Space Situational Awareness - Revision history

Linares2: /* Research to be Accomplished */

2012-04-28T18:58:12Z

Research to be Accomplished

← Older revision		Revision as of 18:58, 28 April 2012
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	The objectives of this work are to research and develop methods of detecting, tracking, characterizing, and discriminating space objects (RSOs) to support Space Control and Space Situational Awareness (SSA), which requires the tracking, identifying, and predicting of future intentions, actions, and positions of RSOs with known accuracy and precision. To meet these objectives advanced estimation strategies, i.e. multiple model adaptive estimation, will be employed to reduce astrometric and photometric data simultaneously to recover the orbital and physical characteristics for one or more RSOs. Initially, simulated data for a cluster of controlled spacecraft will be used to prove the concepts, with increasingly more realistic scenarios being developed. Actual optical observational data (astrometry and multi-band temporal photometry) will be utilized to test the utility of these techniques in estimating (recovering) RSO orbit and physical states in near-real time. This work plan leverages a high value data set of multi-band temporal photometry collected as part of GEO cluster characterization campaign that will be used in the research outlined in this proposal. As the techniques mature, uncontrolled RSOs (i.e. near-GEO debris) will be simulated and observed.		The objectives of this work are to research and develop methods of detecting, tracking, characterizing, and discriminating space objects (RSOs) to support Space Control and Space Situational Awareness (SSA), which requires the tracking, identifying, and predicting of future intentions, actions, and positions of RSOs with known accuracy and precision. To meet these objectives advanced estimation strategies, i.e. multiple model adaptive estimation, will be employed to reduce astrometric and photometric data simultaneously to recover the orbital and physical characteristics for one or more RSOs. Initially, simulated data for a cluster of controlled spacecraft will be used to prove the concepts, with increasingly more realistic scenarios being developed. Actual optical observational data (astrometry and multi-band temporal photometry) will be utilized to test the utility of these techniques in estimating (recovering) RSO orbit and physical states in near-real time. This work plan leverages a high value data set of multi-band temporal photometry collected as part of GEO cluster characterization campaign that will be used in the research outlined in this proposal. As the techniques mature, uncontrolled RSOs (i.e. near-GEO debris) will be simulated and observed.

	==Research ~~to be Accomplished~~==		==Research==

	Shape estimation is an important issue in the observation of RSOs, because the shape influences the dynamics of the object and may provide valuable information on the object’s origin or intent. There exists a number of methods for estimating the shape of an object. These methods vary in the sensor type used, technique used to resolve shape, and effective ranges for proper shape resolution. Radar-based methods have been extensively used for shape estimation, which include radar cross-sectioning approaches and range Doppler interferometry. These techniques were first developed in the field of planetary radar astronomy to estimate the shape of natural satellites, but then were later applied to the imaging of artificial Earth orbiting satellites. These methods are limited by the RSO size and distance. RSOs can be imaged in low-Earth orbits that are much larger in the dimension than the wavelength of the radar signal. To image RSOs smaller and farther than these ranges requires very powerful radar devices, making these economically unattractive.		Shape estimation is an important issue in the observation of RSOs, because the shape influences the dynamics of the object and may provide valuable information on the object’s origin or intent. There exists a number of methods for estimating the shape of an object. These methods vary in the sensor type used, technique used to resolve shape, and effective ranges for proper shape resolution. Radar-based methods have been extensively used for shape estimation, which include radar cross-sectioning approaches and range Doppler interferometry. These techniques were first developed in the field of planetary radar astronomy to estimate the shape of natural satellites, but then were later applied to the imaging of artificial Earth orbiting satellites. These methods are limited by the RSO size and distance. RSOs can be imaged in low-Earth orbits that are much larger in the dimension than the wavelength of the radar signal. To image RSOs smaller and farther than these ranges requires very powerful radar devices, making these economically unattractive.
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	Preliminary results for shape estimation of the approach are shown in Ref. [5]. For the development of the measured light curve data a six-faceted RSO is used. Five shapes are tested in a multiple hypothesis approach to assess the performance of the method. Results from the MMAE solution are shown in Figure 2. The solution shows that the approach is viable by identifying the correct shape. This provides a basis for optimism but much more work needs to be done. This includes: 1) using more complex shape models in the shape model bank, 2) incorporating a generalized MMAE [6] approach to obtain faster convergence rates, 3) using multiband data to improve performance, and 4) extend the work to assess the observability of estimating other intrinsic properties, such as the spacecraft material properties.		Preliminary results for shape estimation of the approach are shown in Ref. [5]. For the development of the measured light curve data a six-faceted RSO is used. Five shapes are tested in a multiple hypothesis approach to assess the performance of the method. Results from the MMAE solution are shown in Figure 2. The solution shows that the approach is viable by identifying the correct shape. This provides a basis for optimism but much more work needs to be done. This includes: 1) using more complex shape models in the shape model bank, 2) incorporating a generalized MMAE [6] approach to obtain faster convergence rates, 3) using multiband data to improve performance, and 4) extend the work to assess the observability of estimating other intrinsic properties, such as the spacecraft material properties.


