Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “recursive least squares”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS2020

Global Aerodynamic Modeling Using Automated Local Model Networks in Real Time

A novel method is presented for automated real-time global aerodynamic modeling using local model networks, known as Smoothed Partitioning with Localized Trees in Real Time (SPLITR), as part of NASA’s Learn-to-Fly technology development initiative. The global nonlinear aerodynamics are partitioned into several local regions known as cells, with the dimension, location, and timing of each partition automatically selected based on a residual characterization procedure, under the constraints of real-time operation. Regression trees represent the successive partitioning of the global flight envelope and describe the evolution of the cell structure. Recursive equation-error least-squares parameter estimation in the time domain is used to estimate a model that represents the local aerodynamics in each region, so that it can be updated independently with non-contiguous data in the range of each cell over time. A weighted superposition of these piecewise local models across the flight envelope forms a global nonlinear model that also accurately captures the local aerodynamics. The SPLITR approach is demonstrated using both simulation and flight data, and the results are analyzed in terms of model predictive capabilities as well as interpretability. The results show that SPLITR can be used to automatically partition complex nonlinear aerodynamic behavior, produce an accurate model, and provide valuable physical insight into the local and global aerodynamics.

Weinstein, Rose↗
NASA NTRS1971

State estimation with small nonlinearities

A variety of techniques is available for estimating the states of nonlinear dynamic systems from noisy data. The differences among several of these procedures in the presence of small dynamic and observational nonlinearities are investigated. Four discrete estimation algorithms are analyzed. The first is a strictly least square estimator, while the others are recursive algorithms similar to the Kalman filter used for estimating the states of linear systems. A group of analytic expressions is developed for the mean and covariance of the error in each of these estimators so that they may be compared without lengthy Monte Carlo simulations. The covariance expressions show that, to first order, all the estimators have the same covariance. Expressions for the means show that each estimator has a different bias. Several examples are carried out demonstrating that the relative magnitudes of the bias errors in the various estimators can be a strong function of such parameters as initial covariances and number of data points. Under some circumstances, more complicated algorithms can have larger biases than smaller ones.

Conrad, B.↗
NASA NTRS1972

A comparison of the effects of small nonlinearities on several estimation schemes.

A variety of techniques are available for estimating the states of nonlinear dynamic systems from noisy data. These procedures are generally equivalent when applied to linear systems. This paper investigates the difference between several of these procedures in the presence of small dynamic and observational nonlinearities. In particular, it examines one least square batch processing algorithm, and three recursive algorithms similar to the Kalman filter. To first order, all the estimators have the same covariance. Expressions for the means, however, show that each estimator has a different bias. The examples presented show that the biases can be a strong function of such parameters as initial covariances and number of data points being considered.

Conrad, B.↗
NASA NTRS2012

Real-Time Frequency Response Estimation Using Joined-Wing SensorCraft Aeroelastic Wind-Tunnel Data

A new method is presented for estimating frequency responses and their uncertainties from wind-tunnel data in real time. The method uses orthogonal phase-optimized multi- sine excitation inputs and a recursive Fourier transform with a least-squares estimator. The method was first demonstrated with an F-16 nonlinear flight simulation and results showed that accurate short period frequency responses were obtained within 10 seconds. The method was then applied to wind-tunnel data from a previous aeroelastic test of the Joined- Wing SensorCraft. Frequency responses describing bending strains from simultaneous control surface excitations were estimated in a time-efficient manner.

Grauer, Jared A↗
NASA NTRS1993

Fault detection and isolation

Erroneous measurements in multisensor navigation systems must be detected and isolated. A recursive estimator can find fast growing errors; a least squares batch estimator can find slow growing errors. This process is called fault detection. A protection radius can be calculated as a function of time for a given location. This protection radius can be used to guarantee the integrity of the navigation data. Fault isolation can be accomplished using either a snapshot method or by examining the history of the fault detection statistics.

