Nonlinear least-squares estimation for sensor and navigation biases

Herman, Shawn M.; Poore, Aubrey B.

doi:10.1117/12.673524

Cited by 7 publications

(5 citation statements)

References 4 publications

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“…In this equation, fv k g is a p-dimensional zero-mean Gaussian white noise sequence with covariance matrix R k . More general filter models can be formulated from measurement models with non-Gaussian or correlated (e.g., colored) noise terms [13] and sensor biases [14].…”

Section: Overview Of Nonlinear Filteringmentioning

confidence: 99%

Gaussian Sum Filters for Space Surveillance: Theory and Simulations

Horwood

Aragon

Poore

2011

Journal of Guidance, Control, and Dynamics

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108

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While standard Kalman-based filters, Gaussian assumptions, and covariance-weighted metrics are very effective in data-rich tracking environments, their use in the data-sparse environment of space surveillance is more limited. To properly characterize non-Gaussian density functions arising in the problem of long-term propagation of state uncertainties, a Gaussian sum filter adapted to the two-body problem in space surveillance is proposed and demonstrated to achieve uncertainty consistency. The proposed filter is made efficient by using only a onedimensional Gaussian sum in equinoctial orbital elements, thereby avoiding the expensive representation of a full six-dimensional mixture and hence the "curse of dimensionality." Additionally, an alternate set of equinoctial elements is proposed and is shown to provide enhanced uncertainty consistently over the traditional element set. Simulation studies illustrate the improvements in the Gaussian sum approach over the traditional unscented Kalman filter and the impact of correct uncertainty representation in the problems of data association (correlation) and anomaly (maneuver) detection. Nomenclature A= lower-triangular Cholesky factor of a covariance matrix a = semimajor axis a pert = perturbing acceleration a; h; k; p; q; ' = equinoctial orbital elements c = parameter controlling the accuracy of the Gaussian sum filter f = system dynamics vector G = process noise shape matrix h = measurement function vector k = (subscript) time index '= mean longitude N = number of mixture components N = Gaussian probability density function n = mean motion n; h; k; p; q; '= alternate equinoctial orbital elements P = covariance of a Gaussian distribution PE = prediction error p = probability density function Qt = process noise covariance matrix R k = measurement noise covariance matrix r = Cartesian Earth-Centered Inertial (ECI) position coordinates _ r = Cartesian ECI velocity coordinates r = Cartesian ECI acceleration coordinates t 0 , t = initial and current times u = orbital element coordinates (sixdimensional) fv 1 ; . . . ; v k g = Gaussian white noise sequence wt = Gaussian white noise process w ; w ; . . . = mixture weights x = dynamic state vector Z k fz 1 ; . . . ; z k g = measurement sequence ; ; . . . = (subscripts) indices of mixture components kj = Kronecker delta symbol = mean of a Gaussian distribution = Earth gravitational constant (398600:4418 km 3 =s 2 ) = standard deviation of a univariate Gaussian distribution = inverse solution flow r x = gradient operator with respect to x (column oriented)

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Section: Overview Of Nonlinear Filteringmentioning

confidence: 99%

Gaussian Sum Filters for Space Surveillance: Theory and Simulations

Horwood

Aragon

Poore

2011

Journal of Guidance, Control, and Dynamics

Self Cite

108

View full text Add to dashboard Cite

show abstract

“…The geographic coordinates of the i th ship are latitude Ls i , longitude Rs i , and altitude Hs i , which are known in real time. Four reference frames will be defined first for further discussions (Herman and Poore, 2006). The body frame or platform frame is defined as a Cartesian rectangular coordinate system fixed relative to the ship.…”

Section: Problem Descriptionmentioning

confidence: 99%

Section: P Ro B L E M D E S C R I P T I O Nmentioning

confidence: 99%

“…Since these variations are small, OBEM and URM have approximate performances. (5) For UGSP mobile radars, Herman and Poore (2006) and Kragel et al (2007) analysed the dependencies between different biases qualitatively by using Singular Value Decomposition (SVD), yielding similar possible dependencies among different biases as those of Chen et al (2012).…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Mobile 3-D Radar Error Registration when Radar Sways with Platform

Chen

Wang

et al. 2013

J. Navigation

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For mobile radars installed on a gyro-stabilised platform (GSP) that can steadily follow an East-North-Up (ENU) frame, attitude biases (ABs) of the platform and offset biases (OBs) of the radar are linear dependent variables. Therefore ABs and OBs are unobservable in the linearized registration equations; however, when combining them as new variables, the system becomes observable, and this model has been called the unified registration model (URM). Unlike GSP mobile radars, un-stabilised GSP (or UGSP) mobile radars are installed on the platform directly and rotate with the platform simultaneously. For UGSP, it is testified that both types of biases are independent and observable because the time-varying attitude angles (AAs) 1 of the platform are included in the registration equations, which destroy the dependencies of both kinds of biases and lead us to propose a completely different linearized registration model-the All Augmented Model (AAM). AAM employs all OBs and ABs in the state vector and a Kalman filter (KF) to produce their estimates. Numerical simulation results show that the estimated performance of AAM is close to the Cramér-Rao lower bound (CRLB) and that the Root Mean Square Errors (RMSEs) of the rectified measurements by using AAM are more than 500 m smaller than by URM in all directions. K E Y

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“…Then Herman and Poore [5] and Kragel et al [6] gave registration model by using the least squares method and used the singular value decomposition (SVD) of the coefficient matrix (CM) of the registration equations. Possible dependencies among all biases are analyzed qualitatively according to magnitudes of different column vector elements in the unitary matrix obtained from SVD.…”

Section: Introductionmentioning

confidence: 99%

Unified Registration Model for Both Stationary and Mobile 3D Radar Alignment

Chen

Wang

Progri³

2014

Journal of Electrical and Computer Engineering

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For mobile radar, offset biases and attitude biases influence radar measurements simultaneously. Attitude biases generated from the errors of the inertial navigation system (INS) of the platform can be converted into equivalent radar measurement errors by three analytical expressions (range, azimuth, and elevation, resp.). These expressions are unique and embody the dependences between the offset and attitude biases. The dependences indicate that all the attitude biases can be viewed as and merged into some kind of offset biases. Based on this, a unified registration model (URM) is proposed which only contains radar "offset biases" in the form of system variables in the registration equations, where, in fact, the "offset biases" contain the influences of the attitude biases. URM has the same form as the registration model of stationary radar network where no attitude biases exist. URM can compensate radar offset and attitude biases simultaneously and has minor computation burden compared with other registration models for mobile radar network.

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Nonlinear least-squares estimation for sensor and navigation biases

Cited by 7 publications

References 4 publications

Gaussian Sum Filters for Space Surveillance: Theory and Simulations

Gaussian Sum Filters for Space Surveillance: Theory and Simulations

Analysis of Mobile 3-D Radar Error Registration when Radar Sways with Platform

Unified Registration Model for Both Stationary and Mobile 3D Radar Alignment

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