	==References==		==References==

Linares2 at 18:57, 28 April 2012

2012-04-28T18:57:56Z

← Older revision		Revision as of 18:57, 28 April 2012
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	==Abstract==		==Abstract==

	A new method is ~~proposed~~, based on an unsupervised learning state variable method that uses a multiple-model adaptive estimation approach to determine the most probable shape and other intrinsic features of a space object in orbit among a number of candidate models while simultaneously recovering the observed resident space object’s inertial orientation and trajectory. Multiple-model adaptive estimation uses a parallel bank of filters to provide multiple space object state estimates, where each filter is purposefully dependent on a mutually unique resident space object model. Estimates on the conditional probability of each model given the available measurements are provided from the multiple-model adaptive estimation approach. Each filter employs the Unscented (or Sigma-Point) estimation approach, reducing passively-collected electro-optical data to infer the unknown state vector comprised of the space object inertial-to-body orientation, position and their respective temporal rates. Each hypothesized model results in a different observed optical cross-sectional area. The effect of solar radiation pressure may be recovered from accurate angles-data alone, if the collected measurements span a sufficiently long period of time so as to make the non-conservative mismodeling effects noticeable. However, for relatively short data arcs, this effect is weak and thus the temporal brightness of the resident space object can be used in concert with the angles data to exploit the fused sensitivity to both space object characteristics and associated trajectory, the very same ones which drive the non-conservative dynamic effects. Recovering these characteristics and trajectories with sufficient accuracy is shown in this proposal, where the characteristics are inherent in unique space object models.		A new method is discussed, based on an unsupervised learning state variable method that uses a multiple-model adaptive estimation approach to determine the most probable shape and other intrinsic features of a space object in orbit among a number of candidate models while simultaneously recovering the observed resident space object’s inertial orientation and trajectory. Multiple-model adaptive estimation uses a parallel bank of filters to provide multiple space object state estimates, where each filter is purposefully dependent on a mutually unique resident space object model. Estimates on the conditional probability of each model given the available measurements are provided from the multiple-model adaptive estimation approach. Each filter employs the Unscented (or Sigma-Point) estimation approach, reducing passively-collected electro-optical data to infer the unknown state vector comprised of the space object inertial-to-body orientation, position and their respective temporal rates. Each hypothesized model results in a different observed optical cross-sectional area. The effect of solar radiation pressure may be recovered from accurate angles-data alone, if the collected measurements span a sufficiently long period of time so as to make the non-conservative mismodeling effects noticeable. However, for relatively short data arcs, this effect is weak and thus the temporal brightness of the resident space object can be used in concert with the angles data to exploit the fused sensitivity to both space object characteristics and associated trajectory, the very same ones which drive the non-conservative dynamic effects. Recovering these characteristics and trajectories with sufficient accuracy is shown in this proposal, where the characteristics are inherent in unique space object models.

