Space Operations Research Articles

Small-Scale Cosmology Independent of the Standard Model

‘Small-scale cosmology’ is a theory designed to incorporate the linear redshift versus distance relation, which is inferred from observations, into the theoretical framework independent of the global Robertson–Walker–Friedman (RWF)-type models. The motivation behind this is that the RWF cosmological models, based on the assumptions of homogeneity and a constant matter density, as well as the concept of expanding space inherent to them are not applicable on the scales of observations from which the linear Hubble law is inferred. Therefore, explaining the Hubble law as the small redshift limit of the RWF model or as an effect of expanding space is inconsistent. Thus, the Hubble linear relation between the redshift of an extragalactic object and its distance should be considered an independent law of nature valid in the range of the distances where the RWF cosmology is not valid. In general, the theory, based on that concept, can be developed in different ways. In the present paper, ‘small-scale cosmology’ is formulated as a theory operating in the (redshift–object coordinates) space, which allows developing a conceptual and computational basis of the theory along the lines of that of special relativity. In such a theory, the condition of invariance of the Hubble law with respect to a change in the observer acceleration plays a central role. In pursuing this approach, the effectiveness of group theoretical methods is exploited. Applying the Lie group method yields transformations of the variables (the redshift and space coordinates of a cosmological object) between the reference frames of the accelerated observers. In this paper, the transformations are applied to studying the effects of the solar system observer acceleration on the observed shape, distribution and rotation curves of galaxy clusters.

Micro-Doppler Signature Analysis for Space Domain Awareness Using VHF Radar

The large quantity of resident space objects orbiting Earth poses a threat to safety and efficient operations in space. Radar sensors are well suited to detecting objects in space including decommissioned satellites and debris, whereas the more commonly used optical sensors are limited by daylight and weather conditions. Observations of three non-operational satellites using a VHF radar system are presented in this paper in the form of micro Doppler signatures associated with rotational motion. Micro Doppler signatures are particularly useful for characterising resident space objects at VHF given the limited bandwidth resulting in poor range resolution. Electromagnetic simulations of the micro Doppler signatures of the defunct satellites are also presented using simple computer-aided design (CAD) models to assist with interpretation of the radar observations. The simulated micro Doppler results are verified using the VHF radar data and provide insight into the attitude and spin axis of the three resident space objects. As future work, this approach will be extended to a larger number of resident space objects which requires a automated processing.

Cultural Elite in A Local Space

My study focuses on the shapers Debrecen's – the second biggest city of Hungary –  culture, and my research aimed at getting to know the cultural life of Debrecen, the opinion leaders who have the most influence on it, the members of the local cultural elite, and to reveal patterns and trends in their medium as a function of locality. The question was how a cultural elite operating in a local space interprets its role as a culture shaper, what kind of elite image and roles and functions it usually attributes to members of the elite. Semi-structured interviews were conducted between 2017 and 2020 among cultural elite members in Debrecen. I looked for people who had been active in the arts in Debrecen during the period of the research, whose work had been recognised with a state or professional award and/or who had been at the head of a cultural institution in Debrecen during the research period. 

