Slightly non-linear estimation with noisy data.
Nonlinear estimation with noisy data, considering least squares fit, sequential /Kalman/ estimate and iterated sequential scheme
Breakwell, J. V.↗
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AveBoost2: Boosting for Noisy Data
AdaBoost is a well-known ensemble learning algorithm that constructs its constituent or base models in sequence. A key step in AdaBoost is constructing a distribution over the training examples to create each base model. This distribution, represented as a vector, is constructed to be orthogonal to the vector of mistakes made by the pre- vious base model in the sequence. The idea is to make the next base model's errors uncorrelated with those of the previous model. In previous work, we developed an algorithm, AveBoost, that constructed distributions orthogonal to the mistake vectors of all the previous models, and then averaged them to create the next base model s distribution. Our experiments demonstrated the superior accuracy of our approach. In this paper, we slightly revise our algorithm to allow us to obtain non-trivial theoretical results: bounds on the training error and generalization error (difference between training and test error). Our averaging process has a regularizing effect which, as expected, leads us to a worse training error bound for our algorithm than for AdaBoost but a superior generalization error bound. For this paper, we experimented with the data that we used in both as originally supplied and with added label noise-a small fraction of the data has its original label changed. Noisy data are notoriously difficult for AdaBoost to learn. Our algorithm's performance improvement over AdaBoost is even greater on the noisy data than the original data.
Oza, Nikunj C.↗
Identification of a linear system from sampled noisy data, part C Final project report
Step input linear system modeling from nonlinear system sampled noisy data based on method of perturbation or quasilinearization of automatic control system data
Luckinbill, D. L.↗
Neuromorphic Learning From Noisy Data
Two reports present numerical study of performance of feedforward neural network trained by back-propagation algorithm in learning continuous-valued mappings from data corrupted by noise. Two types of noise considered: plant noise which affects dynamics of controlled process and data-processing noise, which occurs during analog processing and digital sampling of signals. Study performed with view toward use of neural networks as neurocontrollers to substitute for, or enhance, performances of human experts in controlling mechanical devices in presence of sensor and actuator noise and to enhance performances of more-conventional digital feedback electronic process controllers in noisy environments.
Merrill, Walter C.↗
Vector splines on the sphere with application to the estimation of vorticity and divergence from discrete, noisy data
Vector smoothing splines on the sphere are defined. Theoretical properties are briefly alluded to. The appropriate Hilbert space norms used in a specific meteorological application are described and justified via a duality theorem. Numerical procedures for computing the splines as well as the cross validation estimate of two smoothing parameters are given. A Monte Carlo study is described which suggests the accuracy with which upper air vorticity and divergence can be estimated using measured wind vectors from the North American radiosonde network.
Wahba, G.↗
Clustering of noisy image data using an adaptive neuro-fuzzy system
Identification of outliers or noise in a real data set is often quite difficult. A recently developed adaptive fuzzy leader clustering (AFLC) algorithm has been modified to separate the outliers from real data sets while finding the clusters within the data sets. The capability of this modified AFLC algorithm to identify the outliers in a number of real data sets indicates the potential strength of this algorithm in correct classification of noisy real data.
Pemmaraju, Surya↗
Terrain evaluation and route designation based on noisy rangefinder data
This paper discusses an approach to terrain evaluation and route designation for an autonomous Mars rover. The evaluation procedure simulates movement of the rover over a terrain model estimated from noisy range readings. During the simulated movement a potential path is analyzed for adverse gradients and minimum vehicle body clearance which could inhibit the rover's progress. The route designation scheme employs dynamic programming to select the optimal path based on the evaluation results.
