A distributed and iterative method for square root filtering in space-time estimation

Caption title.Includes bibliographical references.Supported by the Air Force Office of Scientific Research. F49620-92-J-002 Supported by the Office of Naval Research. N00014-91-J-1120 N00014-91-J-1004 Supported by the Army Research Office. DAAL03-92-G-0115Toshio M. Chin, William C. Karl, Alan S. Willsky

Square-root filtering via covariance SVD factors in the accurate continuous-discrete extended-cubature Kalman filter

This paper continues our research devoted to an accurate nonlinear Bayesian filters' design. Our solution implies numerical methods for solving ordinary differential equations (ODE) when propagating the mean and error covariance of the dynamic state. The key idea is that an accurate implementation strategy implies the methods with a discretization error control involved. This means that the filters' moment differential equations are to be solved accurately, i.e. with negligible error. In this paper, we explore the continuous-discrete extended-cubature Kalman filter that is a hybrid method between Extended and Cubature Kalman filters (CKF). Motivated by recent results obtained for the continuous-discrete CKF in Bayesian filtering realm, we propose the numerically stable (to roundoff) square-root approach within a singular value decomposition (SVD) for the hybrid filter. The new method is extensively tested on a few application examples including stiff systems

Analysis of Square-Root Kalman Filters for Angles-Only Orbital Navigation and the Effects of Sensor Accuracy on State Observability

Angles-only navigation is simple, robust, and well proven in many applications. However, it is sometimes ill-conditioned for orbital rendezvous and proximity operations because, without a direct range measurement, the distance to approaching satellites must be estimated by firing thrusters and observing the change in the target\u27s bearing. Nevertheless, the simplicity of angles-only navigation gives it great appeal. The viability of this technique for relative navigation is examined by building a high-fidelity simulation and evaluating the sensitivity of the system to sensor errors. The relative performances of square-root filtering methods, including Potter, Carlson, and UD factorization filters, are compared to the conventional and Joseph formulations. Filter performance is evaluated during closed-loop station keeping operations in simulation

An ensemble-based approach to climate reconstructions

Data assimilation is a promising approach to obtain climate reconstructions that are both consistent with observations of the past and with our understanding of the physics of the climate system as represented in the climate model used. Here, we investigate the use of ensemble square root filtering (EnSRF) – a technique used in weather forecasting – for climate reconstructions. We constrain an ensemble of 29 simulations from an atmosphere-only general circulation model (GCM) with 37 pseudo-proxy temperature time series. Assimilating spatially sparse information with low temporal resolution (semi-annual) improves the representation of not only temperature, but also other surface properties, such as precipitation and even upper air features such as the intensity of the northern stratospheric polar vortex or the strength of the northern subtropical jet. Given the sparsity of the assimilated information and the limited size of the ensemble used, a localisation procedure is crucial to reduce "overcorrection" of climate variables far away from the assimilated information

Array algorithms for H-infinity estimation

In this paper we develop array algorithms for H-infinity filtering. These algorithms can be regarded as the Krein space generalizations of H-2 array algorithms, which are currently the preferred method for implementing H-2 biters, The array algorithms considered include typo main families: square-root array algorithms, which are typically numerically more stable than conventional ones, and fast array algorithms which, when the system is time-invariant, typically offer an order of magnitude reduction in the computational effort. Both have the interesting feature that one does not need to explicitly check for the positivity conditions required for the existence of H-infinity filters, as these conditions are built into the algorithms themselves. However, since H-infinity square-root algorithms predominantly use J-unitary transformations, rather than the unitary transformations required in the H-2 case, further investigation is needed to determine the numerical behavior of such algorithms

Sequential Least-Squares Using Orthogonal Transformations

Square root information estimation, starting from its beginnings in least-squares parameter estimation, is considered. Special attention is devoted to discussions of sensitivity and perturbation matrices, computed solutions and their formal statistics, consider-parameters and consider-covariances, and the effects of a priori statistics. The constant-parameter model is extended to include time-varying parameters and process noise, and the error analysis capabilities are generalized. Efficient and elegant smoothing results are obtained as easy consequences of the filter formulation. The value of the techniques is demonstrated by the navigation results that were obtained for the Mariner Venus-Mercury (Mariner 10) multiple-planetary space probe and for the Viking Mars space mission

Tracking filter and multi-sensor data fusion

In this paper factorization filtering, fusion filtering strategy and related algorithms are presented. Some results of implementation and validation using realistic data are given

A survey of the state of the art and focused research in range systems, task 2

Contract generated publications are compiled which describe the research activities for the reporting period. Study topics include: equivalent configurations of systolic arrays; least squares estimation algorithms with systolic array architectures; modeling and equilization of nonlinear bandlimited satellite channels; and least squares estimation and Kalman filtering by systolic arrays