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22 pages, 6919 KiB

Open AccessArticle

GMM-Based Adaptive Extended Kalman Filter Design for Satellite Attitude Estimation under Thruster-Induced Disturbances

by Taeho Kim, Natnael S. Zewge, Hyochoong Bang and Hyosang Yoon

Sensors 2023, 23(9), 4212; https://doi.org/10.3390/s23094212 - 23 Apr 2023

Cited by 2 | Viewed by 1782

Abstract

Star images from star trackers are usually defocused to capture stars over an exposure time for better centroid measurements. While a satellite is maneuvering, the star point on the screen of the camera is affected by the satellite, which results in the degradation [...] Read more.

Star images from star trackers are usually defocused to capture stars over an exposure time for better centroid measurements. While a satellite is maneuvering, the star point on the screen of the camera is affected by the satellite, which results in the degradation of centroid measurement accuracy. Additionally, this could result in a worse star vector outcome. For geostationary satellites, onboard thrusters are used to maintain or change orbit parameters under orbit disturbances. Since there is misalignment in the thruster and torque is generated by an impulsive shape signal from the torque command, it is difficult to generate target torque; in addition, it also impacts the star image because the impulsive torque creates a sudden change in the angular velocity in the satellite dynamics. This makes the noise of the star image non-Gaussian, which may require introducing a method for dealing with non-Gaussian measurement noise. To meet this goal, in this study, an adaptive extended Kalman filter is implemented to predict measurement vectors with predicted states. The GMM (Gaussian mixture model) is connected in this sequence, giving weighting parameters to each Gaussian density and resulting in the better prediction of measurement vectors. Simulation results show that the GMM-EKF exhibits a better performance than the EKF for attitude estimation, with 30% improvement in performance. Therefore, the GMM-EKF could be a more attractive approach for use with geostationary satellites during station-keeping maneuvers. Full article

(This article belongs to the Special Issue Attitude Estimation Based on Data Processing of Sensors)

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14 pages, 2678 KiB

Open AccessArticle

Gyro-Free Inertial Navigation Systems Based on Linear Opto-Mechanical Accelerometers

by Jose Sanjuan, Alexander Sinyukov, Mohanad F. Warrayat and Felipe Guzman

Sensors 2023, 23(8), 4093; https://doi.org/10.3390/s23084093 - 19 Apr 2023

Cited by 3 | Viewed by 2274

Abstract

High-sensitivity uniaxial opto-mechanical accelerometers provide very accurate linear acceleration measurements. In addition, an array of at least six accelerometers allows the estimation of linear and angular accelerations and becomes a gyro-free inertial navigation system. In this paper, we analyze the performance of such [...] Read more.

High-sensitivity uniaxial opto-mechanical accelerometers provide very accurate linear acceleration measurements. In addition, an array of at least six accelerometers allows the estimation of linear and angular accelerations and becomes a gyro-free inertial navigation system. In this paper, we analyze the performance of such systems considering opto-mechanical accelerometers with different sensitivities and bandwidths. In the six-accelerometer configuration adopted here, the angular acceleration is estimated using a linear combination of accelerometers’ read-outs. The linear acceleration is estimated similarly but requires a correcting term that includes angular velocities. Accelerometers’ colored noise from experimental data is used to derive, analytically and through simulations, the performance of the inertial sensor. Results for six accelerometers, separated by 0.5 m in a cube configuration show noise levels of 10

^{- 7}

m s

^{- 2}

and 10

^{- 5}

m s

^{- 2}

(in Allan deviation) for time scales of one second for the low-frequency (Hz) and high-frequency (kHz) opto-mechanical accelerometers, respectively. The Allan deviation for the angular velocity at one second is

10^{- 5}

rad s

^{- 1}

and

5 \times 10^{- 4}

rad s

^{- 1}

. Compared to other technologies such as MEMS-based inertial sensors and optical gyroscopes, the high-frequency opto-mechanical accelerometer exhibits better performance than tactical-grade MEMS for time scales shorter than 10 s. For angular velocity, it is only superior for time scales less than a few seconds. The linear acceleration of the low-frequency accelerometer outperforms the MEMS for time scales up to 300 s and for angular velocity only for a few seconds. Fiber optical gyroscopes are orders of magnitude better than the high- and low-frequency accelerometers in gyro-free configurations. However, when considering the theoretical thermal noise limit of the low-frequency opto-mechanical accelerometer,

