Attitude Determination Algorithm Research Articles

A Dual-Purpose Camera for Attitude Determination and Resident Space Object Detection on a Stratospheric Balloon.

Space systems play an integral role in every facet of our daily lives, including national security, communications, and resource management. Therefore, it is critical to protect our valuable assets in space and build resiliency in the space environment. In recent years, we have developed a novel approach to Space Situational Awareness (SSA), in the form of a low-resolution, Wide Field-of-View (WFOV) camera payload for attitude determination and Resident Space Object (RSO) detection. Detection is the first step in tracking, identification, and characterization of RSOs, including natural and artificial objects orbiting the Earth. A space-based dual-purpose camera that can provide attitude information alongside RSO detection can enhance the current SSA technologies which rely on ground infrastructure. A CubeSat form factor payload with real-time attitude determination and RSO detection algorithms was developed and flown onboard the CSA/CNES stratospheric balloon platform in August 2023. Sub-degree pointing information and multiple RSO detections were demonstrated during operation, with opportunities for improvement discussed. This paper outlines the hardware and software architecture, system design methodology, on-ground testing, and in-flight results of the dual-purpose camera payload.

Adaptive Absolute Attitude Determination Algorithm for a Fine Guidance Sensor

In order to ensure the attitude determination accuracy and speed of a fine guidance sensor (FGS) in a space telescope with limited onboard hardware computing resources, an adaptive absolute attitude determination algorithm was proposed. The more stars involved in the attitude determination, the higher the attitude accuracy, but more hardware resources will be consumed. By analyzing the relationship between the attitude determination accuracy and the number of stars (NOS) in the field of view (FOV), and the relationship between the detector exposure time and the NOS, an adaptive method of adjusting the NOS in the FOV was proposed to keep the number of observed stars in the FOV of the detector at a target value. The star map recognition algorithm based on improved log-polar transformation has a higher recognition speed than the traditional algorithm but cannot accurately identify and match the corresponding guide star when the number of observed stars is less than the number of guide stars. Thus, a comparison-AND star identification algorithm based on polar coordinates was proposed. In the case of a given line-of-sight pointing and 100-frame image simulation calculation, the root mean square (RMS) value of the line-of-sight pointing error was less than 37 mas in the direction of a right ascension, and less than 25 mas in the direction of declination, as concluded from the experimental simulation.

Evaluation of Attitude Determination Algorithms via Model-in-the-Loop and Processor-in-the-Loop

Evaluation of Attitude Determination Algorithms via Model-in-the-Loop and Processor-in-the-Loop

The UPMQube: An Academic/Educational PocketQube Proposal for the EU2Space Challenge

In the present paper, the UPMQube PocketQube proposal for the EU2Space challenge is described. This proposal has been developed by a group of master’s degree students led by Ph.D. students and professors from the Instituto Universitario de Microgravedad “Ignacio Da Riva” (IDR/UPM) at Universidad Politécnica de Madrid (UPM). PocketQube is a recent new picosatellite concept, which is currently under development. Its reduced size and mass require a significant effort to reduce the characteristic size of the elementary subsystems. One of the subsystems that offers the greatest capacity for improvement is the Attitude Determination and Control Subsystem (ADCS), since most PocketQubes do not usually have one due to lack of space. The most relevant technical aspect of this proposal is the development of a new ADCS which fits the high restrictive size and mass requirements, and it is based on Commercial Off-The-Shelf (COTS) components. This ADCS is composed by: (i) a purely Autonomous Magnetic Controller (AMC) based on magnetorquers and magnetometers on board the spacecraft (S/C platform; (ii) an Attitude Determination System (ADS) based on solar sensors and thermal sensors on board the S/C and an On Ground Attitude Determination Algorithm (for post processing the sensors flight data. The work carried out by Master s degree students is integrated within the academic program of the UPM’s Master in Space Systems as a Case of Study. It also provides an excellent training program for the Ph.D. Assistant Professors included in the proposals Team. The tasks assignments and responsibilities of all members of the Team are fully described in the paper. Additionally, it should be underlined that this proposal is quite well balanced in terms of gender, as 40% of the Team (including the Principal Investigator) are women. This figure is higher than the mean percentage of women present in STEAM Sciences, Technology, Engineering, and Mathematics careers (29% of the workforce, 19% of company board members, 3% industry CEOs). Keywords: UPMQube, PocketQube, MUSE, magnetic ADCS, space engineering challenge

