# Design and Verification of an Integrated Panoramic Sun Sensor atop a Small Spherical Satellite

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## Abstract

**:**

## 1. Introduction

- (1)
- IPSS has a panoramic field of view of 4$\pi $ and can work under any attitude;
- (2)
- When a subset of solar cells is damaged, IPSS can still provide reliable measurement;
- (3)
- IPSS has a negligible power consumption;
- (4)
- The spherical structure is maintained to the most compared with COTS products.

## 2. Mechatronic Design and Modeling of IPSS

#### 2.1. Overview of the Small Spherical Satellite Q-SAT

#### 2.2. The Integrated Panoramic Sun Sensor

- 1
- Photoelectric Model of the Solar Cell

- 2.
- The Kelly Cosine Characteristic of the Solar Cell

- 3.
- Temperature Correction

#### 2.3. The Sun Vector Inversion Principle

## 3. Accuracy and Redundancy Analyses of IPSS

#### 3.1. Accuracy Analyses

- 1.
- Sampling Error

- 2.
- Manufacturing and Installation Error

- 3.
- Parameter Calibration Error

- 4.
- Seasonal Variations in Sunlight Intensity and Earth Albedo Effect

#### 3.2. Redundancy Analyses

## 4. Experimental Results and On-Orbit Performance

#### 4.1. Ground Experiments with Artificial Sunlight

#### 4.2. Simulation in Various Orbits and Seasons

#### 4.3. On-Orbit Verification of IPSS

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

IPSS | Integrated Panoramic Sun Sensor |

GNSS | Global Navigation Satellite System |

ADC | Attitude Determination and Control |

FOV | Field of View |

CCD | Charge Coupied Device |

A/D | Analog to Digital |

CNC | Computerised Numerical Control Machine |

COTS | commercial-off-the-shelf |

IGRF | International Geomagnetic Reference Frame |

TOMS-EP | Total Ozone Mapping Spectrometer Earth Probe |

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**Figure 1.**The structure, layout, and body frame definition of Q-SAT. Solar cells marked in red are used for joint estimation of the sun vector.

**Figure 2.**The IPSS consists of 16 evenly distributed solar cells, 16 thermistors underneath each solar cell, and corresponding sampling circuits.

**Figure 3.**The equivalent circuit of a solar cell consists of a constant current source, a diode D, a shunt resistor ${R}_{sh}$, and a series resistor ${R}_{s}$. Resistor ${R}_{p}$ on the right-hand side is the payload resistor.

**Figure 4.**The volt-ampere curve of each solar cell under perpendicular illumination of the artificial sunlight. Solar cells with similar photoelectric characteristics are selected.

**Figure 5.**Sampled voltage curve of a solar cell with various incident angles. The proposed empirical formula fits the experimental data well. A 2−ohm precise resistor is connected in series to measure the current.

**Figure 6.**The sun vector inversion accuracy considering voltage sampling error of various magnitudes.

**Figure 8.**The sun vector inversion accuracy considering reference current error of various magnitudes.

**Figure 10.**The albedo intensity in various directions normalized with respect to the solar constant at (

**a**–

**c**) the Spring Equinox and (

**d**–

**f**) the Summer Solstice at the altitude of 500 km.

**Figure 12.**The impact of Earth albedo on different solar cells. ${O}_{b}M$ is the radius of the influence area of the albedo effect, and ${O}_{b}N$ is perpendicular to ${O}_{b}M$. Solar cells in red are sheltered from the sunlight. Solar cells in green cannot be influenced by the albedo effect. Solar cells in the yellow region can be influenced by both the sunlight and the albedo effect.

**Figure 13.**The sun vector inversion accuracy before and after invalid measurements culling. At the Spring Equinox (

**a**,

**b**) the overall accuracy improves from 4.84${}^{\circ}$ to 1.84${}^{\circ}$. At the Summer Solstice (

**c**,

**d**), the overall accuracy improves from 7.41${}^{\circ}$ to 2.16${}^{\circ}$.

**Figure 14.**Percentage of solar cells with valid measurement when the threshold of (

**a**) 65${}^{\circ}$, (

**b**) 75${}^{\circ}$ and (

**c**) 85${}^{\circ}$ are imposed respectively.

**Figure 15.**Q-SAT before launch. (

**a**) Totally 991 solar cells are mounted on the spherical surface. (

**b**) Q-SAT is undergoing the ground experiment to test the feasibility and performance of the proposed IPSS using artificial sunlight.

