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The fixed-point smoothing problem of sequentially correlated processes is considered. The filtering technique of such processes is extended to smoothing problems by simultaneously estimating the state and the accumulated contribution of process noise. Suboptimal filtering and smoothing are also discussed when data noise is regarded white in designing filters although it is actually sequentially correlated.-
Smoothing equations for a linear continuous dynamic system with linear discrete measurements, derived from the discrete results of Rauch, Tung, and Striebel (1965), (R-T-S), are used to extend, through recursive updating, the previously published results of Bryson and Frazier (1963), (B-F), and yield a modified Bryson and Frazier, (M-B-F), algorithm. A comparison of the (M-B-F) and (R-T-S) algorithms leads to the conclusion that the former is to be preferred because it entails less computation, less storage, and less instability. It is felt that the presented (M-B-F) smoothing algorithm is a practical mechanization and should be of value in smoothing discretely observed dynamic linear systems.
It is shown that for satellites in circular Earth orbits with altitudes of 500 kilometers to 1500 kilometers, and for satellites in elliptical orbits with an approximate 4000 kilometer height of perigee, a high degree least squares polynomial (e.g., a 9th or 10th degree in some cases) is required to smooth both range and range rate data for purposes of input to orbit determination programs. In order to circumvent this problem, functions of range and range rate are smoothed with lower degree least squares polynomials (e.g., 3rd and 4th degree) and it is shown that under the above geometric constraints the standard deviation of fit can be reduced to levels commensurate with typical S-band tracking system resolution which is 1 to 2 meters in range and 0.005 meters/second in range rate for a 1 per second data rate. Also shown are the effects of Gaussian random noise, biases, and periodic noise. This analysis includes numerous examples applied to the 44 point data smoothing interval currently used in much of the operational preprocessing at the Goddard Space Flight Center.
An algorithm is presented which is able to locate isolated bad points and correct them without contaminating the rest of the good data. This work has been greatly influenced and motivated by what is currently done in the manual loft. It is not within the scope of this work to handle small random errors characteristic of a noisy system, and it is therefore assumed that the bad points are isolated and relatively few when compared with the total number of points. Motivated by the desire to imitate the loftsman a visual experiment was conducted to determine what is considered smooth data. This criterion is used to determine how much the data should be smoothed and to prove that this method produces such data. The method utimately converges to a set of points that lies on the polynomial that interpolates the first and last points; however convergence to such a set is definitely not the purpose of our algorithm. The proof of convergence is necessary to demonstrate that oscillation does not take place and that in a finite number of steps the method produces a set as smooth as desired.
Various theories have been published that consider the material of the Cayley Formation (a lunar smooth plain) to be ejecta of distant multiringed basins. Results presented in this paper indicate that the material cannot be solely basin ejecta. If smooth-plains are a result of formation of these basins or other distant large craters, then the plains materials are mainly ejecta of secondary craters of these basins or craters with only minor contributions of primary-crater or basin ejecta. Primary-crater ejecta can be a significant fraction of a deposit emplaced by an impact crater only if the primary crater is nearby. Other proposed mechanisms for emplacement of smooth-plains formations are discussed, and implications regarding the origin of material in the continuous aprons surrounding large lunar craters is considered. It is emphasized that the importance of secondary-impact cratering in the highlands has in general been underestimated and that this process must have been important in the evolution of the lunar surface.
In this paper filtering and smoothing criteria for maximum-likelihood parameter estimation are described and compared. It is shown that the parameter estimate using the smoothing criterion may be obtained independently of the smoothed state estimate. Monte Carlo test results are presented comparing the efficiency of the estimation procedures.
Optimum linear smoothing is utilized to estimate certain distortions in LANDSAT-D images. Measurements that are processed by the smoother consist of designated control of point locations within the images. Image distortions that are estimated by the smoother are those induced by LANDSAT-D satellite navigation errors and slowly varying attitude and sensor alignment uncertainties. Preliminary results indicate that optimum smoothing produces substantially more accurate distortion estimates than optimum filtering and that optimum smoothing may reduce the number of control points needed to yield desired image correction accuracy.
Two programs smooth and scale arbitrary airfoil coordinates. Airfoil smoothing program (AFSMO) utilizes both least-squares polynomial and leastsquares cubic-spline techniques to smooth iteratively second derivatives of y-axis airfoil coordinates with respect to transformed x-axis system that unwraps airfoil and stretches nose and trailing-edge regions.
Experimental strain measurements have been made at the highly strained regions on notched plate specimens that were made of Hastelloy X. Tests were performed at temperatures up to 1,600 F. Variable load patterns were chosen so as to produce plastic and creep strains. Were appropriate, notch root stresses were experimentally estimated by subjecting a smooth specimen to the measured notch root strains. The results of three analysis techniques are presented and compared to the experimental data. The most accurate results were obtained from an analysis procedure that used a smooth specimen and the Neuber relation to simulate the notch root stress-strain response. When a generalized constitutive relation was used with the Neuber relation, good results were also obtained, however, these results were not as accurate as those obtained when the smooth specimen was used directly. Finally, a general finite element program, ANYSIS, was used which resulted in acceptable solutions, but, these were the least accurate predictions.
