Covariance consistency for track initiation using Gauss-Hermite quadrature

Horwood, Joshua T.; Aragon, Nathan D.; Poore, Aubrey B.

doi:10.1117/12.851880

Cited by 8 publications

(9 citation statements)

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“…Precise details of the generation of these initial Gaussian PDFs is not treated in this paper. The reader is referred to the earlier paper of Horwood et al [23], which treats the initial orbit determination problem in space surveillance.…”

Section: Simulation Studiesmentioning

confidence: 99%

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Adaptive Gaussian Sum Filters for Space Surveillance Tracking

2012

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While orbital propagators have been investigated extensively over the last fifty years, the consistent propagation of state covariances and more general (non-Gaussian) probability densities has received relatively little attention. The representation of state uncertainty by a Gaussian mixture is well suited for problems in space situational awareness. Advantages of this approach, which are demonstrated in this paper, include the potential for long-term propagation in data-starved environments, the capturing of higher-order statistics and more accurate representation of nonlinear dynamical models, the ability to make the filter adaptive using real-time metrics, and parallelizability. Case studies are presented establishing uncertainty consistency and the effectiveness of the proposed adaptive Gaussian sum filter.

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Section: Simulation Studiesmentioning

confidence: 99%

“…Although more elaborate gravity models could be used, the model equation (23) is sufficiently nonlinear to challenge the proposed adaptive Gaussian sum filter.…”

Section: Simulation Studiesmentioning

confidence: 99%

Adaptive Gaussian Sum Filters for Space Surveillance Tracking

2012

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“…The correction step, while equally important, is addressed elsewhere. 7 We remark that the Gaussian assumption is usually well-preserved following a measurement update or a batch estimation procedure for orbit determination 18,19 (track initiation). It is the prediction step where one sees the most benefit from using a Gaussian sum due to the potentially long time gaps between updates and the need to propagate the uncertainty under a highly nonlinear dynamical model.…”

Section: Features Of the Proposed Gaussian Sum Filtermentioning

confidence: 99%

A Gaussian sum filter framework for space surveillance

2011

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While standard Kalman-based filters, Gaussian assumptions, and covariance-weighted metrics work remarkably well in data-rich tracking environments such as air and ground, their use in the data-sparse environment of space surveillance is more limited. In order to properly characterize non-Gaussian density functions arising in the problem of long term propagation of state uncertainties in the two-body problem, a framework for a Gaussian sum filter is described which achieves uncertainty (covariance) consistency and an accurate approximation to the Fokker-Planck equation up to a prescribed accuracy. The filter is made efficient and practical by (i) using coordinate systems adapted to the physics (i.e., orbital elements), (ii) only requiring a Gaussian sum to be defined along one of the six state space dimensions, and (iii) the ability to initially select the component means, covariances, and weights by way of a lookup table generated by solving an offline nonlinear optimization problem. The efficacy of the Gaussian sum filter and the improvements over the traditional unscented Kalman filter are demonstrated within the problems of data association and maneuver detection.

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“…II.B], the Kalman filter update can be derived by choosing the gain to minimize the trace of the preposterior MSE matrix of a linear estimator. In other words, rather than starting out with the optimal gain given in (94), one decides that the filtering algorithm must update the state as (132) and one must find the value of W k that minimizes the trace of (133) where the conditioning on Z 1:(k−1) on the right-hand side was omitted for brevity. The left-hand side was expanded by substituting (132).…”

Section: B Derivation As a Preposterior Mse Matrixmentioning

confidence: 99%

“…In other words, rather than starting out with the optimal gain given in (94), one decides that the filtering algorithm must update the state as (132) and one must find the value of W k that minimizes the trace of (133) where the conditioning on Z 1:(k−1) on the right-hand side was omitted for brevity. The left-hand side was expanded by substituting (132). The estimate is "preposterior" in that the MSE matrix of an updated (posterior) estimate at time k given only the measurements up to time k − 1 is found.…”

Section: B Derivation As a Preposterior Mse Matrixmentioning

confidence: 99%

Basic tracking using nonlinear 3D monostatic and bistatic measurements

Crouse¹

2014

IEEE Aerosp. Electron. Syst. Mag.

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Monostatic and bistatic position and Doppler measurements used in radar and sonar systems are nonlinear transformations of a Cartesian state. These nonlinearities pose a challenge for many target tracking algorithms, causing the so-called contact lens problem, which describes the nonlinear appearance of the measurement probability density function in Cartesian coordinates. This tutorial considers methods for measurement filtering (tracking without considering data association) using a single-Gaussian approximation when monostatic and bistatic position and Doppler measurements are available. The connection between the cubature Kalman filter and numerous other filtering algorithms is shown, and the accuracy and consistency of different algorithms are compared through simulation. An effort is made to express the geometric relationships associated with multistatic tracking in a simple vectorial manner. This tutorial focuses on basic tracking, and the companion tutorials "Tracking Using 3D Monostatic and Bistatic Measurements in Refractive Environments" and "Basic Tracking Using Nonlinear Continuous-Time Dynamic Models" extend the results to more sophisticated physical models.

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Covariance consistency for track initiation using Gauss-Hermite quadrature

Cited by 8 publications

References 0 publications

Adaptive Gaussian Sum Filters for Space Surveillance Tracking

Adaptive Gaussian Sum Filters for Space Surveillance Tracking

A Gaussian sum filter framework for space surveillance

Basic tracking using nonlinear 3D monostatic and bistatic measurements

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