Bernath, Greg↗
NASA NTRS2008

Sparse Regression as a Sparse Eigenvalue Problem

We extend the l0-norm "subspectral" algorithms for sparse-LDA [5] and sparse-PCA [6] to general quadratic costs such as MSE in linear (kernel) regression. The resulting "Sparse Least Squares" (SLS) problem is also NP-hard, by way of its equivalence to a rank-1 sparse eigenvalue problem (e.g., binary sparse-LDA [7]). Specifically, for a general quadratic cost we use a highly-efficient technique for direct eigenvalue computation using partitioned matrix inverses which leads to dramatic x103 speed-ups over standard eigenvalue decomposition. This increased efficiency mitigates the O(n4) scaling behaviour that up to now has limited the previous algorithms' utility for high-dimensional learning problems. Moreover, the new computation prioritizes the role of the less-myopic backward elimination stage which becomes more efficient than forward selection. Similarly, branch-and-bound search for Exact Sparse Least Squares (ESLS) also benefits from partitioned matrix inverse techniques. Our Greedy Sparse Least Squares (GSLS) generalizes Natarajan's algorithm [9] also known as Order-Recursive Matching Pursuit (ORMP). Specifically, the forward half of GSLS is exactly equivalent to ORMP but more efficient. By including the backward pass, which only doubles the computation, we can achieve lower MSE than ORMP. Experimental comparisons to the state-of-the-art LARS algorithm [3] show forward-GSLS is faster, more accurate and more flexible in terms of choice of regularization

Exact Sparse Least Squares (ESLS)↗
NASA NTRS1985

Adaptive identification and control of structural dynamics systems using recursive lattice filters

A new approach for adaptive identification and control of structural dynamic systems by using least squares lattice filters thar are widely used in the signal processing area is presented. Testing procedures for interfacing the lattice filter identification methods and modal control method for stable closed loop adaptive control are presented. The methods are illustrated for a free-free beam and for a complex flexible grid, with the basic control objective being vibration suppression. The approach is validated by using both simulations and experimental facilities available at the Langley Research Center.

Sundararajan, N.↗
NASA NTRS1980

Design of a recursive vector processor using polynomial splines

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.

Kim, C. S.↗
NASA NTRS1976

DHARMA - Discriminant hyperplane abstracting residuals minimization algorithm for separating clusters with fuzzy boundaries

Learning of discriminant hyperplanes in imperfectly supervised or unsupervised training sample sets with unreliably labeled samples along the fuzzy joint boundaries between sample clusters is discussed, with the discriminant hyperplane designed to be a least-squares fit to the unreliably labeled data points. (Samples along the fuzzy boundary jump back and forth from one cluster to the other in recursive cluster stabilization and are considered unreliably labeled.) Minimization of the distances of these unreliably labeled samples from the hyperplanes does not sacrifice the ability to discriminate between classes represented by reliably labeled subsets of samples. An equivalent unconstrained linear inequality problem is formulated and algorithms for its solution are indicated. Landsat earth sensing data were used in confirming the validity and computational feasibility of the approach, which should be useful in deriving discriminant hyperplanes separating clusters with fuzzy boundaries, given supervised training sample sets with unreliably labeled boundary samples.

Dasarathy, B. V.↗
NASA NTRS1996

REQUEST: A Recursive QUEST Algorithm for Sequential Attitude Determination

In order to find the attitude of a spacecraft with respect to a reference coordinate system, vector measurements are taken. The vectors are pairs of measurements of the same generalized vector, taken in the spacecraft body coordinates, as well as in the reference coordinate system. We are interested in finding the best estimate of the transformation between these coordinate system.s The algorithm called QUEST yields that estimate where attitude is expressed by a quarternion. Quest is an efficient algorithm which provides a least squares fit of the quaternion of rotation to the vector measurements. Quest however, is a single time point (single frame) batch algorithm, thus measurements that were taken at previous time points are discarded. The algorithm presented in this work provides a recursive routine which considers all past measurements. The algorithm is based on on the fact that the, so called, K matrix, one of whose eigenvectors is the sought quaternion, is linerly related to the measured pairs, and on the ability to propagate K. The extraction of the appropriate eigenvector is done according to the classical QUEST algorithm. This stage, however, can be eliminated, and the computation simplified, if a standard eigenvalue-eigenvector solver algorithm is used. The development of the recursive algorithm is presented and illustrated via a numerical example.

Bar-Itzhack, Itzhack Y.↗
NASA NTRS1987

Differential sampling for fast frequency acquisition via adaptive extended least squares algorithm

This paper presents a differential signal model along with appropriate sampling techinques for least squares estimation of the frequency and frequency derivatives and possibly the phase and amplitude of a sinusoid received in the presence of noise. The proposed algorithm is recursive in mesurements and thus the computational requirement increases only linearly with the number of measurements. The dimension of the state vector in the proposed algorithm does not depend upon the number of measurements and is quite small, typically around four. This is an advantage when compared to previous algorithms wherein the dimension of the state vector increases monotonically with the product of the frequency uncertainty and the observation period. Such a computational simplification may possibly result in some loss of optimality. However, by applying the sampling techniques of the paper such a possible loss in optimality can made small.

