# Optimal Constellation Design for Space Based Situational Awareness Applications A Numerical Approach

50 %
50 %
Information about Optimal Constellation Design for Space Based Situational Awareness...
Technology

Published on March 21, 2014

Author: BelindaMarchand

Source: slideshare.net

## Description

Talk charts from AAS/AIAA Astrodynamics Specialist Conference, held July 31-August 4, 2011, in Girdwood, Alaska.

Note, this presentation has three animations in it on slides 12, 14, and 17. They will not display on slideshare but you can download and play from your computer. A special codec download may be required.

Optimal Constellation Design for Space Based Situational Awareness Applications A Numerical Approach Andrew T. Takano Belinda G. Marchand The University of Texas at Austin Department of Aerospace Engineering and Engineering Mechanics AAS/AIAA Astrodynamics Specialist Conference July 31–August 4, 2011 Girdwood, Alaska

Coverage Regions Above vs. Below the Horizon → Volumetric to Planar Sensor Regions Target Regions Takano, Marchand Constellation Design for SBSA 1 / 17

Boolean Operations: 1× Coverage RSE1 ∪ RSE2 = T1 T1 ∪ RSE3 = T2 Takano, Marchand Constellation Design for SBSA 2 / 17

Boolean Operations: 1× Coverage (cont.) T4 ∪ RSE6 = RST E RST E ∩ AS = C1× Takano, Marchand Constellation Design for SBSA 3 / 17

Boolean Operations: 2× Coverage RSE1 ∩ RSE2 = T1 RSE2 ∩ RSE3 = T2 Takano, Marchand Constellation Design for SBSA 4 / 17

Boolean Operations: 2× Coverage (cont.) T1 ∪ T2 = T3 RST E ∩ AS = C2× Takano, Marchand Constellation Design for SBSA 5 / 17

Boolean Operation Sequences Region of 1× coverage inside target region: C1× =    n i=1 RSEi i-th sensor region    total region of 1× coverage ∩ AS target region Region of 2× coverage inside target region: C2× =        n−1 i1=1 n i2=i1+1 RSEi1 ∩ RSEi2 region of 2× coverage between sensors i1, i2        total region of 2× coverage ∩ AS target region Takano, Marchand Constellation Design for SBSA 6 / 17

Boolean Operation Sequences Region of p× coverage inside target region: Cp× =         n−p+1 i1=1 n−p+2 i2=i1+1 ... n−1 ip−1=ip−2+1 n ip=ip−1+1 RSEi1 ∩ · · · ∩ RSEip region of p× coverage between sensors i1, i2, . . . , ip         total region of p× coverage ∩AS Takano, Marchand Constellation Design for SBSA 7 / 17

System Classiﬁcation Time-invariant: satellite/target region separations ﬁxed Can solve analytically Occurs under special conditions Time-varying: satellite/target region separations variable Numerical approach: Approximate solutions Easier to implement a wide variety of analyses Fewer necessary assumptions Takano, Marchand Constellation Design for SBSA 8 / 17

Time-Invariant: Examples 1 & 2 Assumptions: Single circular orbit n satellites equally distributed Omni-directional sensor range Annular target region Takano, Marchand Constellation Design for SBSA 9 / 17

Time-Invariant: Example 1 Objective: Fewest satellites for full 1×, 2×, 3× ATH coverage Minimum Constellation Population vs. Altitude 1× cov., 3 sat. 2× cov., 6 sat. 3× cov., 10 sat. Takano, Marchand Constellation Design for SBSA 10 / 17

Time-Invariant: Example 2 Objective: Fewest satellites for full 1× ATH coverage Min. Constellation Population vs. Altitude & Sensor Range Takano, Marchand Constellation Design for SBSA 11 / 17

Time-Varying Coverage Analysis Takano, Marchand Constellation Design for SBSA 12 / 17