	==Objectives==		==Objectives==

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	</center>		</center>

	The objectives of ~~the proposed~~ work are to research and develop methods of detecting, tracking, characterizing, and discriminating space objects (RSOs) to support Space Control and Space Situational Awareness (SSA), which requires the tracking, identifying, and predicting of future intentions, actions, and positions of RSOs with known accuracy and precision. To meet these objectives advanced estimation strategies, i.e. multiple model adaptive estimation, will be employed to reduce astrometric and photometric data simultaneously to recover the orbital and physical characteristics for one or more RSOs. Initially, simulated data for a cluster of controlled spacecraft will be used to prove the concepts, with increasingly more realistic scenarios being developed. Actual optical observational data (astrometry and multi-band temporal photometry) will be utilized to test the utility of these techniques in estimating (recovering) RSO orbit and physical states in near-real time. ~~The proposed~~ work plan leverages a high value data set of multi-band temporal photometry collected as part of GEO cluster characterization campaign that will be used in the research outlined in this proposal. As the techniques mature, uncontrolled RSOs (i.e. near-GEO debris) will be simulated and observed.		The objectives of this work are to research and develop methods of detecting, tracking, characterizing, and discriminating space objects (RSOs) to support Space Control and Space Situational Awareness (SSA), which requires the tracking, identifying, and predicting of future intentions, actions, and positions of RSOs with known accuracy and precision. To meet these objectives advanced estimation strategies, i.e. multiple model adaptive estimation, will be employed to reduce astrometric and photometric data simultaneously to recover the orbital and physical characteristics for one or more RSOs. Initially, simulated data for a cluster of controlled spacecraft will be used to prove the concepts, with increasingly more realistic scenarios being developed. Actual optical observational data (astrometry and multi-band temporal photometry) will be utilized to test the utility of these techniques in estimating (recovering) RSO orbit and physical states in near-real time. This work plan leverages a high value data set of multi-band temporal photometry collected as part of GEO cluster characterization campaign that will be used in the research outlined in this proposal. As the techniques mature, uncontrolled RSOs (i.e. near-GEO debris) will be simulated and observed.

	==Research to be Accomplished==		==Research to be Accomplished==
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	Attitude estimation using light curve data has been demonstrated in Ref. [4]. The main goal of this current work is to use light curve data to, autonomously and in near real-time, determine the shape and intrinsic properties of a RSO along with its attitude (rotational) and translational states. In order to accomplish this task a multiple-model adaptive estimation (MMAE) approach is used (see Figure 1); running a number of parallel Unscented Kalman filters (UKF) the MMAE approach determines the most probable shape or property of a RSO in orbit among a number of candidate models. Each filter uses a different assumed model, and the state estimate is given by the weighted sum of each filter’s estimate. The weights correspond to the conditional probabilities derived from Bayes’ rule using the likelihood information of the unknown states conditioned on the current-time measurement residual and innovations covariance.		Attitude estimation using light curve data has been demonstrated in Ref. [4]. The main goal of this current work is to use light curve data to, autonomously and in near real-time, determine the shape and intrinsic properties of a RSO along with its attitude (rotational) and translational states. In order to accomplish this task a multiple-model adaptive estimation (MMAE) approach is used (see Figure 1); running a number of parallel Unscented Kalman filters (UKF) the MMAE approach determines the most probable shape or property of a RSO in orbit among a number of candidate models. Each filter uses a different assumed model, and the state estimate is given by the weighted sum of each filter’s estimate. The weights correspond to the conditional probabilities derived from Bayes’ rule using the likelihood information of the unknown states conditioned on the current-time measurement residual and innovations covariance.