Attitude Determination for Unmanned Cooperative Navigation Swarm Based on Multivectors in Covisibility Graph

To reduce costs, an unmanned swarm usually consists of nodes with high-accuracy navigation sensors (HAN) and nodes with low-accuracy navigation sensors (LAN). Transmitting and fusing the navigation information obtained by HANs enables LANs to improve their positioning accuracy, which in general is called cooperative navigation (CN). In this method, the accuracy of relative observation between platforms in the swarm have dramatic effects on the positioning results. In the popular research, constructing constraints in three-dimensional (3D) frame could only optimize the position and velocity of LANs but neglected the attitude estimation so LANs cannot maintain a high attitude accuracy when utilizing navigation information obtained by sensors installed during maneuvers over long periods. Considering the performance of the inertial measurement unit (IMU) and other common sensors, this paper advances a new method to estimate the attitude of LANs in a swarm. Because the small unmanned nodes are strictly limited by relevant practical engineering problems such as size, weight and power, the method proposed could compensate for the attitude error caused by strapdown gyroscopic drift, which only use visual vectors built by the targets detected by cameras with the function of range finding. In our method, the coordinates of targets are mainly given by the You Only Look Once (YOLO) algorithm, then the visual vectors are built by connecting the targets in the covisibility graph of the nodes in the swarm. The attitude transformation matrices between each camera frame are calculated using the multivector attitude determination algorithm. Finally, we design an information filter (IF) to determine the attitude of LANs based on the observation of HANs. Considering the problem of positioning reference, the field test was conducted in the open air and we chose to use two-wheeled robots and one UAV to carry out the experiment. The results show that the relative attitude error between nodes is less than 4 degrees using the visual vector. After filtering, the attitude divergence of LANs’ installed low precision IMU can be effectively constrained, and the high-precision attitude estimation in an unmanned CN swarm can be realized.

Development of Engineering Models of Nanosatellites for Student Training

AbstractThe work purpose is the development of BSUIM-1 and BSUIM-2 complexes for training specialists in the aerospace industry with the used engineering test beds and experimental facilities.Two sets of nanosatellite engineering models and ground stations had developed. They allow testing hardware and software of the onboard equipment and payload, simulating operation modes, and flight programs, and enable students to gain practical skills in working with ultra-small satellites. The complexes include ground stations, 2 ultra-small satellite simulators, BSUSAT-1 low-orbit nanosatellite, remote access laboratory, local and external servers for data storage. The complexes' website and database allow for full-time and remote training. The experience gained in conducting experiments, processing telemetry, and structuring information in the database is used for further development. All the developed equipment is made based on commercial off-the-shelf elements. It has reduced development costs, flexible equipment reconfiguration, and easier access to the simulator's internal architecture for demonstration purposes.The developed complexes allow students to practically study the ultra-small satellite components design and ground stations, methods for receiving and processing telemetry and scientific information, attitude determination and control algorithms. The complexes allow to conduct of research in the development of individual onboard systems and special-purpose equipment of the nanosatellite and their testing in the loop. The results obtained are introduced into the educational process and are used in lectures and laboratory classes for aerospace specialties students. The developed complexes make it possible to carry out term papers, theses, and master’s works related to the design of hardware and software for nanosatellites and a ground station, the setting up of space experiments, the development of new algorithms and a flight program for ultra-small satellites.