Netch, A.↗
A Numerical Method for Calculating Stellar Occultation Light Curves from an Arbitrary Atmospheric Model
We present a method for speeding up numerical calculations of a light curve for a stellar occultation by a planetary atmosphere with an arbitrary atmospheric model that has spherical symmetry. This improved speed makes least-squares fitting for model parameters practical. Our method takes as input several sets of values for the first two radial derivatives of the refractivity at different values of model parameters, and interpolates to obtain the light curve at intermediate values of one or more model parameters. It was developed for small occulting bodies such as Pluto and Triton, but is applicable to planets of all sizes. We also present the results of a series of tests showing that our method calculates light curves that are correct to an accuracy of 10(exp -4) of the unocculted stellar flux. The test benchmarks are (i) an atmosphere with a l/r dependence of temperature, which yields an analytic solution for the light curve, (ii) an atmosphere that produces an exponential refraction angle, and (iii) a small-planet isothermal model. With our method, least-squares fits to noiseless data also converge to values of parameters with fractional errors of no more than 10(exp -4), with the largest errors occurring in small planets. These errors are well below the precision of the best stellar occultation data available. Fits to noisy data had formal errors consistent with the level of synthetic noise added to the light curve. We conclude: (i) one should interpolate refractivity derivatives and then form light curves from the interpolated values, rather than interpolating the light curves themselves; (ii) for the most accuracy, one must specify the atmospheric model for radii many scale heights above half light; and (iii) for atmospheres with smoothly varying refractivity with altitude, light curves can be sampled as coarsely as two points per scale height.
Chamberlain, D. M.↗
Digital Twin Technology for Aviation
As technology progresses, so have the tools for data visualization. This project presents a digital twin model of the San Francisco airport displaying a 10-minute window of historical flight data, visualizing the trajectory data of airplanes and vehicles in three dimensions. Multiple different cameras where implemented to fully utilize the 3D visualization. This is a 100:1 feet scale model created in Autodesk Maya, using the airport center as the origin and recalculating all coordinates accordingly featuring the airport, some surrounding buildings, and the bay. For this project, six different models of airplanes were modeled at a 50:1 feet scale with texturing to mimic real-world aircraft models along with certain airlines. The animation is driven through archived data captured from NASA’s Sherlock Open-Data Portal, cleaned of noisy data points, processed into useable data formats, and implemented into a Maya ASCII file of animation paths with the corresponding previously-stated airplane models attached all using Java based conversion program.
Aleksander Schade↗
Asteroid taxonomic classifications
Asteroid taxonomic classification according to the schemes of Tholen (1984) and Baracci et al. (1987) are presented in a table. Inconsistent data are indicated. Special notions are given for unusual spectra, noisy and very noisy data, and data too noisy to permit classification.
Tholen, D. J.↗
Discrete Tchebycheff orthonormal polynomials and applications
Discrete Tchebycheff orthonormal polynomials offer a convenient way to make least squares polynomial fits of uniformly spaced discrete data. Computer programs to do so are simple and fast, and appear to be less affected by computer roundoff error, for the higher order fits, than conventional least squares programs. They are useful for any application of polynomial least squares fits: approximation of mathematical functions, noise analysis of radar data, and real time smoothing of noisy data, to name a few.
Lear, W. M.↗
Performance Analysis of Apollo Navigational Starter Routine
The focus of this project is to recreate and analyze the effectiveness of the original Apollo Starter Routine (ASR) which was used to generate the state vector of the Apollo spacecraft based on a series of radiometric observations. The original Apollo navigation software is unavailable in a modern programming language and the original coding has not been preserved. This necessitates its recreation using the original software documentation. Space Shuttle navigation software does not typically use the ASR or an algorithm like it since the Shuttle s state vector is easily deduced from GPS information or other sources. However, this tactic will be ineffective when trying to determine the state vector of a craft approaching, departing or in orbit around the Moon since the GPS network faces the surface of the Earth, not outer space. The recreation of the ASR from the original documentation is therefore vital as a simulation baseline for the navigation software under development for the Constellation program. The algorithms that make up the ASR will be extracted from the original documentation and adapted for and then implemented in a modern programming language; the majority of it will be coded in Matlab. The ASR s effectiveness will then be tested using simulated tracking data. The ability of the ASR to handle realistically noisy data and the accuracy with which it generates state vectors were analyzed. The ASR proved to be robust enough to process data with range and angle noise as large as 10,000 meters and 10(exp -6) radians together and 300,000 meters and 5x10(exp -4) radians separately at Lunar distances. The ASR was able to handle marginally more noise at distances closer to the Earth where the angle noise was less significant. The ASR is capable of effectively processing 40-80 data points gathered at a rate of one per 20 seconds at close Earth orbit and up to 28-40 data points gathered at a rate of one per minute at distant Earth orbit and Lunar orbit.