	Preliminary results for shape estimation of the ~~proposed~~ approach are shown in Ref. [5]. For the development of the measured light curve data a six-faceted RSO is used. Five shapes are tested in a multiple hypothesis approach to assess the performance of the ~~proposed~~ method. Results from the MMAE solution are shown in Figure 2. The solution shows that the ~~proposed~~ approach is viable by identifying the correct shape. This provides a basis for optimism but much more work needs to be done. This includes: 1) using more complex shape models in the shape model bank, 2) incorporating a generalized MMAE [6] approach to obtain faster convergence rates, 3) using multiband data to improve performance, and 4) extend the work to assess the observability of estimating other intrinsic properties, such as the spacecraft material properties.		Preliminary results for shape estimation of the approach are shown in Ref. [5]. For the development of the measured light curve data a six-faceted RSO is used. Five shapes are tested in a multiple hypothesis approach to assess the performance of the method. Results from the MMAE solution are shown in Figure 2. The solution shows that the approach is viable by identifying the correct shape. This provides a basis for optimism but much more work needs to be done. This includes: 1) using more complex shape models in the shape model bank, 2) incorporating a generalized MMAE [6] approach to obtain faster convergence rates, 3) using multiband data to improve performance, and 4) extend the work to assess the observability of estimating other intrinsic properties, such as the spacecraft material properties.


	==References==		==References==

Linares2: /* Research to be Accomplished */

2012-04-28T18:53:53Z

Research to be Accomplished

← Older revision		Revision as of 18:53, 28 April 2012
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	There is a coupling between RSO attitude and non-conservative accelerations. This can be exploited to assist in the estimation of the RSO trajectory. The measurement of the apparent magnitude is a function of several RSO characteristics that are those which drive certain non-conservative forces (i.e. solar radiation pressure (SRP)). The acceleration due to SRP is modeled as function of an object’s Sun-facing area, surface properties and attitude. It has a very small magnitude compared to gravitational accelerations, and typically has an order of magnitude around 10−7 to 10−9 km/sec2, but is the dominant non-conservative acceleration for objects above 1,000 km. Below 1,000 km, drag caused by the atmospheric neutral density is the dominating non-conservative acceleration.		There is a coupling between RSO attitude and non-conservative accelerations. This can be exploited to assist in the estimation of the RSO trajectory. The measurement of the apparent magnitude is a function of several RSO characteristics that are those which drive certain non-conservative forces (i.e. solar radiation pressure (SRP)). The acceleration due to SRP is modeled as function of an object’s Sun-facing area, surface properties and attitude. It has a very small magnitude compared to gravitational accelerations, and typically has an order of magnitude around 10−7 to 10−9 km/sec2, but is the dominant non-conservative acceleration for objects above 1,000 km. Below 1,000 km, drag caused by the atmospheric neutral density is the dominating non-conservative acceleration.



	Attitude estimation using light curve data has been demonstrated in Ref. [4]. The main goal of this current work is to use light curve data to, autonomously and in near real-time, determine the shape and intrinsic properties of a RSO along with its attitude (rotational) and translational states. In order to accomplish this task a multiple-model adaptive estimation (MMAE) approach is used (see Figure 1); running a number of parallel Unscented Kalman filters (UKF) the MMAE approach determines the most probable shape or property of a RSO in orbit among a number of candidate models. Each filter uses a different assumed model, and the state estimate is given by the weighted sum of each filter’s estimate. The weights correspond to the conditional probabilities derived from Bayes’ rule using the likelihood information of the unknown states conditioned on the current-time measurement residual and innovations covariance.		Attitude estimation using light curve data has been demonstrated in Ref. [4]. The main goal of this current work is to use light curve data to, autonomously and in near real-time, determine the shape and intrinsic properties of a RSO along with its attitude (rotational) and translational states. In order to accomplish this task a multiple-model adaptive estimation (MMAE) approach is used (see Figure 1); running a number of parallel Unscented Kalman filters (UKF) the MMAE approach determines the most probable shape or property of a RSO in orbit among a number of candidate models. Each filter uses a different assumed model, and the state estimate is given by the weighted sum of each filter’s estimate. The weights correspond to the conditional probabilities derived from Bayes’ rule using the likelihood information of the unknown states conditioned on the current-time measurement residual and innovations covariance.