Adaptive weighted particle swarm optimization (AWPSO) attitude determination algorithm based on Chi-square test

The optimal search algorithm based on double-difference carrier phase is one of the methods to solve the attitude angle. An adaptive weighted particle swarm optimization (AWPSO) algorithm based on the Chi-square test is proposed to solve the attitude angle of ultra-short baseline. We establish the fitness function by introducing the relationship between attitude angle and baseline vector into the observation equations of double-difference carrier phase. Searching the attitude according to the fitness model instead of calculating the angle directly, which avoids solving the integer ambiguity. Using adaptive inertial weights and synchronous adaptive learning factors to speed up the convergence of attitude search. Constructing the candidate solution sequence to save the search result and calculating the Mahalanobis distance of the candidate solution. The local optimal solution is eliminated by the Chi-square test, and the attitude angle is gained by weighting the filtered sequence. Various static experimental results show that the new algorithm performs better than the direct solution method, the least square estimation method, and the PSO-based attitude solution method. The root mean square error of yaw angle and pitch angle is 0.245° and 0.236° directly at 0.575 m baseline.

Comparison of TRIAD+EKF and TRIAD+UKF Algorithms for Nanosatellite Attitude Estimation

Two most commonly used sensors on nanosatellites are magnetometer and sun sensor. In this paper, magnetometer and sun sensor measurements are combined gyro measurements to produce enhanced attitude estimation. Tri-Axial Attitude Determination (TRIAD) algorithm is used with Kalman filter to form a complete attitude filter. Sun sensor and magnetometer measurements are selected as inputs to TRIAD algorithm and output is fed to Kalman filter as a measurement. Two different Kalman filters, extended and unscented, are used with TRIAD algorithm. A comparison is given between performances of both Kalman filter.

The pre-process DV-UKF algorithm for high-precision attitude measurement with low-cost inertial sensor

PurposeThe purpose of this paper is to propose a high-precision attitude solution to solve the attitude drift problem caused by the dispersion of low-cost micro-electro-mechanical system devices in strap-down inertial navigation attitude solution of micro-quadrotor.Design/methodology/approachIn this study, a three-stage attitude estimation scheme that combines data preprocessing, gyro drifts prediction and enhanced unscented Kalman filtering (UKF) is proposed. By introducing a preprocessing model, the quaternion orientation is calculated as the composition of two algebraic quaternions, and the decoupling feature of the two quaternions makes the roll and pitch components independent of magnetic interference. A novel real-time based on differential value (DV) estimation algorithm is proposed for gyro drift. This novel solution prevents the impact of quartic characteristics and uses the iterative method to meet the requirement of real-time applications. A novel attitude determination algorithm, the pre-process DV-UKF algorithm, is proposed in combination with UKF based on the above solution and its characteristics.FindingsCompared to UKF, both simulation and experimental results demonstrate that the pre-process DV-UKF algorithm has higher reliability in attitude determination. The dynamic errors in the three directions of the attitude are below 2.0°, the static errors are all less than 0.2° and the absolute attitude errors tailored by average are about 47.98% compared to the UKF.Originality/valueThis paper fulfils an identified need to achieve high-precision attitude estimation when using low-cost inertial devices in micro-quadrotor. The accuracy of the pre-process DV-UKF algorithm is superior to other products in the market.

GNSS Single-Frequency, Single-Epoch Attitude Determination Method with Orthogonal Constraints

Attitude determination is one of the most considerable applications in high-precision GNSS (Global Navigation Satellite System) positioning and navigation. For rigid-body applications, the baseline is approximately fixed on the same plane and its relative position does not change over time. This provides an important constraint that can be exploited to directly aid the attitude determination process. This study provides an attitude determination algorithm with orthogonal constraints for single frequency and single epoch by fully integrating the baseline orthogonal constraints into the observation equations. Carrier phase and pseudo-range measurement from more than two antennas are used to construct the double-difference observation equations. Given the inclusion analysis of the two search spaces, the LAMBDA algorithm is used to transform the non-ellipsoid space search into the ellipsoid space search. The attitude matrix is solved directly by the Lagrange multiplier method and the optimal solution is selected by search space verification. The analysis focuses on single-frequency, single-epoch, rigid-body attitude accuracy and calculation amount. Experimental results demonstrate that the proposed approach can effectively improve the success rate and reliability of single-frequency and single-epoch attitude resolution.