**Figure 16.**Raw measurements of IPSS and the inversed sun vector in satellite body frame during the ground experiment. (

**a**) the inversed artificial sun vector in the satellite body frame. (

**b**) sampled voltage curves of solar cells in the upper hemisphere. (

**c**) sampled temperature curves of solar cells in the upper hemisphere.

**Figure 17.**Performance of IPSS to support three-axis attitude determination in various orbits and seasons. (

**a-1**,

**a-2**,

**a-3**) 18:00 sun−synchronous orbit at the Spring Equinox. (

**b-1**,

**b-2**,

**b-3**) 12:00 sun−synchronous orbit at the Spring Equinox. (

**c-1**,

**c-2**,

**c-3**) 18:00 sun−synchronous orbit at the Summer Solstice. (

**d-1**,

**d-2**,

**d-3**) 12:00 sun−synchronous orbit at the Summer Solstice.

**Figure 18.**Raw measurements of IPSS extracted from the real−time telemetry data from 25 March 2021 03:04:45 UTC to 03:13:22 UTC. (

**a**) sampled voltage curves of the 16 solar cells. (

**b**) sampled temperature curves of the 16 solar cells. (

**c**) the inversed sun vector in the satellite body frame by Q-SAT.

**Figure 19.**The on−orbit attitude determination results are calculated in real-time by Q-SAT. The data starts from 25 March 2021 03:04:45 UTC to 03:13:22 UTC. (

**a**) The attitude is represented by Euler angles (3-2-1) with respect to the orbital coordination frame. (

**b**) The angular velocities are defined with respect to the inertial system. The estimated angular velocity in the satellite body Y axis is close to the orbital angular velocity of Q-SAT.

COSPAR ID | 2020-054B |
---|---|

diameter | 510 mm |

weight | 23 kg |

payload | dual frequency GNSS receiver |

separation system | electromagnetic separation system |

perigee | 488.0 km |

apogee | 513.9 km |

inclination angle | 97.5${}^{\circ}$ |

orbit period | 84.5 min |

semi-major axis | 6871 km |

Category | Factor | Parameter | Magnitude | Introduced Error |
---|---|---|---|---|

sampling error | current/voltage sampling error of solar cells | $I/V$ | 2.5 mA/5 mV | 1.04${}^{\circ}$ |

temperature sampling error | T | <3 ${}^{\circ}$C | <0.64${}^{\circ}$ | |

manufacturing and installation | installation matrix error of solar cells | ${\overrightarrow{n}}_{i}$ | 0.5${}^{\circ}$ | 0.16${}^{\circ}$ |

parameter error | resistance error of current sampling resistor | ${R}_{p}$ | 0.5% | 0.14${}^{\circ}$ |

temperature compensation coefficient error | K | 10% | <0.50${}^{\circ}$ | |

error in max. generated current at ${T}_{0}$ | ${I}_{\mathrm{max},{T}_{0}}$ | 2 mA | 0.48${}^{\circ}$ | |

albedo and seasonal variations | Earth albedo effect | E | up to 40% | depends |

seasonal variations in sunlight intensity | E | 3.4% | negligible |

Parameter | Value |
---|---|

satellite weight | 23 kg |

satellite inertial matrix | ${I}_{xx}$ = 0.6349 kg · m${}^{2}$ |

${I}_{yy}$ = 0.7960 kg · m${}^{2}$ | |

${I}_{zz}$ = 0.6238 kg · m${}^{2}$ | |

${I}_{xy}$ = 0.0023 kg · m${}^{2}$ | |

${I}_{yz}$ = 0.0019 kg · m${}^{2}$ | |

${I}_{zx}$ = −0.0086 kg · m${}^{2}$ | |

inertial matrix error of attitude filter | 10% |

magnetometer measurement error | 250 nT |

magnetic momentum of magnetorquer | 3.4 A · m${}^{2}$ |

inertial of the bias momentum wheel | 1.067 × 10${}^{-4}$ kg · m${}^{2}$ |

rotational speed of bias momentum wheel | 2000.0 rpm |

control frequency | 1 Hz |

Season/Time of the Year | Local Time of Descending | Average Accuracy of IPSS | Attitude Determination Accuracy | |
---|---|---|---|---|

Angle | Angular Rate | |||

Spring Equinox | 18:00 | 1.62${}^{\circ}$ | 0.32${}^{\circ}$ | 0.0014${}^{\circ}$/s |

12:00 | 3.12${}^{\circ}$ | 0.43${}^{\circ}$ | 0.0007${}^{\circ}$/s | |

Summer Solstice | 18:00 | 2.30${}^{\circ}$ | 0.38${}^{\circ}$ | 0.0013${}^{\circ}$/s |

12:00 | 3.24${}^{\circ}$ | 0.61${}^{\circ}$ | 0.0013${}^{\circ}$/s |

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## Share and Cite

**MDPI and ACS Style**

Zhang, Q.; Zhang, Y.
Design and Verification of an Integrated Panoramic Sun Sensor atop a Small Spherical Satellite. *Sensors* **2022**, *22*, 8130.
https://doi.org/10.3390/s22218130

**AMA Style**

Zhang Q, Zhang Y.
Design and Verification of an Integrated Panoramic Sun Sensor atop a Small Spherical Satellite. *Sensors*. 2022; 22(21):8130.
https://doi.org/10.3390/s22218130

**Chicago/Turabian Style**

Zhang, Qi, and Yulin Zhang.
2022. "Design and Verification of an Integrated Panoramic Sun Sensor atop a Small Spherical Satellite" *Sensors* 22, no. 21: 8130.
https://doi.org/10.3390/s22218130