Linares2: /* Objectives */

2012-04-28T18:48:32Z

Objectives

← Older revision		Revision as of 18:48, 28 April 2012
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	==Objectives==		==Objectives==

			<center>
			{\|
			\|[[File:figure1.png\|400px]]
			<span style="color:#000000; font-size:130%"> '''Figure 1 MMAE Process'''</span>
			\|[[File:figure2.png\|400px]]
			<span style="color:#000000; font-size:130%"> '''Figure 2 MMAE with Five RSO Models'''</span>
			\|}
			</center>

	The objectives of the proposed work are to research and develop methods of detecting, tracking, characterizing, and discriminating space objects (RSOs) to support Space Control and Space Situational Awareness (SSA), which requires the tracking, identifying, and predicting of future intentions, actions, and positions of RSOs with known accuracy and precision. To meet these objectives advanced estimation strategies, i.e. multiple model adaptive estimation, will be employed to reduce astrometric and photometric data simultaneously to recover the orbital and physical characteristics for one or more RSOs. Initially, simulated data for a cluster of controlled spacecraft will be used to prove the concepts, with increasingly more realistic scenarios being developed. Actual optical observational data (astrometry and multi-band temporal photometry) will be utilized to test the utility of these techniques in estimating (recovering) RSO orbit and physical states in near-real time. The proposed work plan leverages a high value data set of multi-band temporal photometry collected as part of GEO cluster characterization campaign that will be used in the research outlined in this proposal. As the techniques mature, uncontrolled RSOs (i.e. near-GEO debris) will be simulated and observed.		The objectives of the proposed work are to research and develop methods of detecting, tracking, characterizing, and discriminating space objects (RSOs) to support Space Control and Space Situational Awareness (SSA), which requires the tracking, identifying, and predicting of future intentions, actions, and positions of RSOs with known accuracy and precision. To meet these objectives advanced estimation strategies, i.e. multiple model adaptive estimation, will be employed to reduce astrometric and photometric data simultaneously to recover the orbital and physical characteristics for one or more RSOs. Initially, simulated data for a cluster of controlled spacecraft will be used to prove the concepts, with increasingly more realistic scenarios being developed. Actual optical observational data (astrometry and multi-band temporal photometry) will be utilized to test the utility of these techniques in estimating (recovering) RSO orbit and physical states in near-real time. The proposed work plan leverages a high value data set of multi-band temporal photometry collected as part of GEO cluster characterization campaign that will be used in the research outlined in this proposal. As the techniques mature, uncontrolled RSOs (i.e. near-GEO debris) will be simulated and observed.

Linares2: /* Research to be Accomplished */

2012-04-28T18:48:23Z

Research to be Accomplished

← Older revision		Revision as of 18:48, 28 April 2012
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	There is a coupling between RSO attitude and non-conservative accelerations. This can be exploited to assist in the estimation of the RSO trajectory. The measurement of the apparent magnitude is a function of several RSO characteristics that are those which drive certain non-conservative forces (i.e. solar radiation pressure (SRP)). The acceleration due to SRP is modeled as function of an object’s Sun-facing area, surface properties and attitude. It has a very small magnitude compared to gravitational accelerations, and typically has an order of magnitude around 10−7 to 10−9 km/sec2, but is the dominant non-conservative acceleration for objects above 1,000 km. Below 1,000 km, drag caused by the atmospheric neutral density is the dominating non-conservative acceleration.		There is a coupling between RSO attitude and non-conservative accelerations. This can be exploited to assist in the estimation of the RSO trajectory. The measurement of the apparent magnitude is a function of several RSO characteristics that are those which drive certain non-conservative forces (i.e. solar radiation pressure (SRP)). The acceleration due to SRP is modeled as function of an object’s Sun-facing area, surface properties and attitude. It has a very small magnitude compared to gravitational accelerations, and typically has an order of magnitude around 10−7 to 10−9 km/sec2, but is the dominant non-conservative acceleration for objects above 1,000 km. Below 1,000 km, drag caused by the atmospheric neutral density is the dominating non-conservative acceleration.