Time-Varying: Example 3 Assumptions: Annular target region (prescribed) 2 elliptical orbits, n1 & n2 sats (variables) Opposite periapsis directions Satellites equal distributed in M Phasing between orbits (variable) Same semi-major axis, eccentricity (variables) Dissimilar sensor performance between orbits Approach: MINLP problem – MIDACO – Ant colony optimization Takano, Marchand Constellation Design for SBSA 13 / 17

Time-Varying: Example 3 Objective: Fewest satellites for continuous ATH coverage Takano, Marchand Constellation Design for SBSA 14 / 17

Time-Varying: Example 4 Assumptions: GEO Belt target: ±1000 km alt., 148◦-61◦W longitude n satellites equally distributed across 4 orbits 4 orbits equally spaced in periapsis direction Satellites grouped in orbits – spread by ∆M (variable) Same eccentricity between orbits (variable) Omni-directional sensor range (variable) Fixed semi-major axis (1/2 day period) Synchronized for group apogee during target region passage Approach: NLP problem – fmincon in MATLAB Takano, Marchand Constellation Design for SBSA 15 / 17

Time-Varying: Example 4 Objective: Shortest sensor range for continuous ATH coverage Takano, Marchand Constellation Design for SBSA 16 / 17

Conclusions A new model for SBSA applications is developed Elements from computational geometry used to compute constellation ATH coverage Numerical approach: Versatile, wide range of scenarios require no rederivation Suitable for time-invariant and time-varying cases A new approach to optimal constellation design Model is used as a metric, considering actual ATH coverage provided by a constellation Can use traditional parameter optimization techniques Takano, Marchand Constellation Design for SBSA 17 / 17

 User name: Comment:

## Related presentations

#### Neuquén y el Gobierno Abierto

October 30, 2014

Presentación que realice en el Evento Nacional de Gobierno Abierto, realizado los ...

#### Decision CAMP 2014 - Erik Marutian - Using rules-b...

October 16, 2014

In this presentation we will describe our experience developing with a highly dyna...

#### Schema.org: What It Means For You and Your Library

November 7, 2014

Presentation to the LITA Forum 7th November 2014 Albuquerque, NM

#### WearableTech: Una transformación social de los p...

November 3, 2014

Un recorrido por los cambios que nos generará el wearabletech en el futuro

#### O Impacto de Wearable Computers na vida das pessoa...

November 5, 2014

Um paralelo entre as novidades & mercado em Wearable Computing e Tecnologias Assis...

#### All you need to know about the Microsoft Band

November 6, 2014

Microsoft finally joins the smartwatch and fitness tracker game by introducing the...

## Related pages

### Constellation Design for Space-Based Situational Awareness ...

Constellation Design for Space-Based Situational Awareness Applications: An Analytical Approach ... optimal constellation design for space-based ...

### Analytical approach to the design of optimal satellite ...

Analytical approach to the design of optimal satellite constellations for space-based space situational awareness applications.

### Constellation Design for Space-Based Space Situational ...

... Space Situational Awareness Applications: ... optimal constellation design for space-based space ... approach is the numerical method ...

### Constellation Design for Space-Based Space Situational ...

... space situational awareness applications, ... Applications: An Analytical Approach. ... optimal constellation design for space-based ...

### Numerical Coverage Analysis for Space-Based Space ...

Numerical Coverage Analysis for Space-Based Space Situational Awareness ... the application of numerical ... constellation design for space situational ...

### Analytical approach to the design of optimal satellite ...

... for space-based space situational awareness applications . ... Space-based space situational awareness ... optimal constellation design for ...

### Optimal Constellation Design for Maximum Continuous ...

... optimal design for a constellation of space based ... for situational awareness applications ... Optimal Constellation Design for ...

### Dr. Belinda G. Marchand - College of Engineering - Purdue ...

... Awareness Applications: An Analytical Approach ... Marchand, "Optimal Constellation Design for Space Based Situational Awareness ...