5 \times 10^{- 11}

m s

^{- 2}

, linear acceleration noise is orders of magnitude lower than MEMS navigation systems. Angular velocity precision is around

10^{- 10}

rad s

^{- 1}

at one second and

5 \times 10^{- 7}

rad s

^{- 1}

at one hour, which is comparable to fiber optical gyroscopes. While experimental validation is yet not available, the results shown here indicate the potential of opto-mechanical accelerometers as gyro-free inertial navigation sensors, provided the fundamental noise limit of the accelerometer is reached, and technical limitations such as misalignments and initial conditions errors are well controlled. Full article

(This article belongs to the Special Issue Attitude Estimation Based on Data Processing of Sensors)

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22 pages, 13131 KiB

Open AccessArticle

An Effective Sensor Architecture for Full-Attitude Determination in the HERMES Nano-Satellites

by Andrea Colagrossi, Michèle Lavagna and Roberto Bertacin

Sensors 2023, 23(5), 2393; https://doi.org/10.3390/s23052393 - 21 Feb 2023

Cited by 5 | Viewed by 2494

Abstract

The High Energy Rapid Modular Ensemble of Satellites (HERMES) is a constellation of 3U nano-satellites for high energy astrophysics. The HERMES nano-satellites’ components have been designed, verified, and tested to detect and localize energetic astrophysical transients, such as short gamma-ray bursts (GRBs), which [...] Read more.

The High Energy Rapid Modular Ensemble of Satellites (HERMES) is a constellation of 3U nano-satellites for high energy astrophysics. The HERMES nano-satellites’ components have been designed, verified, and tested to detect and localize energetic astrophysical transients, such as short gamma-ray bursts (GRBs), which are the electromagnetic counterparts of gravitational wave events, thanks to novel miniaturized detectors sensitive to X-rays and gamma-rays. The space segment is composed of a constellation of CubeSats in low-Earth orbit (LEO), ensuring an accurate transient localization in a field of view of several steradians exploiting the triangulation technique. To achieve this goal, guaranteeing a solid support to future multi-messenger astrophysics, HERMES shall determine its attitude and orbital states with stringent requirements. The scientific measurements bind the attitude knowledge within 1 deg (

1 σ_{a}

) and the orbital position knowledge within 10 m (

1 σ_{o}

). These performances shall be reached considering the mass, volume, power, and computation constraints of a 3U nano-satellite platform. Thus, an effective sensor architecture for full-attitude determination was developed for the HERMES nano-satellites. The paper describes the hardware typologies and specifications, the configuration on the spacecraft, and the software elements to process the sensors’ data to estimate the full-attitude and orbital states in such a complex nano-satellite mission. The aim of this study was to fully characterize the proposed sensor architecture, highlighting the available attitude and orbit determination performance and discussing the calibration and determination functions to be implemented on-board. The presented results derived from model-in-the-loop (MIL) and hardware-in-the-loop (HIL) verification and testing activities and can serve as useful resources and a benchmark for future nano-satellite missions. Full article

(This article belongs to the Special Issue Attitude Estimation Based on Data Processing of Sensors)

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21 pages, 3397 KiB

Open AccessArticle

Optimization of Gradient Descent Parameters in Attitude Estimation Algorithms

by Karla Sever, Leonardo Max Golušin and Josip Lončar

Sensors 2023, 23(4), 2298; https://doi.org/10.3390/s23042298 - 18 Feb 2023

Cited by 2 | Viewed by 2137

Abstract

Attitude estimation methods provide modern consumer, industrial, and space systems with an estimate of a body orientation based on noisy sensor measurements. The gradient descent algorithm is one of the most recent methods for optimal attitude estimation, whose iterative nature demands adequate adjustment [...] Read more.

