Generalized Wahba Problems for Spinning Spacecraft Attitude and Rate Determination
Abstract Two generalized versions of Wahba’s attitude determination problem have been developed for a spinning spacecraft, and a restricted version of one problem has been solved in closed-form. These problems seek to estimate both attitude and rate based solely on a time series of vector attitude o...
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| Autor*in: |
Psiaki, Mark L. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2009 |
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| Schlagwörter: |
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| Anmerkung: |
© American Astronautical Society, INC 2009 |
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| Übergeordnetes Werk: |
Enthalten in: The Journal of the Astronautical Sciences - Springer-Verlag, 2006, 57(2009), 1-2 vom: Jan., Seite 73-92 |
|---|---|
| Übergeordnetes Werk: |
volume:57 ; year:2009 ; number:1-2 ; month:01 ; pages:73-92 |
| Links: |
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| DOI / URN: |
10.1007/BF03321495 |
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| 520 | |a Abstract Two generalized versions of Wahba’s attitude determination problem have been developed for a spinning spacecraft, and a restricted version of one problem has been solved in closed-form. These problems seek to estimate both attitude and rate based solely on a time series of vector attitude observations along with a spacecraft dynamic model. Algorithms that solve these problems will be useful for spin-stabilized spacecraft that reduce complexity by omitting rate gyros. The first generalized Wahba problem presumes that the spin axis is known and that the spin rate is constant but unknown, as for a spinning spacecraft that has a nutation damper. The second generalized problem includes full rigid-body Euler dynamics, which allow for nutations, and seeks to estimate the unknown initial attitude rate vector. Both problems are recast into the K-matrix form of Wahba’s problem with K matrices that depend on the unknown rates. Restricted problems are developed that use the minimum number of vector measurements, two for the first problem and three for the second problem. The restricted first problem is solved in closed-form. The restricted second problem is shown to be observable, and it is reduced to a small system of nonlinear equations in the axially symmetric case. The possibility of deriving global solutions for these problems makes them attractive to assist or replace an extended Kaiman filter because a global solution cannot suffer from nonlinear divergence. | ||
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10.1007/BF03321495 doi (DE-627)SPR036437611 (SPR)BF03321495-e DE-627 ger DE-627 rakwb eng Psiaki, Mark L. verfasserin aut Generalized Wahba Problems for Spinning Spacecraft Attitude and Rate Determination 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © American Astronautical Society, INC 2009 Abstract Two generalized versions of Wahba’s attitude determination problem have been developed for a spinning spacecraft, and a restricted version of one problem has been solved in closed-form. These problems seek to estimate both attitude and rate based solely on a time series of vector attitude observations along with a spacecraft dynamic model. Algorithms that solve these problems will be useful for spin-stabilized spacecraft that reduce complexity by omitting rate gyros. The first generalized Wahba problem presumes that the spin axis is known and that the spin rate is constant but unknown, as for a spinning spacecraft that has a nutation damper. The second generalized problem includes full rigid-body Euler dynamics, which allow for nutations, and seeks to estimate the unknown initial attitude rate vector. Both problems are recast into the K-matrix form of Wahba’s problem with K matrices that depend on the unknown rates. Restricted problems are developed that use the minimum number of vector measurements, two for the first problem and three for the second problem. The restricted first problem is solved in closed-form. The restricted second problem is shown to be observable, and it is reduced to a small system of nonlinear equations in the axially symmetric case. The possibility of deriving global solutions for these problems makes them attractive to assist or replace an extended Kaiman filter because a global solution cannot suffer from nonlinear divergence. Extended Kalman Filter (dpeaa)DE-He213 Vector Measurement (dpeaa)DE-He213 Spin Axis (dpeaa)DE-He213 Restricted Version (dpeaa)DE-He213 Restricted Problem (dpeaa)DE-He213 Enthalten in The Journal of the Astronautical Sciences Springer-Verlag, 2006 57(2009), 1-2 vom: Jan., Seite 73-92 (DE-627)SPR036426385 nnns volume:57 year:2009 number:1-2 month:01 pages:73-92 https://dx.doi.org/10.1007/BF03321495 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 57 2009 1-2 01 73-92 |