	~~<center>~~
	{\|
	~~\|[[File:figure1.png\|400px]]~~
	~~<span style="color:#000000; font-size:130%"> '''Figure 1 MMAE Process'''</span>~~
	~~\|[[File:figure2.png\|400px]]~~
	~~<span style="color:#000000; font-size:130%"> '''Figure 2 MMAE with Five RSO Models'''</span>~~
	\|}
	~~</center>~~

Linares2: /* Research to be Accomplished */

2012-04-28T18:48:01Z

Research to be Accomplished

← Older revision		Revision as of 18:48, 28 April 2012
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	<center>		<center>
	{\|~~border="1"~~		{\|
	\|[[File:figure1.png\|400px]]		\|[[File:figure1.png\|400px]]
	<span style="color:#~~003399~~; font-size:~~180~~%"> '''Figure 1 MMAE Process'''</span>		<span style="color:#000000; font-size:130%"> '''Figure 1 MMAE Process'''</span>
	\|[[File:figure2.png\|400px]]		\|[[File:figure2.png\|400px]]
	<span style="color:#~~003399~~; font-size:~~180~~%"> '''Figure 2 MMAE with Five RSO Models'''</span>		<span style="color:#000000; font-size:130%"> '''Figure 2 MMAE with Five RSO Models'''</span>
	\|}		\|}
	</center>		</center>

Linares2: /* Research to be Accomplished */

2012-04-28T18:46:55Z

Research to be Accomplished

← Older revision		Revision as of 18:46, 28 April 2012
Line 23:		Line 23:
	There is a coupling between RSO attitude and non-conservative accelerations. This can be exploited to assist in the estimation of the RSO trajectory. The measurement of the apparent magnitude is a function of several RSO characteristics that are those which drive certain non-conservative forces (i.e. solar radiation pressure (SRP)). The acceleration due to SRP is modeled as function of an object’s Sun-facing area, surface properties and attitude. It has a very small magnitude compared to gravitational accelerations, and typically has an order of magnitude around 10−7 to 10−9 km/sec2, but is the dominant non-conservative acceleration for objects above 1,000 km. Below 1,000 km, drag caused by the atmospheric neutral density is the dominating non-conservative acceleration.		There is a coupling between RSO attitude and non-conservative accelerations. This can be exploited to assist in the estimation of the RSO trajectory. The measurement of the apparent magnitude is a function of several RSO characteristics that are those which drive certain non-conservative forces (i.e. solar radiation pressure (SRP)). The acceleration due to SRP is modeled as function of an object’s Sun-facing area, surface properties and attitude. It has a very small magnitude compared to gravitational accelerations, and typically has an order of magnitude around 10−7 to 10−9 km/sec2, but is the dominant non-conservative acceleration for objects above 1,000 km. Below 1,000 km, drag caused by the atmospheric neutral density is the dominating non-conservative acceleration.

	~~<center>~~
	{
	~~\|[[File:figure1.png\|500px]]~~
	~~\|[[File:figure2.png\|500px]]~~
	}
	~~</center>~~


	<center>		<center>
	{\|border="1"		{\|border="1"
	\|<span style="color:#003399; font-size:180%"> '''~~John L. Crassidis, Ph.D.~~'''</span>		\|[[File:figure1.png\|400px]]
	[[File:~~figure1~~.png\|~~500px~~]]		<span style="color:#003399; font-size:180%"> '''Figure 1 MMAE Process'''</span>
	~~\|[[File~~:~~figure2.png\|500px]]~~		\|[[File:figure2.png\|400px]]
			<span style="color:#003399; font-size:180%"> '''Figure 2 MMAE with Five RSO Models'''</span>
	\|}		\|}
	</center>		</center>
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	~~Figure 1 MMAE Process~~