Attitude estimation methods provide modern consumer, industrial, and space systems with an estimate of a body orientation based on noisy sensor measurements. The gradient descent algorithm is one of the most recent methods for optimal attitude estimation, whose iterative nature demands adequate adjustment of the algorithm parameters, which is often overlooked in the literature. Here, we present the effects of the step size, the maximum number of iterations, and the initial quaternion, as well as different propagation methods on the quality of the estimation in noiseless and noisy conditions. A novel figure of merit and termination criterion that defines the algorithm’s accuracy is proposed. Furthermore, the guidelines for selecting the optimal set of parameters in order to achieve the highest accuracy of the estimate using the fewest iterations are proposed and verified in simulations and experimentally based on the measurements acquired from an in-house developed model of a satellite attitude determination and control system. The proposed attitude estimation method based on the gradient descent algorithm and complementary filter automatically adjusts the number of iterations with the average below 0.5, reducing the demand on the processing power and energy consumption and causing it to be suitable for low-power applications. Full article

(This article belongs to the Special Issue Attitude Estimation Based on Data Processing of Sensors)

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24 pages, 14166 KiB

Open AccessArticle

Common Frame Dynamics for Conically-Constrained Spacecraft Attitude Control

by Arnold Christopher Cruz and Ahmad Bani Younes

Sensors 2022, 22(24), 10003; https://doi.org/10.3390/s222410003 - 19 Dec 2022

Viewed by 1838

Abstract

Attitude control subjected to pointing constraints is a requirement for most spacecraft missions carrying sensitive on-board equipment. Pointing constraints can be divided into two categories: exclusion zones that are defined for sensitive equipment such as telescopes or cameras that can be damaged from [...] Read more.

Attitude control subjected to pointing constraints is a requirement for most spacecraft missions carrying sensitive on-board equipment. Pointing constraints can be divided into two categories: exclusion zones that are defined for sensitive equipment such as telescopes or cameras that can be damaged from celestial objects, and inclusion zones that are defined for communication hardware and solar arrays. This work derives common frame dynamics that are fully derived for Modified Rodrigues Parameters and introduced to an existing novel technique for constrained spacecraft attitude control, which uses a kinematic steering law and servo sub-system. Lyapunov methods are used to redevelop the steering law and servo sub-system in the common frame for the tracking problem for both static and dynamic conic constraints. A numerical example and comparison between the original frame and the common frame for the static constrained tracking problem are presented under both unbounded and limited torque capabilities. Monte Carlo simulations are performed to validate the convergence of the constrained tracking problem for static conic constraints under small perturbations of the initial conditions. The performance of dynamic conic constraints in the tracking problem is addressed and a numerical example is presented. The result of using common frame dynamics in the constrained problem shows decreased control effort required to rotate the spacecraft. Full article

(This article belongs to the Special Issue Attitude Estimation Based on Data Processing of Sensors)

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31 pages, 8942 KiB

Open AccessArticle

The TinyV3RSE Hardware-in-the-Loop Vision-Based Navigation Facility

by Paolo Panicucci and Francesco Topputo

Sensors 2022, 22(23), 9333; https://doi.org/10.3390/s22239333 - 30 Nov 2022

Cited by 4 | Viewed by 2321

Abstract

The increase in number of interplanetary probes has emphasized the need for spacecraft autonomy to reduce overall mission costs and to enable riskier operations without ground support. The perception of the external environment is a critical task for autonomous probes, being fundamental for [...] Read more.

The increase in number of interplanetary probes has emphasized the need for spacecraft autonomy to reduce overall mission costs and to enable riskier operations without ground support. The perception of the external environment is a critical task for autonomous probes, being fundamental for both motion planning and actuation. Perception is often achieved using navigation sensors which provide measurements of the external environment. For space exploration purposes, cameras are among the sensors that provide navigation information with few constraints at the spacecraft system level. Image processing and vision-based navigation algorithms are exploited to extract information about the external environment and the probe’s position within it from images. It is thus crucial to have the capability to generate realistic image datasets to design, validate, and test autonomous algorithms. This goal is achieved with high-fidelity rendering engines and with hardware-in-the-loop simulations. This work focuses on the latter by presenting a facility developed and used at the Deep-space Astrodynamics Research and Technology (DART) Laboratory at Politecnico di Milano. First, the facility design relationships are established to select hardware components. The critical design parameters of the camera, lens system, and screen are identified and analytical relationships are developed among these parameters. Second, the performances achievable with the chosen components are analytically and numerically studied in terms of geometrical accuracy and optical distortions. Third, the calibration procedures compensating for hardware misalignment and errors are defined. Their performances are evaluated in a laboratory experiment to display the calibration quality. Finally, the facility applicability is demonstrated by testing imageprocessing algorithms for space exploration scenarios. Full article