Experimental Results of Attitude Determination Functional Algorithms Implementation in Strapdown Inertial Navigation System.

Strapdown inertial navigation system (SINS) software developers are usually mainly focused on the attitude determination algorithm design and characteristics. Such an algorithm can be based on different mathematical apparatus. An approach to the derivation of attitude determination algorithm equations in strapdown inertial navigation system is proposed. This algorithm is based on direct heading, pitch, and roll calculation. The qualitative differences between the proposed algorithm and the one using a transformation matrix are noted. The main objective of the paper is direct attitude angles calculation algorithm application possibilities analysis in real SINS operating conditions. The analysis is based on a comparison of the proposed algorithm with another frequently used attitude determination algorithm based on the transformation matrix. Attitude determination algorithms performance investigation results based on car and helicopter experimental tests are presented.

Attitude determination and control for the deployment preparation phase of a space tether mission

A compact and low-cost architecture for the sensor and actuators of a deorbit device based on an electrodynamic tether, together with the corresponding attitude determination and control algorithms, is proposed and studied through numerical simulations. The solution, aimed at the tether deployment preparation phase, is based on four sensors (gyroscope, magnetometer, coarse sun sensors and GNSS), magnetorquers for the attitude control, a multiplicative Extended Kalman Filter, and the construction of two independent control laws for the detumbling of the deorbit device and the subsequent deployment pointing stabilization phase. The latter involves the alignment of the longitudinal axis of the deorbit device along a given direction different from nadir with an error below 10°. Monte Carlo analysis revealed the existence of an optimal gain for the control law in the detumbling phase that yields a detumbling time of around one orbit revolution only. The deployment pointing phase was also investigated through Monte Carlo analysis, for which initial conditions, errors in the attitude sensors, and uncertainties in the inertial properties of the device and the residual magnetic dipole were varied. The numerical results indicate that the proposed architecture and algorithms fit the requirements and are suitable for space tether missions in Low Earth Orbit.

A Spacecraft Attitude Determination and Control Algorithm for Solar Arrays Pointing Leveraging Sun Angle and Angular Rates Measurements

The capability to orient the solar arrays of a spacecraft toward the Sun is an ultimate asset for any attitude determination and control subsystem (ADCS). This ability should be maintained in any operative circumstance, either nominal or off-nominal, to avoid the loss of the entire space-borne system. The safe mode implementation should guarantee a positive power generation from the solar arrays, regardless of the health status of the satellite platform. This paper presents a solar array pointing algorithm, to be executed on-board, with a minimal set of sensors and actuators. In fact, the sensors are limited to the solar arrays, exploiting the current/voltage sensing capacity of the electrical power subsystem to measure the Sun angle with respect to the arrays normal, and to the angular rates sensors. The actuators are required to provide a torque only along two axes and, thus, a reduced actuation capacity is still manageable by the proposed algorithm. The paper describes the algorithm, both in the Sun direction determination and in the Sun pointing control capacity. The achieved performance is outlined, considering either an ideal system or a realistic one, being the latter affected by sensors and actuators limitations. The actuation by means of momentum exchange devices or magnetic torquers is discussed, with the purpose to prove the wide applicability range of the presented algorithm, which is capable to guarantee solar array orientation with a minimal hardware set.

Constrained Wrapped Least Squares: A Tool for High-Accuracy GNSS Attitude Determination

Attitude determination is a popular application of Global Navigation Satellite Systems (GNSS). Many methods have been developed to solve the attitude determination problem with different performance offerings. We develop a constrained wrapped least-squares (C-WLS) method for high-accuracy attitude determination. This approach is built on an optimization model that leverages prior information related to the antenna array and the integer nature of the carrier-phase ambiguities in an innovative way. The proposed approach adopts an efficient search strategy to estimate the vehicle's attitude parameters using ambiguous carrier-phase observations directly, without requiring prior carrier-phase ambiguity fixing. The performance of the proposed method is evaluated via simulations and experimentally utilizing data collected using multiple GNSS receivers. The simulation and experimental results demonstrate excellent performance, with the proposed method outperforming the ambiguity function method, the constrained LAMBDA and multivariate constrained LAMBDA methods, three prominent attitude determination algorithms.

