Explicit recursive algorithms for the construction of equivalent canonical transformations
Explicit recursive algorithms for construction of Lie and von Zeipel transformations
Mersman, W. A.↗
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Recursive state estimation for a set-membership de scription of uncertainty
Linear dynamic system recursive state estimation for set-membership description of uncertainty under unknown input disturbances and observation errors
Bertsekas, D. P.↗
Bayesian recursive image estimation.
A procedure for recursively estimating images that are characterized statistically by the mean and correlation functions associated with the random process representing the brightness level is proposed for the case where the images are corrupted by additive noise. First, a dynamic model is developed with a response characteristic which matches that of the scanner output (the input of the estimator is the output of a horizontal line scanner) in a statistical sense. Such models have the form of an ordinary differential or difference equation with white noise input. An insignificant approximation is introduced by using a constant-coefficient model. The appropriate model is a vector valued difference equation with the solution representing a vector Markov process. The next step is to obtain the minimum mean square estimate of the image by using a Kalman filter. Since the image estimation is an interpolation problem, two successive runs over the observation are performed in opposite directions and the resultant estimates are averaged. Examples are included for illustration.
Nahi, N. E.↗
Decision-directed adaptive recursive estimators - Divergence prevention.
A method is proposed for dealing with the divergence phenomenon problem encountered in applications of minimum-variance recursive estimators when the error covariance calculated by the estimator becomes inconsistent with the actual error covariance. The proposed method differs from previous ones in that the state model and statistics are accepted as given. The form of the optimal estimator is used, but a constant check is made on the consistency of the calculated and actual error covariances. The method is independent of the source of error, whether it be inaccuracies in the system model, incorrect values of the a priori and random process statistics, approximations required in the case of nonlinear systems, or computational roundoff. Several simulated examples, in which inconsistencies in the calculated and actual error covariances exist, show a significant improvement in the performance of the estimator when the given procedure is applied.
Nahi, N. E.↗
Recursive filter initialization.
Description of an initialization technique which partially accounts for the interrelation between the true-state vector errors when recursive filtering is applied in space navigation systems. The technique reduces the undesirable transient effects of the first few measurements and inhibits filter divergence when the interval between measurements is inordinately large. The key feature of this technique is the inclusion of the effect of a number of pseudo-measurements of certain orbital parameters into the initial covariance matrix. The pseudo-measurement technique has been shown to be useful when reinitialization of the error covariance matrix is required to prevent filter divergence.
Battin, R. H.↗
Bayesian recursive image estimation.
The enhancement of images that are characterized only by statistical data where the picture contains additive noise is considered. The random process representing the output of the scanner is characterized by the output of a dynamic system with white noise input. The dynamic system describes a first-order vector-Markov process. The procedure of Kalman filtering is then utilized to recursively determine the minimum mean-square error estimate of the image. The result is then extended to obtain the smoothing of the data.
Nahi, N. E.↗
The counting recursive digital filter.
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.
Zohar, S.↗
Recursive ideal observer detection of known M-ary signals in multiplicative and additive Gaussian noise.
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.
Painter, J. H.↗
Recursive identification and tracking of parameters for linear and nonlinear multivariable systems
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.
Sidar, M.↗
Attitude estimation of earth orbiting satellites by decomposed linear recursive filters
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.
Kou, S. R.↗
Chandrasekhar-type algorithms for fast recursive estimation in linear systems with constant parameters
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.
Choudhury, A. K.↗
The recursive maximum likelihood proportion estimator: User's guide and test results
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.
Vanrooy, D. L.↗
Recursive partitioned inversion of large (1500 x 1500) symmetric matrices
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.
Putney, B. H.↗
Comments on 'Synthesis of spectrum shaping digital filters of recursive design'
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.
Shenoi, K.↗
On least-squares design of recursive digital filters
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.
Shenoi, K.↗
Recursive identification and tracking of parameters for linear and non-linear multivariable systems
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.
Sidar, M.↗
On the design of recursive digital filters
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.
Shenoi, K.↗
Recursive estimator for OSO-8 attitude
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.
Headrick, R. D.↗