(This article belongs to the Special Issue Attitude Estimation Based on Data Processing of Sensors)

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28 pages, 16169 KiB

Open AccessArticle

Monocular Pose Estimation of an Uncooperative Spacecraft Using Convexity Defect Features

by Haeyoon Han, Hanik Kim and Hyochoong Bang

Sensors 2022, 22(21), 8541; https://doi.org/10.3390/s22218541 - 6 Nov 2022

Cited by 3 | Viewed by 2193

Abstract

Spacecraft relative pose estimation for an uncooperative spacecraft is challenging because the target spacecraft neither provides sensor information to a chaser spacecraft nor contains markers that assist vision-based navigation. Moreover, the chaser does not have prior pose estimates when initiating the pose estimation. [...] Read more.

Spacecraft relative pose estimation for an uncooperative spacecraft is challenging because the target spacecraft neither provides sensor information to a chaser spacecraft nor contains markers that assist vision-based navigation. Moreover, the chaser does not have prior pose estimates when initiating the pose estimation. This paper proposes a new monocular pose estimation algorithm that addresses these issues in pose initialization situations for a known but uncooperative target spacecraft. The proposed algorithm finds convexity defect features from a target image and uses them as cues for matching feature points on the image to the points on the known target model. Based on this novel method for model matching, it estimates a pose by solving the PnP problem. Pose estimation simulations are carried out in three test scenarios, and each assesses the estimation accuracy and initialization performance by varying relative attitudes and distances. The simulation results show that the algorithm can estimate the poses of spacecraft models when a solar panel length and the number of solar panels are changed. Furthermore, a scenario considering the surface property of the spacecraft emphasizes that robust feature detection is essential for accurate pose estimation. This algorithm can be used for proximity operations with a known but uncooperative target spacecraft. Specifically, one of the main applications is relative navigation for on-orbit servicing. Full article

(This article belongs to the Special Issue Attitude Estimation Based on Data Processing of Sensors)

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16 pages, 2627 KiB

Open AccessArticle

Simplex Back Propagation Estimation Method for Out-of-Sequence Attitude Sensor Measurements

by Shu Ting Goh, M. S. C. Tissera, RongDe Darius Tan, Ankit Srivastava, Kay-Soon Low and Lip San Lim

Sensors 2022, 22(20), 7970; https://doi.org/10.3390/s22207970 - 19 Oct 2022

Cited by 1 | Viewed by 1374

Abstract

For a small satellite, the processor onboard the attitude determination and control system (ADCS) is required to monitor, communicate, and control all the sensors and actuators. In addition, the processor is required to consistently communicate with the satellite bus. Consequently, the processor is [...] Read more.

For a small satellite, the processor onboard the attitude determination and control system (ADCS) is required to monitor, communicate, and control all the sensors and actuators. In addition, the processor is required to consistently communicate with the satellite bus. Consequently, the processor is unable to ensure all the sensors and actuators will immediately respond to the data acquisition request, which leads to asynchronous data problems. The extended Kalman filter (EKF) is commonly used in the attitude determination process, but it assumes fully synchronous data. The asynchronous data problem would greatly degrade the attitude determination accuracy by EKF. To minimize the attitude estimation accuracy loss due to asynchronous data while ensuring a reasonable computational complexity for small satellite applications, this paper proposes the simplex-back-propagation Kalman filter (SBPKF). The proposed SBPKF incorporates the time delay, gyro instability, and navigation error into both the measurement and covariance estimation during the Kalman update process. The performance of SBPKF has been compared with EKF, modified adaptive EKF (MAEKF), and moving–covariance Kalman filter (MC-KF). Simulation results show that the attitude estimation error of SBPKF is at least 30% better than EKF and MC-KF. In addition, the SBPKF’s computational complexity is 17% lower than MAEKF and 29% lower than MC-KF. Full article

(This article belongs to the Special Issue Attitude Estimation Based on Data Processing of Sensors)

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25 pages, 1455 KiB

Open AccessArticle

Optimal Tasking of Ground-Based Sensors for Space Situational Awareness Using Deep Reinforcement Learning

by Peng Mun Siew and Richard Linares

Sensors 2022, 22(20), 7847; https://doi.org/10.3390/s22207847 - 16 Oct 2022

Cited by 6 | Viewed by 2574

Abstract

Space situational awareness (SSA) is becoming increasingly challenging with the proliferation of resident space objects (RSOs), ranging from CubeSats to mega-constellations. Sensors within the United States Space Surveillance Network are tasked to repeatedly detect, characterize, and track these RSOs to retain custody and [...] Read more.