측정치 시간지연을 가진 전자광학 추적장비의 초기 자세 결정 알고리즘

In order to have accurate target positions of the EOTS(Electro-Optical Tracking System), more accurate navigation outputs are required. An IMU(Inertial Measurement Unit) can be attached to the EOTS to have high rate INS ouputs. Due to the time-delay of the vehicle’s navigation outputs, it is not easy to have accurate target positions. When the vehicle moves at high speed and with high maneuverability, the accuracy becomes even worse. In this paper, an initial attitude determination algorithm of the EOTS with measurement time-delay is proposed. In order to compensate the measurement time-delay, the time-delay variable is augmented into the integrated Kalman filter for the IMU of EOTS and vehicle’s measurement output. The proposed algorithm was evaluated for sensor’s model-based measurement generator outputs, and a land vehicle experiments were performed. The evaluation results show that the proposed algorithm compensates the measurement time-delay well and gives more accurate initial attitude.

Attitude determination for nano-satellites \u2013 II. Dead reckoning with a multiplicative extended Kalman filter

This paper is the second part of a series of studies discussing a novel attitude determination method for nano-satellites. Our approach is based on the utilization of thermal imaging sensors to determine the direction of the Sun and the nadir with respect to the satellite with sub-degree accuracy. The proposed method is planned to be applied during the Cubesats Applied for MEasuring and LOcalising Transients (CAMELOT) mission aimed at detecting and localizing gamma-ray bursts with an efficiency and accuracy comparable to large gamma-ray space observatories. In our previous work we determined the spherical projection function of the MLX90640 infrasensors planned to be used for this purpose. We showed that with the known projection function the direction of the Sun can be located with an overall accuracy of sim 40^prime. In this paper we introduce a simulation model aimed at testing the applicability of our attitude determination approach. Its first part simulates the orbit and rotation of a satellite with arbitrary initial conditions while its second part applies our attitude determination algorithm which is based on a multiplicative extended Kalman filter. The simulated satellite is assumed to be equipped with a GPS system, MEMS gyroscopes and the infrasensors. These instruments provide the required data input for the Kalman filter. We demonstrate the applicability of our attitude determination algorithm by simulating the motion of a nano-satellite on Low Earth Orbit. Our results show that the attitude determination may have a 1sigma error of sim 30' even with a large gyroscope drift during the orbital periods when the infrasensors provide both the direction of the Sun and the Earth (the nadir). This accuracy is an improvement on the point source detection accuracy of the infrasensors. However, the attitude determination error can get as high as 25^{circ } during periods when the Sun is occulted by the Earth. We show that following an occultation period the attitude information is immediately recovered by the Kalman filter once the Sun is observed again.

Applications of a Single-Vector Inertial Aiding Scheme for 3U CubeSats

This work presents the design and performance analysis of attitude determination algorithms for CubeSats that fuse rate gyros with a single vector measurement using a sensor set consisting of an inertial measurement unit and a three-axis magnetometer. An extended Kalman filter is used to fuse sensor measurements to estimate the spacecraft’s attitude statistics in three dimensions. The observability (deterministic and stochastic) of the algorithms is assessed for a variety of orbit geometries and CubeSat attitude dynamics. Further, a stochastic observability test is implemented to identify conditions under which the attitude determination filter will converge as the Earth’s magnetic field varies during orbit. This paper demonstrates that the filter converges within two orbits using CubeSat representative altitudes and estimate spacecraft attitude with bias of and estimation errors of (3-) using orbital simulations with a commercial-grade inertial measurement unit.