SAGD Trial in Omani Heavy Oil Field Overcomes Suboptimal Conditions

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 215943, “Short Spacing, Lower Viscosity, and Suboptimal Operating Conditions SAGD Trial in Mukhaizna Heavy Oil Field,” by Buthaina S. Al Yahmadi, Rawaa M. Al Aamri, and Walaa S. Al Suqri, Oxy, et al. The paper has not been peer reviewed. _ Mukhaizna is a heavy oil field in southern Oman. It is a multistacked reservoir that has been producing under steamflood since 2007. The main sandstone reservoirs were developed using horizontal producers in each target zone supported by vertical injectors. Although most of the patterns are thermally mature, a few areas still are awaiting steamflood response. To mature these areas, a steam-assisted gravity drainage (SAGD) pilot was evaluated, customized, and implemented using existing patterns and well configurations. Mukhaizna Field The Mukhaizna heavy oil field contains viscous, low-gravity (14–18 °API) crude oil in the shallow Permian-age sands of the Gharif formation. Porosity is very good (25–35%), as is permeability (1,000–10,000 md). The Gharif formation consists of upper, middle, and lower reservoirs. Different injector and producer configurations were evaluated to ensure good production. Because a shale barrier clearly was present in the Gharif formation in most of the area but absent elsewhere, the development of this formation was affected. After evaluation of various pattern-configuration options, a development plan was based on three vertical injectors and three horizontal producers per pattern. Thermal development of the field with steam injection began in July 2007. Steamflood maturity has been inconsistent across the field. Various methods of optimizing steam-injection volumes or steam reshuffling in the offset injectors in some patterns were attempted in order to accelerate thermal maturity, but some horizontal producers were still cold with low inflow. To solve this, a pilot-project area with two stacked horizontal producers was evaluated for SAGD potential. These two producers targeted the same zone, Upper Gharif 2A, in one of the best reservoirs in the field. This area was supported by a horizontal injector that had strong communication with the lower producer, but because of misalignment between the horizontal injector and the upper producer, the upper producer was cold, with its progressive cavity pump at pumpoff condition. To evaluate this SAGD trial and predict performance, two analogs were reviewed to compare reservoir properties and parameters. The first analog, Jackfish1, is considered a successful SAGD project, exceeding 90% of its nameplate capacity since first steam. The second analog is Xinjiang oil field, which was not a successful SAGD project, with a steam/oil ratio (SOR) reaching 4.3. This SAGD trial aimed to enhance the oil production of cold patterns with two stacked wells while gaining an understanding of the potential challenges and opportunities of applying SAGD in the existing well configurations at Mukhaizna. The upper horizontal well was converted to a steam injector with an insulated tubing completion. The nearby horizontal injector was kept at the same injection rate to avoid any changes in operating conditions around the SAGD trial.

Deployment dynamics and experiments of a tendon-actuated flexible manipulator

The quantity of space debris on Earth orbit has escalated tremendously in recent years, presenting a significant hazard to human space operations. It is urgent to develop effective measures to capture and remove various space debris. For this purpose, this paper presents a tendon-actuated flexible deployable manipulator. The flexible manipulator consists of several deployable units connected by Cardan joints and actuated by tendons. Compared with the present technologies for capturing space debris such as rigid robotic arm or flying net, this flexible manipulator is deployable, reusable, lightweight and applicable to the capture of large space debris. In order to investigate its deployment dynamics, an accurate dynamic model of the flexible manipulator is established based on the natural coordinate formulation (NCF) and the absolute nodal coordinate formulation (ANCF). Subsequently, numerical simulations are carried out to study the effects of system parameters and the base satellite on its deployment dynamics. Finally, ground experiments for both deployment and bending of the flexible manipulator are conducted to verify its effectiveness and feasibility.

Irradiation resistance of thermo-optical properties of zirconium diboride by 3 MeV electrons

Due to good thermal conductivity and thermal shock resistance, ultra-high temperature ceramics such as zirconium diboride (ZrB2) have been investigated as promising materials to be used in reusable thermal protection systems TPSs are vital to the heat balance of a spacecraft during atmospheric reentry and subsequent operation in space. Hence, the thermal and optical properties are especially critical for such applications. Meanwhile, radiation exposure in space can pose risks of degrading such material properties, especially over a prolonged mission duration. The interaction of electron radiation-which can be found in the outer Van Allen belt, with ZrB2 has not been studied previously and was chosen as the main scope of this study. An electron source of 3 MeV with different radiation exposure time was used. The response of thermo-optical properties of ZrB2 to increasing electron radiation fluences was investigated. ZrB2 samples were made through spark plasma sintering into sintered pellets and then exposed to 3 MeV electron irradiation. These ZrB2 samples were characterized by their microstructure, thermal conductivity, coefficient of thermal expansion (CTE), emittance, absorptivity, and surface roughness before and after irradiation. It was found that ZrB2’s thermo-optical properties showed high radiation resistance at these fluences, and no apparent microstructural change was observed after irradiation. However, the irradiated samples had, on average, a 29% lower surface roughness than the unirradiated samples, possibly originating from electron sputtering.