Space situational awareness (SSA) is becoming increasingly challenging with the proliferation of resident space objects (RSOs), ranging from CubeSats to mega-constellations. Sensors within the United States Space Surveillance Network are tasked to repeatedly detect, characterize, and track these RSOs to retain custody and estimate their attitude. The majority of these sensors consist of ground-based sensors with a narrow field of view and must be slew at a finite rate from one RSO to another during observations. This results in a complex combinatorial problem that poses a major obstacle to the SSA sensor tasking problem. In this work, we successfully applied deep reinforcement learning (DRL) to overcome the curse of dimensionality and optimally task a ground-based sensor. We trained several DRL agents using proximal policy optimization and population-based training in a simulated SSA environment. The DRL agents outperformed myopic policies in both objective metrics of RSOs’ state uncertainties and the number of unique RSOs observed over a 90-min observation window. The agents’ robustness to changes in RSO orbital regimes, observation window length, observer’s location, and sensor properties are also examined. The robustness of the DRL agents allows them to be applied to any arbitrary locations and scenarios. Full article

(This article belongs to the Special Issue Attitude Estimation Based on Data Processing of Sensors)

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27 pages, 882 KiB

Open AccessArticle

Attitude Uncertainty Analysis of a Three-Vehicle Constrained Formation

by Pedro Cruz and Pedro Batista

Sensors 2022, 22(10), 3879; https://doi.org/10.3390/s22103879 - 20 May 2022

Viewed by 1396

Abstract

The uncertainty analysis of attitude estimates enables the comparison between different methods, and, thus, it is important for practical applications. This work studies the uncertainty for the attitude determination of a three-vehicle constrained formation. Moreover, the existing solution is improved by including the [...] Read more.

The uncertainty analysis of attitude estimates enables the comparison between different methods, and, thus, it is important for practical applications. This work studies the uncertainty for the attitude determination of a three-vehicle constrained formation. Moreover, the existing solution is improved by including the uncertainty results in a weighted orthogonal Procrustes problem. In the formation considered herein, the vehicles measure inertial references and relative line-of-sight vectors. Nonetheless, the line of sight between two elements of the formation is restricted. The uncertainty analysis uses perturbation theory and, consequently, considers a small first-order perturbation in the measurements. The covariance matrices are obtained for all relative and inertial attitude candidates from the linearization of the solution using a first-order Taylor expansion. Then, the uncertainty is completed by considering the covariance for the weighted orthogonal Procrustes problem, from the literature, and the definition of covariance for the remaining attitudes. The uncertainty characterization is valid for configurations with a unique solution. Finally, the theoretical results are validated by applying Monte Carlo simulations, which show that the predicted errors are statistically consistent with the numerical implementation of the solution with noise. Furthermore, the theoretical uncertainty predicts the accuracy changes near special configurations where there is loss of information. Full article

(This article belongs to the Special Issue Attitude Estimation Based on Data Processing of Sensors)

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32 pages, 1773 KiB

Open AccessArticle

Uncertainty Propagation for Inertial Navigation with Coning, Sculling, and Scrolling Corrections

by James D. Brouk and Kyle J. DeMars

Sensors 2021, 21(24), 8457; https://doi.org/10.3390/s21248457 - 18 Dec 2021

Cited by 1 | Viewed by 4039

Abstract

This paper investigates the propagation of estimation errors through a common coning, sculling, and scrolling architecture used in modern-day inertial navigation systems. Coning, sculling, and scrolling corrections often have an unaccounted for effect on the error statistics of inertial measurements used to describe [...] Read more.

