are compared with a frequency-domain technique. Levy's method, which has been used to estimate transfer functions of continuous-time systems is modified to obtain design equations for digital filters. A special case of Levy's method is shown to be essentially equivalent to the time-domain methods.
The problem of identifying constant and variable parameters in multi-input, multi-output, linear and nonlinear systems is considered, using the maximum likelihood approach. An iterative algorithm, leading to recursive identification and tracking of the unknown parameters and the noise covariance matrix, is developed. Agile tracking and accurate and unbiased identified parameters are obtained. Necessary conditions for a globally asymptotically stable identification process are provided; the conditions proved to be useful and efficient. Among different cases studied, the stability derivatives of an aircraft were identified and some of the results are shown as examples.
A change of variables is described which transforms the problem of designing a recursive digital filter to that of approximation by a ratio of polynomials on a finite interval. Some analytic techniques for the design of low-pass filters are presented, illustrating the use of the transformation. Also considered are methods for the design of phase equalizers.
Modifications and enhancements that have been made to the Recursive Estimation Attitude Program (REAP) are discussed. Continuous attitudes for OSO-8 to + or - 0.05 degree accuracy are determined from Sun and star slit sensors mounted on the spinning portion of the spacecraft. The bulk of the attitude production is performed by a Weighted Least Squares (WLS) batch processor, but REAP is used for problem passes such as those involving gas jet maneuvers, sparse star fields, or star sensor saturation by high energy particles in the South Atlantic Anomaly.
A recursive filter/smoother orbit determination program was developed to refine the ephemerides produced by a batch orbit determination program (e.g., CELEST, GEODYN). The program PREFER can handle a variety of ground and satellite to satellite tracking types as well as satellite altimetry. It was tested on simulated data which contained significant modeling errors and the results clearly demonstrate the superiority of the program compared to batch estimation.
A program was designed toward the demonstration of the feasibility of using two dimensional recursive digital filters for subjective image processing applications that require rapid turn around. The concept of the use of a dedicated minicomputer for the processor for this application was demonstrated. The minicomputer used was the HP1000 series E with a RTE 2 disc operating system and 32K words of memory. A Grinnel 256 x 512 x 8 bit display system was used to display the images. Sample images were provided by NASA Goddard on a 800 BPI, 9 track tape. Four 512 x 512 images representing 4 spectral regions of the same scene were provided. These images were filtered with enhancement filters developed during this effort.
An on line technique is presented for the identification of rotor blade modal damping and frequency from rotorcraft random response test data. The identification technique is based upon a recursive maximum likelihood (RML) algorithm, which is demonstrated to have excellent convergence characteristics in the presence of random measurement noise and random excitation. The RML technique requires virtually no user interaction, provides accurate confidence bands on the parameter estimates, and can be used for continuous monitoring of modal damping during wind tunnel or flight testing. Results are presented from simulation random response data which quantify the identified parameter convergence behavior for various levels of random excitation. The data length required for acceptable parameter accuracy is shown to depend upon the amplitude of random response and the modal damping level. Random response amplitudes of 1.25 degrees to .05 degrees are investigated. The RML technique is applied to hingeless rotor test data. The inplane lag regressing mode is identified at different rotor speeds. The identification from the test data is compared with the simulation results and with other available estimates of frequency and damping.
The problem of obtaining smoothed estimates of function values, particularly their derivatives, from a finite set of inaccurate measurements is considered. A recursive two-dimensional vector processor is introduced as an approximation to the nonrecursive constrained least-squares estimation. Here, piecewise bicubic Hermite polynomials are extensively used as approximating functions, and the smoothing integral is converted to a discrete quadratic form. This makes it possible to convert the problem of fitting an approximating function to one of estimating the function values and derivatives at the nodes.
PREFER is a recursive orbit determination program which is used to refine the ephemerides produced by a batch least squares program (e.g., GTDS). It is intended to be used primarily with GTDS and, thus, is compatible with some of the GTDS input/output files.
A method is presented for decoupling modal amplitudes generated by recursive least squares lattice filters. The proposed method, which involves transformation of basis functions obtained from lattice filters, is illustrated using a free-free beam simulation. The decoupled mode shape functions are required for the implementation of an adaptive control scheme for large space systems.