Kumar, Rajendra↗
NASA NTRS1998

A transition matrix approach to the Davenport gryo calibration scheme

The in-flight gyro calibration scheme commonly used by NASA Goddard Space Flight Center (GSFC) attitude ground support teams closely follows an original version of the Davenport algorithm developed in the late seventies. Its basic idea is to minimize the least-squares differences between attitudes gyro- propagated over the course of a maneuver and those determined using post- maneuver sensor measurements. The paper represents the scheme in a recursive form by combining necessary partials into a rectangular matrix, which is propagated in exactly the same way as a Kalman filters square transition matrix. The nontrivial structure of the propagation matrix arises from the fact that attitude errors are not included in the state vector, and therefore their derivatives with respect to estimated a parameters do not appear in the transition matrix gyro defined in the conventional way. In cases when the required accuracy can be achieved by a single iteration, representation of the Davenport gyro calibration scheme in a recursive form allows one to discard each gyro measurement immediately after it was used to propagate the attitude and state transition matrix. Another advantage of the new approach is that it utilizes the same expression for the error sensitivity matrix as that used by the Kalman filter. As a result the suggested modification of the Davenport algorithm made it possible to reuse software modules implemented in the Kalman filter estimator, where both attitude errors and gyro calibration parameters are included in the state vector. The new approach has been implemented in the ground calibration utilities used to support the Tropical Rainfall Measuring Mission (TRMM). The paper analyzes some preliminary results of gyro calibration performed by the TRMM ground attitude support team. It is demonstrated that an effect of the second iteration on estimated values of calibration parameters is negligibly small, and therefore there is no need to store processed gyro data. This opens a promising opportunity for onboard implementation of the suggested recursive procedure by combining, it with the Kalman filter used to obtain necessary attitude solutions at the beginning and end of each maneuver.

Natanson, G. A.↗
NASA NTRS1985

Progress in adaptive control of flexible spacecraft using lattice filters

This paper reviews the use of the least square lattice filter in adaptive control systems. Lattice filters have been used primarily in speech and signal processing, but they have utility in adaptive control because of their order-recursive nature. They are especially useful in dealing with structural dynamics systems wherein the order of a controller required to damp a vibration is variable depending on the number of modes significantly excited. Applications are presented for adaptive control of a flexible beam. Also, difficulties in the practical implementation of the lattice filter in adaptive control are discussed.

Sundararajan, N.↗
NASA NTRS1992

Several recursive techniques for observer/Kalman filter system identification from data

This paper derives algorithms for identifying autoregressive models, with external input, of multi-input multi-output systems from data using a fast transversal filter or a least-squares lattice filter. The autoregressive models including external inputs are used to identify state-space models and the corresponding observer/Kalman filter gains of the system. The derivation is an extension of scalar autoregressive model approaches, modified to cope with multivariables, external inputs and an extra direct-influence term. Comparisons between the fast transversal filter, the least-squares lattice filter and the classical least-squares method are made in terms of complexity, computational cost and practical applications issues. A numerical example is included to illustrate the approach.