This paper investigates the propagation of estimation errors through a common coning, sculling, and scrolling architecture used in modern-day inertial navigation systems. Coning, sculling, and scrolling corrections often have an unaccounted for effect on the error statistics of inertial measurements used to describe the state and uncertainty propagation for position, velocity, and attitude estimates. Through the development of an error analysis for a set of coning, sculling, and scrolling algorithms, mappings of the measurement and estimation errors through the correction term are adaptively generated. Using the developed mappings, an efficient and consistent propagation of the state and uncertainty, within the multiplicative extended Kalman filter architecture, is achieved. Monte Carlo analysis is performed, and results show that the developed system has favorable attributes when compared to the traditional mechanization. Full article

(This article belongs to the Special Issue Attitude Estimation Based on Data Processing of Sensors)

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13 pages, 2451 KiB

Open AccessArticle

An Efficient and Robust Star Identification Algorithm Based on Neural Networks

by Bendong Wang, Hao Wang and Zhonghe Jin

Sensors 2021, 21(22), 7686; https://doi.org/10.3390/s21227686 - 19 Nov 2021

Cited by 14 | Viewed by 4071

Abstract

A lost-in-space star identification algorithm based on a one-dimensional Convolutional Neural Network (1D CNN) is proposed. The lost-in-space star identification aims to identify stars observed with corresponding catalog stars when there is no prior attitude information. With the help of neural networks, the [...] Read more.

A lost-in-space star identification algorithm based on a one-dimensional Convolutional Neural Network (1D CNN) is proposed. The lost-in-space star identification aims to identify stars observed with corresponding catalog stars when there is no prior attitude information. With the help of neural networks, the robustness and the speed of the star identification are improved greatly. In this paper, a modified log-Polar mapping is used to constructed rotation-invariant star patterns. Then a 1D CNN is utilized to classify the star patterns associated with guide stars. In the 1D CNN model, a global average pooling layer is used to replace fully-connected layers to reduce the number of parameters and the risk of overfitting. Experiments show that the proposed algorithm is highly robust to position noise, magnitude noise, and false stars. The identification accuracy is

98.1 %

with 5 pixels position noise,

97.4 %

with 5 false stars, and

97.7 %

with 0.5 Mv magnitude noise, respectively, which is significantly higher than the identification rate of the pyramid, optimized grid and modified log-polar algorithms. Moreover, the proposed algorithm guarantees a reliable star identification under dynamic conditions. The identification accuracy is

82.1 %

with angular velocity of 10 degrees per second. Furthermore, its identification time is as short as 32.7 miliseconds and the memory required is about 1920 kilobytes. The algorithm proposed is suitable for current embedded systems. Full article

(This article belongs to the Special Issue Attitude Estimation Based on Data Processing of Sensors)

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24 pages, 1272 KiB

Open AccessArticle

In-Orbit Attitude Determination of the UVSQ-SAT CubeSat Using TRIAD and MEKF Methods

by Adrien Finance, Christophe Dufour, Thomas Boutéraon, Alain Sarkissian, Antoine Mangin, Philippe Keckhut and Mustapha Meftah

Sensors 2021, 21(21), 7361; https://doi.org/10.3390/s21217361 - 5 Nov 2021

Cited by 9 | Viewed by 4402

Abstract

Ultraviolet and infrared sensors at high quantum efficiency on-board a small satellite (UVSQ-SAT) is a CubeSat dedicated to the observation of the Earth and the Sun. This satellite has been in orbit since January 2021. It measures the Earth’s outgoing shortwave and longwave [...] Read more.

Ultraviolet and infrared sensors at high quantum efficiency on-board a small satellite (UVSQ-SAT) is a CubeSat dedicated to the observation of the Earth and the Sun. This satellite has been in orbit since January 2021. It measures the Earth’s outgoing shortwave and longwave radiations. The satellite does not have an active pointing system. To improve the accuracy of the Earth’s radiative measurements and to resolve spatio-temporal fluctuations as much as possible, it is necessary to have a good knowledge of the attitude of the UVSQ-SAT CubeSat. The attitude determination of small satellites remains a challenge, and UVSQ-SAT represents a real and unique example to date for testing and validating different methods to improve the in-orbit attitude determination of a CubeSat. This paper presents the flight results of the UVSQ-SAT’s attitude determination. The Tri-Axial Attitude Determination (TRIAD) method was used, which represents one of the simplest solutions to the spacecraft attitude determination problem. Another method based on the Multiplicative Extended Kalman Filter (MEKF) was used to improve the results obtained with the TRIAD method. In sunlight, the CubeSat attitude is determined at an accuracy better than 3

^{°}

(at one

σ

) for both methods. During eclipses, the accuracy of the TRIAD method is 14

^{°}

, while it reaches 10

^{°}

(at one

σ

) for the recursive MEKF method. Many future satellites could benefit from these studies in order to validate methods and configurations before launch. Full article