	~~[[File:figure2.png\|500px]]~~

	~~Figure 2 MMAE with Five RSO Models~~

	Attitude estimation using light curve data has been demonstrated in Ref. [4]. The main goal of this current work is to use light curve data to, autonomously and in near real-time, determine the shape and intrinsic properties of a RSO along with its attitude (rotational) and translational states. In order to accomplish this task a multiple-model adaptive estimation (MMAE) approach is used (see Figure 1); running a number of parallel Unscented Kalman filters (UKF) the MMAE approach determines the most probable shape or property of a RSO in orbit among a number of candidate models. Each filter uses a different assumed model, and the state estimate is given by the weighted sum of each filter’s estimate. The weights correspond to the conditional probabilities derived from Bayes’ rule using the likelihood information of the unknown states conditioned on the current-time measurement residual and innovations covariance.		Attitude estimation using light curve data has been demonstrated in Ref. [4]. The main goal of this current work is to use light curve data to, autonomously and in near real-time, determine the shape and intrinsic properties of a RSO along with its attitude (rotational) and translational states. In order to accomplish this task a multiple-model adaptive estimation (MMAE) approach is used (see Figure 1); running a number of parallel Unscented Kalman filters (UKF) the MMAE approach determines the most probable shape or property of a RSO in orbit among a number of candidate models. Each filter uses a different assumed model, and the state estimate is given by the weighted sum of each filter’s estimate. The weights correspond to the conditional probabilities derived from Bayes’ rule using the likelihood information of the unknown states conditioned on the current-time measurement residual and innovations covariance.

Linares2: /* Research to be Accomplished */

2012-04-28T18:45:59Z

Research to be Accomplished

← Older revision		Revision as of 18:45, 28 April 2012
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	{\|border="1"		{\|border="1"
	\|<span style="color:#003399; font-size:180%"> '''John L. Crassidis, Ph.D.'''</span>		\|<span style="color:#003399; font-size:180%"> '''John L. Crassidis, Ph.D.'''</span>
	\|[[File:~~Crassidis~~.~~jpg~~\|~~150px~~]]		[[File:figure1.png\|500px]]
			\|[[File:figure2.png\|500px]]
	\|}		\|}
	</center>		</center>

Linares2: /* Research to be Accomplished */

2012-04-28T18:45:10Z

Research to be Accomplished

← Older revision		Revision as of 18:45, 28 April 2012
Line 28:		Line 28:
	\|[[File:figure2.png\|500px]]		\|[[File:figure2.png\|500px]]
	}		}
			</center>


			<center>
			{\|border="1"
			\|<span style="color:#003399; font-size:180%"> '''John L. Crassidis, Ph.D.'''</span>
			\|[[File:Crassidis.jpg\|150px]]
			\|}
	</center>		</center>

Linares2: /* Research to be Accomplished */

2012-04-28T18:43:39Z

Research to be Accomplished

← Older revision		Revision as of 18:43, 28 April 2012
Line 23:		Line 23:
	There is a coupling between RSO attitude and non-conservative accelerations. This can be exploited to assist in the estimation of the RSO trajectory. The measurement of the apparent magnitude is a function of several RSO characteristics that are those which drive certain non-conservative forces (i.e. solar radiation pressure (SRP)). The acceleration due to SRP is modeled as function of an object’s Sun-facing area, surface properties and attitude. It has a very small magnitude compared to gravitational accelerations, and typically has an order of magnitude around 10−7 to 10−9 km/sec2, but is the dominant non-conservative acceleration for objects above 1,000 km. Below 1,000 km, drag caused by the atmospheric neutral density is the dominating non-conservative acceleration.		There is a coupling between RSO attitude and non-conservative accelerations. This can be exploited to assist in the estimation of the RSO trajectory. The measurement of the apparent magnitude is a function of several RSO characteristics that are those which drive certain non-conservative forces (i.e. solar radiation pressure (SRP)). The acceleration due to SRP is modeled as function of an object’s Sun-facing area, surface properties and attitude. It has a very small magnitude compared to gravitational accelerations, and typically has an order of magnitude around 10−7 to 10−9 km/sec2, but is the dominant non-conservative acceleration for objects above 1,000 km. Below 1,000 km, drag caused by the atmospheric neutral density is the dominating non-conservative acceleration.

	[[File:figure1.png\|500px]]		<center>
			{
			\|[[File:figure1.png\|500px]]
			\|[[File:figure2.png\|500px]]
			}
			</center>



	Figure 1 MMAE Process		Figure 1 MMAE Process