Chen, Chung-Wen↗
NASA NTRS2011

Orbit Determination of Spacecraft in Earth-Moon L1 and L2 Libration Point Orbits

The ARTEMIS mission, part of the THEMIS extended mission, is the first to fly spacecraft in the Earth-Moon Lissajous regions. In 2009, two of the five THEMIS spacecraft were redeployed from Earth-centered orbits to arrive in Earth-Moon Lissajous orbits in late 2010. Starting in August 2010, the ARTEMIS P1 spacecraft executed numerous stationkeeping maneuvers, initially maintaining a lunar L2 Lissajous orbit before transitioning into a lunar L1 orbit. The ARTEMIS P2 spacecraft entered a L1 Lissajous orbit in October 2010. In April 2011, both ARTEMIS spacecraft will suspend Lissajous stationkeeping and will be maneuvered into lunar orbits. The success of the ARTEMIS mission has allowed the science team to gather unprecedented magnetospheric measurements in the lunar Lissajous regions. In order to effectively perform lunar Lissajous stationkeeping maneuvers, the ARTEMIS operations team has provided orbit determination solutions with typical accuracies on the order of 0.1 km in position and 0.1 cm/s in velocity. The ARTEMIS team utilizes the Goddard Trajectory Determination System (GTDS), using a batch least squares method, to process range and Doppler tracking measurements from the NASA Deep Space Network (DSN), Berkeley Ground Station (BGS), Merritt Island (MILA) station, and United Space Network (USN). The team has also investigated processing of the same tracking data measurements using the Orbit Determination Tool Kit (ODTK) software, which uses an extended Kalman filter and recursive smoother to estimate the orbit. The orbit determination results from each of these methods will be presented and we will discuss the advantages and disadvantages associated with using each method in the lunar Lissajous regions. Orbit determination accuracy is dependent on both the quality and quantity of tracking measurements, fidelity of the orbit force models, and the estimation techniques used. Prior to Lissajous operations, the team determined the appropriate quantity of tracking measurements that would be needed to meet the required orbit determination accuracies. Analysts used the Orbit Determination Error Analysis System (ODEAS) to perform covariance analyses using various tracking data schedules. From this analysis, it was determined that 3.5 hours of DSN TRK-2-34 range and Doppler tracking data every other day would suffice to meet the predictive orbit knowledge accuracies in the Lissajous region. The results of this analysis are presented. Both GTDS and ODTK have high-fidelity environmental orbit force models that allow for very accurate orbit estimation in the lunar Lissajous regime. These models include solar radiation pressure, Earth and Moon gravity models, third body gravitational effects from the Sun, and to a lesser extent third body gravitational effects from Jupiter, Venus, Saturn, and Mars. Increased position and velocity uncertainties following each maneuver, due to small execution performance errors, requires that several days of post-maneuver tracking data be processed to converge on an accurate post-maneuver orbit solution. The effects of maneuvers on orbit determination accuracy will be presented, including a comparison of the batch least squares technique to the extended Kalman filter/smoother technique. We will present the maneuver calibration results derived from processing post-maneuver tracking data. A dominant error in the orbit estimation process is the uncertainty in solar radiation pressure and the resultant force on the spacecraft. An estimation of this value can include many related factors, such as the uncertainty in spacecraft reflectivity and surface area which is a function of spacecraft orientation (spin-axis attitude), uncertainty in spacecraft wet mass, and potential seasonal variability due to the changing direction of the Sun line relative to the Earth-Moon Lissajous reference frame. In addition, each spacecraft occasionally enters into Earth or Moon penumbra or umbra and these shadow crossings reduche solar radiation force for several hours. The effects of these events on orbit determination accuracy will be presented. In order to plan for upcoming stationkeeping maneuvers, the maneuver planning team must take the current orbit estimate, propagate it forward to the planned maneuver time, and determine the optimal maneuver to maintain the Lissajous orbit for one or more revolutions. The propagation is performed using a Runge-Kutta 7/8 integrator and typically the position and velocity uncertainty increases with propagation time, increasing the overall uncertainty of the orbit state at the maneuver execution time. The effect of orbit knowledge uncertainty on stationkeeping operations will be presented.

Woodard, Mark↗
NASA NTRS1987

Least squares linear lags and limited memory filters

Pure autoregressive (AR) models which are linear in the short term, that is when a variable can be predicted by linear regression on a limited number of past observations, are discussed. When evenly spaced observations are available, a fixed set of AR coefficients can be calculated independent of the data. For filtering purposes, such a lag structure can be implemented recursively with an efficient algorithm. The method of computing variance recursively is also derived. A complete algorithm is presented in the appendix.

Discenza, Joseph H.↗
NASA NTRS1982

Self-tuning regulators for multicyclic control of helicopter vibration

A class of algorithms for the multicyclic control of helicopter vibration and loads is derived and discussed. This class is characterized by a linear, quasi-static, frequency-domain model of the helicopter response to control; identification of the helicopter model by least-squared-error or Kalman filter methods; and a minimum variance or quadratic performance function controller. Previous research on such controllers is reviewed. The derivations and discussions cover the helicopter model; the identification problem, including both off-line and on-line (recursive) algorithms; the control problem, including both open-loop and closed-loop feedback; and the various regulator configurations possible within this class. Conclusions from analysis and numerical simulations of the regulators provide guidance in the design and selection of algorithms for further development, including wind tunnel and flight tests.

Johnson, W.↗