(This article belongs to the Special Issue Attitude Estimation Based on Data Processing of Sensors)

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23 pages, 3738 KiB

Open AccessArticle

Evaluation of Murrell’s EKF-Based Attitude Estimation Algorithm for Exploiting Multiple Attitude Sensor Configurations

by Sharanabasaweshwara Asundi, Norman Fitz-Coy and Haniph Latchman

Sensors 2021, 21(19), 6450; https://doi.org/10.3390/s21196450 - 27 Sep 2021

Cited by 1 | Viewed by 2510

Abstract

Pico- and nano-satellites, due to their form factor and size, are limited in accommodating multiple or redundant attitude sensors. For such satellites, Murrell’s implementation of the extended Kalman filter (EKF) can be exploited to accommodate multiple sensor configurations from a set of non [...] Read more.

Pico- and nano-satellites, due to their form factor and size, are limited in accommodating multiple or redundant attitude sensors. For such satellites, Murrell’s implementation of the extended Kalman filter (EKF) can be exploited to accommodate multiple sensor configurations from a set of non redundant attitude sensors. The paper describes such an implementation involving a sun sensor suite and a magnetometer as attitude sensors. The implementation exploits Murrell’s EKF to enable three sensor configurations, which can be operationally commanded, for satellite attitude estimation. Among the three attitude estimation schemes, (i) sun sensor suite and magnetometer, (ii) magnetic field vector and its time derivative and (iii) magnetic field vector, it is shown that the third configuration is better suited for attitude estimation in terms of precision and accuracy, but can consume more time to converge than the other two. Full article

(This article belongs to the Special Issue Attitude Estimation Based on Data Processing of Sensors)

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19 pages, 1841 KiB

Open AccessArticle

High Accurate Mathematical Tools to Estimate the Gravity Direction Using Two Non-Orthogonal Inclinometers

by Daniele Mortari and Anthony Gardner

Sensors 2021, 21(17), 5727; https://doi.org/10.3390/s21175727 - 25 Aug 2021

Cited by 1 | Viewed by 2465

Abstract

This study provides two mathematical tools to best estimate the gravity direction when using a pair of non-orthogonal inclinometers whose measurements are affected by zero-mean Gaussian errors. These tools consist of: (1) the analytical derivation of the gravity direction expectation and its covariance [...] Read more.

This study provides two mathematical tools to best estimate the gravity direction when using a pair of non-orthogonal inclinometers whose measurements are affected by zero-mean Gaussian errors. These tools consist of: (1) the analytical derivation of the gravity direction expectation and its covariance matrix, and (2) a continuous description of the geoid model correction as a linear combination of a set of orthogonal surfaces. The accuracy of the statistical quantities is validated by extensive Monte Carlo tests and the application in an Extended Kalman Filter (EKF) has been included. The continuous geoid description is needed as the geoid represents the true gravity direction. These tools can be implemented in any problem requiring high-precision estimates of the local gravity direction. Full article

(This article belongs to the Special Issue Attitude Estimation Based on Data Processing of Sensors)

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24 pages, 8585 KiB

Open AccessArticle

Design, Ground Testing and On-Orbit Performance of a Sun Sensor Based on COTS Photodiodes for the UPMSat-2 Satellite

by Angel Porras-Hermoso, Daniel Alfonso-Corcuera, Javier Piqueras, Elena Roibás-Millán, Javier Cubas, Javier Pérez-Álvarez and Santiago Pindado

Sensors 2021, 21(14), 4905; https://doi.org/10.3390/s21144905 - 19 Jul 2021

Cited by 10 | Viewed by 3839

Abstract

This paper presents the development of the UPMSat-2 sun sensor, from the design to on-orbit operation. It also includes the testing of the instrument, one of the most important tasks that needs to be performed to operate a sensor with precision. The UPMSat-2 [...] Read more.