Forward and inverse dynamics solved using Kalman filtering and Bryson-Frazier smoothing. Dynamics of serial-link robot arm solved by using recursive techniques from linear filtering and smoothing theory. Solutions of dynamical equations give forces, moments, and accelerations at joints between links, and multilink inertia matrix and its inverse. Theoretical developments lay foundation for use of filtering and smoothing techniques in design of robot controls.
This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.
Turbulent flow in tubes with and without longitudinal grooves is examined. The discovery of fine grooves forming a sort of streamline pattern on the body of sharks led to the expectation that the grooves on a surface reduce the momentum change, and thus the drag. To test this thesis, drag law, velocity profile and the profile of the velocity fluctuation were determined. Results show that for moderate Reynolds numbers the drag coefficient for grooved tubes is about 3 percent smaller than that of the smooth tubes. At higher Reynolds numbers, however, the drag coefficient for grooved tubes becomes larger than that for smooth tubes. No significant differences in the velocity profiles between grooved tubes and smooth tubes are found.
The napthalene sublimation technique was employed to study the detailed mass transfer distributions around the sharp 180 deg turns in a two-pass, square, smooth channel and in an identical channel with two rib-roughened opposite walls. Experiments conducted for Reynolds numbers of 15,000, 30,000, and 60,000 indicate that the Sherwood numbers on the top, outer, and inner walls around the turn in the rib-roughened channel are higher than the corresponding Sherwood numbers around the turn in the smooth channel. Sherwood numbers after the sharp turn are found to be higher than those before the turn for both the smooth and the ribbed channels.
Analyses of several carbonaceous chondrites (including the Orgueil samples 626, 629, and 630; and Ivuna samples 627, 628, and 631) for elements from Fe through Ru were performed using proton-induced X-rays, in order to test the smoothness of the elemental abundances in these chondrites. In general, the results confirm previously published abundance curves. The abundances were exceptionally smooth and strongly decreasing in the mass region 60-75. From the mass number 75 to 101, a smooth curve could be drawn, within limits of intersample variability, except for Y peak. Over the whole periodic table, a large number of peaks of probable nucleosynthetic origin could be identified.
A smooth three-dimensional mass distribution is approximated by a model with multiple thin screens, with surface mass density varying smoothly on each screen. It is found that 16 screens are sufficient for a good approximation of the three-dimensional distribution of matter. It is also found that in this multiscreen model the distribution of amplifications of single images is dominated by the convergence due to matter within the beam. The shear caused by matter outside the beam has no significant effect. This finding considerably simplifies the modeling of lensing by a smooth three-dimensional mass distribution by effectively reducing the problem to one dimension, as it is sufficient to know the mass distribution along a straight light ray.
The Planetary Radio Astronomy (PRA) experiment Warwick et al., (1977) on the spacecraft Voyager 2 observed three types of smooth emission: (1) numerous recurrent episodes are modeled by filled emission cones from midlatitude conjugate sources; (2) an 'equatorial' feature seen soon after closest approach includes electron cyclotron harmonic emission above the upper hybrid resonance, as well as smooth recurrent emission, its strange appearance is a result of rapid change in Voyager's magnetic latitude and; (3) unique 'high-latitude' emission is seen near closest approach during Voyager's single excursion to high north (+) magnetic latitude when fc, the electron cyclotron frequency at the spacecraft, lies in the observable range. The stronger component covers a broad band of frequencies above 2fc; its sensitivity to magnetic field identifies it as extraordinary (X) mode. The weaker component extends smoothly through f = fc and is identified as ordinary (O) mode. At each frequency f the observed sense of polarization reverses when f = 2fc.
The effects of deficient labyrinthine function on smooth visual tracking with the eyes and head were investigated, using ten patients with bilateral peripheral vestibular disease and ten normal controls. Active, combined eye-head tracking (EHT) was significantly better in patients than smooth pursuit with the eyes alone, whereas normal subjects pursued equally well in both cases. Compensatory eye movements during active head rotation in darkness were always less in patients than in normal subjects. These data were used to examine current hypotheses that postulate central cancellation of the vestibulo-ocular reflex (VOR) during EHT. A model that proposes summation of an integral smooth pursuit command and VOR/compensatory eye movements is consistent with the findings. Observation of passive EHT (visual fixation of a head-fixed target during en bloc rotation) appears to indicate that in this mode parametric gain changes contribute to modulation of the VOR.
In improved method for generating trajectory of robotic manipulator, each straight-line segment of trajectory composed of constant-velocity main portion sandwiched between smooth acceleration at start and smooth deceleration at finish. Algorithm implementing method computes velocity in each accelerating portion as sinusoidal function of position along line. This motion chosen for two reasons: closely approximates motion of human hand along straight-line trajectory, and provides very smooth transitions between constant-velocity portion and accelerated and decelerational end portions.