Ivanov, Stoyan I.↗
The Calculation of Fractal Dimension in the Presence of Non-Fractal Clutter
The area of information processing has grown dramatically over the last 50 years. In the areas of image processing and information storage the technology requirements have far outpaced the ability of the community to meet demands. The need for faster recognition algorithms and more efficient storage of large quantities of data has forced the user to accept less than lossless retrieval of that data for analysis. In addition to clutter that is not the object of interest in the data set, often the throughput requirements forces the user to accept "noisy" data and to tolerate the clutter inherent in that data. It has been shown that some of this clutter, both the intentional clutter (clouds, trees, etc) as well as the noise introduced on the data by processing requirements can be modeled as fractal or fractal-like. Traditional methods using Fourier deconvolution on these sources of noise in frequency space leads to loss of signal and can, in many cases, completely eliminate the target of interest. The parameters that characterize fractal-like noise (predominately the fractal dimension) have been investigated and a technique to reduce or eliminate noise from real scenes has been developed. Examples of clutter reduced images are presented.
Herren, Kenneth A.↗
Future possibilities in objective analysis and data assimilation for atmospheric dynamics
The role that dynamics plays in estimating the state of the atmosphere from incomplete and noisy data is reviewed. Objective analysis represents an attempt at relying mostly on the data and minimizing the role of dynamics in the estimation. Data assimilation tries to balance properly the roles of dynamical and observational information. Sequential estimation is presented as the proper framework for understanding this balance, and the Kalman filter as the ideal, optimal procedure for data assimilation. The optimal filter computes forecast error covariances of a given atmospheric model exactly, and hence data assimilation should be closely connected with predictability studies. This connection is described, and consequences drawn for currently active areas of the atmospheric and related sciences, namely, mesoscale meteorology, long range forecasting, and upper ocean dynamics. Possibilities offered by judicious data assimilation in understanding barotropic adjustment, a phenomenon that appears to play a crucial role in atmospheric behavior on the scale of weeks to months, and hence in long range forecasting are addressed.
Ghil, M.↗
Simple data-smoothing and noise-suppression technique
Algorithm, based on the Borel method of summing divergent sequences, is used for smoothing noisy data where knowledge of frequency content is not required. Technique's effectiveness is demonstrated by a series of graphs.
Duty, R. L.↗
Sequential estimation and satellite data assimilation in meteorology and oceanography
The role of dynamics in estimating the state of the atmosphere and ocean from incomplete and noisy data is discussed and the classical applications of four-dimensional data assimilation to large-scale atmospheric dynamics are presented. It is concluded that sequential updating of a forecast model with continuously incoming conventional and remote-sensing data is the most natural way of extracting the maximum amount of information from the imperfectly known dynamics, on the one hand, and the inaccurate and incomplete observations, on the other.
Ghil, M.↗
Identification and interpretation of patterns in rocket engine data: Artificial intelligence and neural network approaches
This paper describes an expert system which is designed to perform automatic data analysis, identify anomalous events, and determine the characteristic features of these events. We have employed both artificial intelligence and neural net approaches in the design of this expert system. The artificial intelligence approach is useful because it provides (1) the use of human experts' knowledge of sensor behavior and faulty engine conditions in interpreting data; (2) the use of engine design knowledge and physical sensor locations in establishing relationships among the events of multiple sensors; (3) the use of stored analysis of past data of faulty engine conditions; and (4) the use of knowledge-based reasoning in distinguishing sensor failure from actual faults. The neural network approach appears promising because neural nets (1) can be trained on extremely noisy data and produce classifications which are more robust under noisy conditions than other classification techniques; (2) avoid the necessity of noise removal by digital filtering and therefore avoid the need to make assumptions about frequency bands or other signal characteristics of anomalous behavior; (3) can, in effect, generate their own feature detectors based on the characteristics of the sensor data used in training; and (4) are inherently parallel and therefore are potentially implementable in special-purpose parallel hardware.
Ali, Moonis↗
Abstracts for the 2002 Meeting of the AIAA Working Group on Dynamic Space Simulation
Undersampling is sometimes used in order to save memory and reducing digitizing speed requirements for pyroshock data. Many interpolation techniques have been used to estimate the missing peaks due undersampling. The more exotic techniques may not work well when real data that contains noise is used as an input. Various peak interpolation techniques will be evaluated using noisy data in this presentation.
Simpson, Alda D.↗