This paper presents the development of the UPMSat-2 sun sensor, from the design to on-orbit operation. It also includes the testing of the instrument, one of the most important tasks that needs to be performed to operate a sensor with precision. The UPMSat-2 solar sensor has been designed, tested, and manufactured at the Universidad Politécnica de Madrid (UPM) using 3D printing and COTS (photodiodes). The work described in this paper was carried out by students and teachers of the Master in Space Systems (Máster Universitario en Sistemas Espaciales—MUSE). The solar sensor is composed of six photodiodes that are divided into two sets; each set is held and oriented on the satellite by its corresponding support printed in Delrin. The paper describes the choice of components, the electrical diagram, and the manufacture of the supports. The methodology followed to obtain the response curve of each photodiode is simple and inexpensive, as it requires a limited number of instruments and tools. The selected irradiance source was a set of red LEDs and halogen instead of an AM0 spectrum irradiance simulator. Some early results from the UPMSat-2 mission have been analyzed in the present paper. Data from magnetometers and the attitude control system have been used to validate the data obtained from the sun sensor. The results indicate a good performance of the sensors during flight, in accordance with the data from the ground tests. Full article

(This article belongs to the Special Issue Attitude Estimation Based on Data Processing of Sensors)

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30 pages, 1511 KiB

Open AccessArticle

Characterization of Degenerate Configurations in Attitude Determination of Three-Vehicle Heterogeneous Formations

by Pedro Cruz and Pedro Batista

Sensors 2021, 21(14), 4631; https://doi.org/10.3390/s21144631 - 6 Jul 2021

Cited by 1 | Viewed by 1662

Abstract

The existence of multiple solutions to an attitude determination problem impacts the design of estimation schemes, potentially increasing the errors by a significant value. It is therefore essential to identify such cases in any attitude problem. In this paper, the cases where multiple [...] Read more.

The existence of multiple solutions to an attitude determination problem impacts the design of estimation schemes, potentially increasing the errors by a significant value. It is therefore essential to identify such cases in any attitude problem. In this paper, the cases where multiple attitudes satisfy all constraints of a three-vehicle heterogeneous formation are identified. In the formation considered herein, the vehicles measure inertial references and relative line-of-sight vectors. Nonetheless, the line of sight between two elements of the formation is restricted, and these elements are denoted as deputies. The attitude determination problem is characterized relative to the number of solutions associated with each configuration of the formation. There are degenerate and ambiguous configurations that result in infinite or exactly two solutions, respectively. Otherwise, the problem has a unique solution. The degenerate configurations require some collinearity between independent measurements, whereas the ambiguous configurations result from symmetries in the formation measurements. The conditions which define all such configurations are determined in this work. Furthermore, the ambiguous subset of configurations is geometrically interpreted resorting to the planes defined by specific measurements. This subset is also shown to be a zero-measure subset of all possible configurations. Finally, a maneuver is simulated to illustrate and validate the conclusions. As a result of this analysis, it is concluded that, in general, the problem has one attitude solution. Nonetheless, there are configurations with two or infinite solutions, which are identified in this work. Full article

(This article belongs to the Special Issue Attitude Estimation Based on Data Processing of Sensors)

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15 pages, 366 KiB

Open AccessTechnical Note

Adaptive Lag Smoother for State Estimation

by Shashi Poddar and John L. Crassidis

Sensors 2022, 22(14), 5310; https://doi.org/10.3390/s22145310 - 15 Jul 2022

Cited by 3 | Viewed by 1675

Abstract

Fixed-lag smoothing has been used across different disciplines for offline analysis in many applications. With rising computational power and parallel processing architectures, fixed-lag smoothers are increasingly integrated into online processing system with small delays. This delay is directly related to the lag-length used [...] Read more.

Fixed-lag smoothing has been used across different disciplines for offline analysis in many applications. With rising computational power and parallel processing architectures, fixed-lag smoothers are increasingly integrated into online processing system with small delays. This delay is directly related to the lag-length used in system design, which needs to be chosen appropriately. In this work, an adaptive approach is devised to choose an appropriate lag-length that provides a good trade-off between accuracy and computational requirements. The analysis shown in this paper for the error dynamics of the fixed-lag smoother over the lags helps in understanding its saturation over increasing lags. In order to provide the empirical results, simulations are carried out over a second-order Newtonian system, single-axis attitude estimation, Van der Pol’s oscillator, and three-axis attitude estimation. The simulation results demonstrate the performance achieved with an adaptive-lag smoother as compared to a fixed-lag smoother with very high lag-length. Full article

(This article belongs to the Special Issue Attitude Estimation Based on Data Processing of Sensors)

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