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All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

An application of the square root information filter to large scale linear interconnected systems

It is demonstrated that use of the square root information filter (SRIF) can reduce the storage and computation required for estimation of certain classes of large-scale interconnected systems. The SRIF uses an information array that is related to the Kalman filter covariance and estimate. The SRIF algorithm, which is optimal, is a direct application of matrix partitioning to some optimal filtering algorithms described in the literature. The SRIF algorithm is able to reduce the storage requirements of a 40-subsystem 10-state problem by a full order of magnitude.

Bierman, G. J.↗
NASA NTRS1988

Applications of square-root information filtering and smoothing in spacecraft orbit determination

The JPL (Jet Propulsion Laboratory) Orbit Determination Software System is a set of computer programs developed for the primary purpose of determining the flight path of deep-space mission spacecraft in NASA's Planetary Program and highly elliptical orbiting spacecraft in Earth orbit. The filtering processes available within the JPL Orbit Determination Software are discussed, and several examples are presented. In particular, solutions obtained by the Square Root Information Filter (SRIF) using Bierman's Estimation Subroutine Library (ESL) are discussed and compared with the solutions obtained by the singular value decomposition (SVD) technique. It is concluded that the SRIF filtering and smoothing algorithms are efficient and numerically stable for well-conditioned systems. The use of Bierman's ESL simplifies the task of maintaining the orbit determination software by providing efficient, tested filtering tools. For solving a large well-conditioned system (rank higher than 120), SRIF is approximately four times faster than SVD; however, for solving an ill-conditioned system, SVD is recommended.

Wang, Tseng-Chan↗
NASA NTRS1990

Downdating a time-varying square root information filter

A new method to efficiently downdate an estimate and covariance generated by a discrete time Square Root Information Filter (SRIF) is presented. The method combines the QR factor downdating algorithm of Gill and the decentralized SRIF algorithm of Bierman. Efficient removal of either measurements or a priori information is possible without loss of numerical integrity. Moreover, the method includes features for detecting potential numerical degradation. Performance on a 300 parameter system with 5800 data points shows that the method can be used in real time and hence is a promising tool for interactive data analysis. Additionally, updating a time-varying SRIF filter with either additional measurements or a priori information proceeds analogously.

Muellerschoen, Ronald J.↗
NASA NTRS1994

A Continuous Square Root in Formation Filter-Swoother with Discrete Data Update

A differential equation for the square root information matrix is derived and adapted to the problems of filtering and smoothing. The resulting continuous square root information filter (SRIF) performs the mapping of state and process noise by numerical integration of the SRIF matrix and admits data via a discrete least square update.

SRIF mapping↗
NASA NTRS1978

An application of the square-root information filter to large scale linear interconnected systems

The paper considers the use of numerically stable square-root information filter (SRIF) algorithms to reduce the computation and storage requirements of a certain class of large-scale linear interconnected systems (multistation satellite tracking is examined as an example). The reductions are in comparison with conventional sequential covariance type formulations. To illustrate the SRIF algorithm: a 40 subsystem, 10 state problem, for example, has its storage requirements reduced by a full order of magnitude (from 84255 to 8100).

Bierman, G. J.↗
NASA NTRS1985

A decentralized square root information filter/smoother

A number of developments has recently led to a considerable interest in the decentralization of linear least squares estimators. The developments are partly related to the impending emergence of VLSI technology, the realization of parallel processing, and the need for algorithmic ways to speed the solution of dynamically decoupled, high dimensional estimation problems. A new method is presented for combining Square Root Information Filters (SRIF) estimates obtained from independent data sets. The new method involves an orthogonal transformation, and an information matrix filter 'homework' problem discussed by Schweppe (1973) is generalized. The employed SRIF orthogonal transformation methodology has been described by Bierman (1977).