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10.1007/BF03321495 doi (DE-627)SPR036437611 (SPR)BF03321495-e DE-627 ger DE-627 rakwb eng Psiaki, Mark L. verfasserin aut Generalized Wahba Problems for Spinning Spacecraft Attitude and Rate Determination 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © American Astronautical Society, INC 2009 Abstract Two generalized versions of Wahba’s attitude determination problem have been developed for a spinning spacecraft, and a restricted version of one problem has been solved in closed-form. These problems seek to estimate both attitude and rate based solely on a time series of vector attitude observations along with a spacecraft dynamic model. Algorithms that solve these problems will be useful for spin-stabilized spacecraft that reduce complexity by omitting rate gyros. The first generalized Wahba problem presumes that the spin axis is known and that the spin rate is constant but unknown, as for a spinning spacecraft that has a nutation damper. The second generalized problem includes full rigid-body Euler dynamics, which allow for nutations, and seeks to estimate the unknown initial attitude rate vector. Both problems are recast into the K-matrix form of Wahba’s problem with K matrices that depend on the unknown rates. Restricted problems are developed that use the minimum number of vector measurements, two for the first problem and three for the second problem. The restricted first problem is solved in closed-form. The restricted second problem is shown to be observable, and it is reduced to a small system of nonlinear equations in the axially symmetric case. The possibility of deriving global solutions for these problems makes them attractive to assist or replace an extended Kaiman filter because a global solution cannot suffer from nonlinear divergence. Extended Kalman Filter (dpeaa)DE-He213 Vector Measurement (dpeaa)DE-He213 Spin Axis (dpeaa)DE-He213 Restricted Version (dpeaa)DE-He213 Restricted Problem (dpeaa)DE-He213 Enthalten in The Journal of the Astronautical Sciences Springer-Verlag, 2006 57(2009), 1-2 vom: Jan., Seite 73-92 (DE-627)SPR036426385 nnns volume:57 year:2009 number:1-2 month:01 pages:73-92 https://dx.doi.org/10.1007/BF03321495 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 57 2009 1-2 01 73-92 |
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10.1007/BF03321495 doi (DE-627)SPR036437611 (SPR)BF03321495-e DE-627 ger DE-627 rakwb eng Psiaki, Mark L. verfasserin aut Generalized Wahba Problems for Spinning Spacecraft Attitude and Rate Determination 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © American Astronautical Society, INC 2009 Abstract Two generalized versions of Wahba’s attitude determination problem have been developed for a spinning spacecraft, and a restricted version of one problem has been solved in closed-form. These problems seek to estimate both attitude and rate based solely on a time series of vector attitude observations along with a spacecraft dynamic model. Algorithms that solve these problems will be useful for spin-stabilized spacecraft that reduce complexity by omitting rate gyros. The first generalized Wahba problem presumes that the spin axis is known and that the spin rate is constant but unknown, as for a spinning spacecraft that has a nutation damper. The second generalized problem includes full rigid-body Euler dynamics, which allow for nutations, and seeks to estimate the unknown initial attitude rate vector. Both problems are recast into the K-matrix form of Wahba’s problem with K matrices that depend on the unknown rates. Restricted problems are developed that use the minimum number of vector measurements, two for the first problem and three for the second problem. The restricted first problem is solved in closed-form. The restricted second problem is shown to be observable, and it is reduced to a small system of nonlinear equations in the axially symmetric case. The possibility of deriving global solutions for these problems makes them attractive to assist or replace an extended Kaiman filter because a global solution cannot suffer from nonlinear divergence. Extended Kalman Filter (dpeaa)DE-He213 Vector Measurement (dpeaa)DE-He213 Spin Axis (dpeaa)DE-He213 Restricted Version (dpeaa)DE-He213 Restricted Problem (dpeaa)DE-He213 Enthalten in The Journal of the Astronautical Sciences Springer-Verlag, 2006 57(2009), 1-2 vom: Jan., Seite 73-92 (DE-627)SPR036426385 nnns volume:57 year:2009 number:1-2 month:01 pages:73-92 https://dx.doi.org/10.1007/BF03321495 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 57 2009 1-2 01 73-92 |
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10.1007/BF03321495 doi (DE-627)SPR036437611 (SPR)BF03321495-e DE-627 ger DE-627 rakwb eng Psiaki, Mark L. verfasserin aut Generalized Wahba Problems for Spinning Spacecraft Attitude and Rate Determination 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © American Astronautical Society, INC 2009 Abstract Two generalized versions of Wahba’s attitude determination problem have been developed for a spinning spacecraft, and a restricted version of one problem has been solved in closed-form. These problems seek to estimate both attitude and rate based solely on a time series of vector attitude observations along with a spacecraft dynamic model. Algorithms that solve these problems will be useful for spin-stabilized spacecraft that reduce complexity by omitting rate gyros. The first generalized Wahba problem presumes that the spin axis is known and that the spin rate is constant but unknown, as for a spinning spacecraft that has a nutation damper. The second generalized problem includes full rigid-body Euler dynamics, which allow for nutations, and seeks to estimate the unknown initial attitude rate vector. Both problems are recast into the K-matrix form of Wahba’s problem with K matrices that depend on the unknown rates. Restricted problems are developed that use the minimum number of vector