Replacement of In-Orbit Spacecraft Attitude Determination Algorithms with Adaptive Neuro-Fuzzy Inference System via Subtractive Clustering

Traditional spacecraft attitude determination algorithms suffer from accuracy versus computational load dilemma. As algorithm complexity increases, its computational load increases and also its accuracy. This limits algorithm applicability in real-time (In-Orbit) environment. In this article, a solution based on Adaptive Neuro-Fuzzy Inference System (ANFIS) has been developed. The number of inputs to ANFIS is 12, which implies an extremely large number of rules of the membership functions to be utilized. Consequently, the proposed solution blows up. Hence, a clustering technique should be utilized in order to minimize the number of rules. Design simulations of the former Egyptian spacecraft EGYPTSAT-1 have been utilized as test case. During the standby operational mode, the spacecraft is assumed to have attitude errors within ±10°. ANFIS is a multi-input single-output algorithm. Therefore, a separate ANFIS is developed for each one of the attitude angles. Each one of them is trained based on two data sets, provided by TRIAD and Q-method simulators. Thus, six ANFISs are developed. The results have shown that the developed ANFISs can work in the stand-by operational mode and provide attitude estimates of ±10°. Moreover, the average execution time for ANFIS is about 40% of the average execution time for the analogous Cascade-Forward Neural Network algorithms (CFNN) and 25% of the Extended Kalman Filter average execution time. The computational overhead of the proposed ANFIS algorithms is constant regardless of the attitude determination or estimation algorithm to be replaced by ANFIS. Consequently, very accurate and sophisticated models could be built in order to provide training data set and then replaced by ANFIS without increasing the ANFIS computational load.

An Improved Single-Epoch Attitude Determination Method for Low-Cost Single-Frequency GNSS Receivers

GNSS attitude determination has been widely used in various navigation and positioning applications, due to its advantages of low cost and high efficiency. The navigation positioning and attitude determination modules in the consumer market mostly use low-cost receivers and face many problems such as large multipath effects, frequent cycle slips and even loss of locks. Ambiguity fixing is the key to GNSS attitude determination and will face more challenges in the complex urban environment. Based on the CLAMBDA algorithm, this paper proposes a CLAMBDA-search algorithm based on the multi-baseline GNSS model. This algorithm improves the existing CLAMBDA method through a fixed geometry constraint among baselines in the vehicle coordinate system. A fixed single-baseline solution reduces two degrees of freedom of vehicle rigid body, and a global minimization search for the ambiguity objective function in the other degree of freedom is conducted to calculate the baseline vector and its Euler angles. In addition, in order to make up for the shortcomings of short baseline ambiguity in complex environments, this paper proposes different validation strategies. Using three low-cost receivers (ublox M8T) and patch antennas, static and dynamic on-board experiments with different baseline length set-ups were carried out in different environments. Both the experiments prove that the method proposed in this paper has greatly improved the ambiguity fixing performance and also the Euler angle calculation accuracy, with an acceptable calculation burden. It is a practical vehicle-mounted attitude determination algorithm.

Replacement of In-Orbit Modern Spacecraft Attitude Determination and Estimation Algorithms with Neural Networks

In-orbit spacecraft attitude determination or estimation algorithms are considered to be of utmost importance and criticality. In the current research article, several In-Orbit attitude determinations and estimation algorithms are reviewed. These algorithms are TRIAD, Q-method, and Extended Kalman Filter (EKF). Three analogous algorithms are developed based on Cascade-Forward Neural Networks (CFNN) in order to replace these traditional in-orbit estimation and determination algorithms. In order to prove the concept, the former Egyptian spacecraft EGYPTSAT-1 is utilized as a test case. The objective of the developed CFNNs is to mimic the performance of the presented attitude determination and estimation algorithms. The performance of the proposed CFNNs is evaluated. The proposed CFNN algorithms have the same accuracy level of TRIAD, Q-method, and EKF. The maximum error achieved has been ±0.1° with an average execution time about half of the average execution time of EKF. The proposed CFNN are proven to be generic and could replace any determination or estimation algorithm within the same accuracy levels. The computational load of CFNN is independent of the complexity level of the attitude determination or estimation algorithm that it tries to mimic. This enables the usage of more elaborated models to increase the accuracy within the same computational load.