Bierman, G. J.↗
NASA NTRS1988

Storage and computationally efficient permutations of factorized covariance and square-root information matrices

A unified method to permute vector-stored upper-triangular diagonal factorized covariance (UD) and vector stored upper-triangular square-root information filter (SRIF) arrays is presented. The method involves cyclical permutation of the rows and columns of the arrays and retriangularization with appropriate square-root-free fast Givens rotations or elementary slow Givens reflections. A minimal amount of computation is performed and only one scratch vector of size N is required, where N is the column dimension of the arrays. To make the method efficient for large SRIF arrays on a virtual memory machine, three additional scratch vectors each of size N are used to avoid expensive paging faults. The method discussed is compared with the methods and routines of Bierman's Estimation Subroutine Library (ESL).

Muellerschoen, R. J.↗
NASA NTRS1975

The treatment of bias in the square-root information filter/smoother

The Dyer-McReynolds square-root information filter (SRIF) is rederived, using recursive least-square arguments. The result is applied to a system composed partly of biases. The filter sensitivity matrix, computed covariance, and consider covariance for this augmented system are reviewed. A new computationally attractive representation for the smoothed estimates, in terms of a smoothed sensitivity matrix and a smoothed computed covariance is presented.

Bierman, G. J.↗
NASA NTRS1979

Modern estimation techniques applied to microwave sensing of the marine boundary layer

Previous efforts in the area of satellite microwave sensing of the marine boundary layer have relied upon linear regression techniques to extract geophysical parameters from the microwave measurement data. The approach used in the present paper shifts emphasis away from the generation of regression weighting matrices which implicitly assume that the data are linear in the parameters to be determined and that the problem is statistically stationary. The idea is simply to employ modern computational estimation techniques to obtain parameter estimates from nonlinear noisy measurements. The approach is limited only to the region of validity of Grody's (1976) model. Attention is focused on documenting how estimation techniques, in particular the square root information filter (SRIF), are used to solve a nonlinear function optimization problem.

Bierman, G. J.↗
NASA NTRS1989

Estimation and filtering techniques for high-accuracy GPS applications

Techniques for determination of very precise orbits for satellites of the Global Positioning System (GPS) are currently being studied and demonstrated. These techniques can be used to make cm-accurate measurements of station locations relative to the geocenter, monitor earth orientation over timescales of hours, and provide tropospheric and clock delay calibrations during observations made with deep space radio antennas at sites where the GPS receivers have been collocated. For high-earth orbiters, meter-level knowledge of position will be available from GPS, while at low altitudes, sub-decimeter accuracy will be possible. Estimation of satellite orbits and other parameters such as ground station positions is carried out with a multi-satellite batch sequential pseudo-epoch state process noise filter. Both square-root information filtering (SRIF) and UD-factorized covariance filtering formulations are implemented in the software.

Lichten, S. M.↗
NASA NTRS1989

Stable Kalman filters for processing clock measurement data

Kalman filters have been used for some time to process clock measurement data. Due to instabilities in the standard Kalman filter algorithms, the results have been unreliable and difficult to obtain. During the past several years, stable forms of the Kalman filter have been developed, implemented, and used in many diverse applications. These algorithms, while algebraically equivalent to the standard Kalman filter, exhibit excellent numerical properties. Two of these stable algorithms, the Upper triangular-Diagonal (UD) filter and the Square Root Information Filter (SRIF), have been implemented to replace the standard Kalman filter used to process data from the Deep Space Network (DSN) hydrogen maser clocks. The data are time offsets between the clocks in the DSN, the timescale at the National Institute of Standards and Technology (NIST), and two geographically intermediate clocks. The measurements are made by using the GPS navigation satellites in mutual view between clocks. The filter programs allow the user to easily modify the clock models, the GPS satellite dependent biases, and the random noise levels in order to compare different modeling assumptions. The results of this study show the usefulness of such software for processing clock data. The UD filter is indeed a stable, efficient, and flexible method for obtaining optimal estimates of clock offsets, offset rates, and drift rates. A brief overview of the UD filter is also given.

Clements, P. A.↗