measurements, two for the first problem and three for the second problem. The restricted first problem is solved in closed-form. The restricted second problem is shown to be observable, and it is reduced to a small system of nonlinear equations in the axially symmetric case. The possibility of deriving global solutions for these problems makes them attractive to assist or replace an extended Kaiman filter because a global solution cannot suffer from nonlinear divergence. Extended Kalman Filter (dpeaa)DE-He213 Vector Measurement (dpeaa)DE-He213 Spin Axis (dpeaa)DE-He213 Restricted Version (dpeaa)DE-He213 Restricted Problem (dpeaa)DE-He213 Enthalten in The Journal of the Astronautical Sciences Springer-Verlag, 2006 57(2009), 1-2 vom: Jan., Seite 73-92 (DE-627)SPR036426385 nnns volume:57 year:2009 number:1-2 month:01 pages:73-92 https://dx.doi.org/10.1007/BF03321495 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 57 2009 1-2 01 73-92 |
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10.1007/BF03321495 doi (DE-627)SPR036437611 (SPR)BF03321495-e DE-627 ger DE-627 rakwb eng Psiaki, Mark L. verfasserin aut Generalized Wahba Problems for Spinning Spacecraft Attitude and Rate Determination 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © American Astronautical Society, INC 2009 Abstract Two generalized versions of Wahba’s attitude determination problem have been developed for a spinning spacecraft, and a restricted version of one problem has been solved in closed-form. These problems seek to estimate both attitude and rate based solely on a time series of vector attitude observations along with a spacecraft dynamic model. Algorithms that solve these problems will be useful for spin-stabilized spacecraft that reduce complexity by omitting rate gyros. The first generalized Wahba problem presumes that the spin axis is known and that the spin rate is constant but unknown, as for a spinning spacecraft that has a nutation damper. The second generalized problem includes full rigid-body Euler dynamics, which allow for nutations, and seeks to estimate the unknown initial attitude rate vector. Both problems are recast into the K-matrix form of Wahba’s problem with K matrices that depend on the unknown rates. Restricted problems are developed that use the minimum number of vector measurements, two for the first problem and three for the second problem. The restricted first problem is solved in closed-form. The restricted second problem is shown to be observable, and it is reduced to a small system of nonlinear equations in the axially symmetric case. The possibility of deriving global solutions for these problems makes them attractive to assist or replace an extended Kaiman filter because a global solution cannot suffer from nonlinear divergence. Extended Kalman Filter (dpeaa)DE-He213 Vector Measurement (dpeaa)DE-He213 Spin Axis (dpeaa)DE-He213 Restricted Version (dpeaa)DE-He213 Restricted Problem (dpeaa)DE-He213 Enthalten in The Journal of the Astronautical Sciences Springer-Verlag, 2006 57(2009), 1-2 vom: Jan., Seite 73-92 (DE-627)SPR036426385 nnns volume:57 year:2009 number:1-2 month:01 pages:73-92 https://dx.doi.org/10.1007/BF03321495 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 57 2009 1-2 01 73-92 |
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Generalized Wahba Problems for Spinning Spacecraft Attitude and Rate Determination |
| abstract |
Abstract Two generalized versions of Wahba’s attitude determination problem have been developed for a spinning spacecraft, and a restricted version of one problem has been solved in closed-form. These problems seek to estimate both attitude and rate based solely on a time series of vector attitude observations along with a spacecraft dynamic model. Algorithms that solve these problems will be useful for spin-stabilized spacecraft that reduce complexity by omitting rate gyros. The first generalized Wahba problem presumes that the spin axis is known and that the spin rate is constant but unknown, as for a spinning spacecraft that has a nutation damper. The second generalized problem includes full rigid-body Euler dynamics, which allow for nutations, and seeks to estimate the unknown initial attitude rate vector. Both problems are recast into the K-matrix form of Wahba’s problem with K matrices that depend on the unknown rates. Restricted problems are developed that use the minimum number of vector measurements, two for the first problem and three for the second problem. The restricted first problem is solved in closed-form. The restricted second problem is shown to be observable, and it is reduced to a small system of nonlinear equations in the axially symmetric case. The possibility of deriving global solutions for these problems makes them attractive to assist or replace an extended Kaiman filter because a global solution cannot suffer from nonlinear divergence. © American Astronautical Society, INC 2009 |
| abstractGer |
Abstract Two generalized versions of Wahba’s attitude determination problem have been developed for a spinning spacecraft, and a restricted version of one problem has been solved in closed-form. These problems seek to estimate both attitude and rate based solely on a time series of vector attitude observations along with a spacecraft dynamic model. Algorithms that solve these problems will be useful for spin-stabilized spacecraft that reduce complexity by omitting rate gyros. The first generalized Wahba problem presumes that the spin axis is known and that the spin rate is constant but unknown, as for a spinning spacecraft that has a nutation damper. The second generalized problem includes full rigid-body Euler dynamics, which allow for nutations, and seeks to estimate the unknown initial attitude rate vector. Both problems are recast into the K-matrix form of Wahba’s problem with K matrices that depend on the unknown rates. Restricted problems are developed that use the minimum number of vector measurements, two for the first problem and three for the second problem. The restricted first problem is solved in closed-form. The restricted second problem is shown to be observable, and it is reduced to a small system of nonlinear equations in the axially symmetric case. The possibility of deriving global solutions for these problems makes them attractive to assist or replace an extended Kaiman filter because a global solution cannot suffer from nonlinear divergence. © American Astronautical Society, INC 2009 |
| abstract_unstemmed |
Abstract Two generalized versions of Wahba’s attitude determination problem have been developed for a spinning spacecraft, and a restricted version of one problem has been solved in closed-form. These problems seek to estimate both attitude and rate based solely on a time series of vector attitude observations along with a spacecraft dynamic model. Algorithms that solve these problems will be useful for spin-stabilized spacecraft that reduce complexity by omitting rate gyros. The first generalized Wahba problem presumes that the spin axis is known and that the spin rate is constant but unknown, as for a spinning spacecraft that has a nutation damper. The second generalized problem includes full rigid-body Euler dynamics, which allow for nutations, and seeks to estimate the unknown initial attitude rate vector. Both problems are recast into the K-matrix form of Wahba’s problem with K matrices that depend on the unknown rates. Restricted problems are developed that use the minimum number of vector measurements, two for the first problem and three for the second problem. The restricted first problem is solved in closed-form. The restricted second problem is shown to be observable, and it is reduced to a small system of nonlinear equations in the axially symmetric case. The possibility of deriving global solutions for these problems makes them attractive to assist or replace an extended Kaiman filter because a global solution cannot suffer from nonlinear divergence. © American Astronautical Society, INC 2009 |
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Generalized Wahba Problems for Spinning Spacecraft Attitude and Rate Determination |
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https://dx.doi.org/10.1007/BF03321495 |
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10.1007/BF03321495 |
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2024-07-03T17:36:43.594Z |
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These problems seek to estimate both attitude and rate based solely on a time series of vector attitude observations along with a spacecraft dynamic model. Algorithms that solve these problems will be useful for spin-stabilized spacecraft that reduce complexity by omitting rate gyros. The first generalized Wahba problem presumes that the spin axis is known and that the spin rate is constant but unknown, as for a spinning spacecraft that has a nutation damper. The second generalized problem includes full rigid-body Euler dynamics, which allow for nutations, and seeks to estimate the unknown initial attitude rate vector. Both problems are recast into the K-matrix form of Wahba’s problem with K matrices that depend on the unknown rates. Restricted problems are developed that use the minimum number of vector measurements, two for the first problem and three for the second problem. The restricted first problem is solved in closed-form. The restricted second problem is shown to be observable, and it is reduced to a small system of nonlinear equations in the axially symmetric case. The possibility of deriving global solutions for these problems makes them attractive to assist or replace an extended Kaiman filter because a global solution cannot suffer from nonlinear divergence.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Extended Kalman Filter</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Vector Measurement</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Spin Axis</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Restricted Version</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Restricted Problem</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">The Journal of the Astronautical Sciences</subfield><subfield code="d">Springer-Verlag, 2006</subfield><subfield code="g">57(2009), 1-2 vom: Jan., Seite 73-92</subfield><subfield code="w">(DE-627)SPR036426385</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:57</subfield><subfield code="g">year:2009</subfield><subfield code="g">number:1-2</subfield><subfield code="g">month:01</subfield><subfield code="g">pages:73-92</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/BF03321495</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">57</subfield><subfield code="j">2009</subfield><subfield code="e">1-2</subfield><subfield code="c">01</subfield><subfield code="h">73-92</subfield></datafield></record></collection>
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