On-ground validation of orbital GNC: Visual navigation assessment in robotic testbed facility

AbstractCubeSats have become versatile platforms for various space missions (e.g., on-orbit servicing and debris removal) owing to their low cost and flexibility. Many space tasks involve proximity operations that require precise guidance, navigation, and control (GNC) algorithms. Vision-based navigation is attracting interest for such operations. However, extreme lighting conditions in space challenge optical techniques. The on-ground validation of such navigation systems for orbital GNC becomes crucial to ensure their reliability during space operations. These systems undergo rigorous testing within their anticipated operational parameters, including the exploration of potential edge cases. The ability of GNC algorithms to function effectively under extreme space conditions that exceed anticipated scenarios is crucial, particularly in space missions where the scope of errors is negligible. This paper presents the ground validation of a GNC algorithm designed for autonomous satellite rendezvous by leveraging hardware-in-the-loop experiments. This study focuses on two key areas. First, the rationale underlying the augmentation of the robot workspace (six-degree-of-freedom UR10e robot + linear rail) is investigated to emulate relatively longer trajectories with complete position and orientation states. Second, the control algorithm is assessed in response to uncertain pose observations from a vision-based navigation system. The results indicate increased control costs with uncertain navigation and exemplify the importance of on-ground testing for system validation before launch, particularly in extreme cases that are typically difficult to assess using software-based testing.

A consistent test of equality of distributions for Hilbert-valued random elements

Two independent random elements taking values in a separable Hilbert space are considered. The aim is to develop a test with bootstrap calibration to check whether they have the same distribution or not. A transformation of both random elements into a new separable Hilbert space is considered so that the equality of expectations of the transformed random elements is equivalent to the equality of distributions. Thus, a bootstrap test procedure to check the equality of means can be used in order to solve the original problem. It will be shown that both the asymptotic and bootstrap approaches proposed are asymptotically correct and consistent. The results can be applied, for example, in functional data analysis. In practice, the test can be solved with simple operations in the original space without applying the mentioned transformation, which is used only to guarantee the theoretical results. Empirical results and comparisons with related methods support and complement the theory.

Leveraging open science machine learning challenges for data constrained planetary mission instruments

Abstract We set up two open-science machine learning (ML) challenges focusing on building models to automatically analyze mass spectrometry (MS) data for Mars exploration. ML challenges provide an excellent way to engage a diverse set of experts with benchmark training data, explore a wide range of ML and data science approaches, and identify promising models based on empirical results, as well as to get independent external analyses to compare to those of the internal team. These two challenges were proof-of-concept projects to analyze the feasibility of combining data collected from different instruments in a single ML application. We selected mass spectrometry data from 1) commercial instruments and 2) the Sample Analysis at Mars (SAM, an instrument suite that includes a mass spectrometer subsystem onboard the Curiosity rover) testbed. These challenges, organized with DrivenData, gathered more than 1,150 unique participants from all over the world, and obtained more than 600 solutions contributing powerful models to the analysis of rock and soil samples relevant to planetary science using various mass spectrometry datasets. These two challenges demonstrated the suitability and value of multiple ML approaches to classifying planetary analog datasets from both commercial and flight-like instruments. We present the processes from the problem identification, challenge setups, and challenge results that gathered creative and diverse solutions from worldwide participants, in some cases with no backgrounds in mass spectrometry. We also present the potential and limitations of these solutions for ML application in future planetary missions. Our longer-term goal is to deploy these powerful methods onboard the spacecraft to autonomously guide space operations and reduce ground-in-the-loop reliance.

Electric Sail Test Cube–Lunar Nanospacecraft, ESTCube-LuNa: Solar Wind Propulsion Demonstration Mission Concept

The electric solar wind sail, or E-sail, is a propellantless interplanetary propulsion system concept. By deflecting solar wind particles off their original course, it can generate a propulsive effect with nothing more than an electric charge. The high-voltage charge is applied to one or multiple centrifugally deployed hair-thin tethers, around which an electrostatic sheath is created. Electron emitters are required to compensate for the electron current gathered by the tether. The electric sail can also be utilised in low Earth orbit, or LEO, when passing through the ionosphere, where it serves as a plasma brake for deorbiting—several missions have been dedicated to LEO demonstration. In this article, we propose the ESTCube-LuNa mission concept and the preliminary cubesat design to be launched into the Moon’s orbit, where the solar wind is uninterrupted, except for the lunar wake and when the Moon is in the Earth’s magnetosphere. This article introduces E-sail demonstration experiments and the preliminary payload design, along with E-sail thrust validation and environment characterisation methods, a cis-lunar cubesat platform solution and an early concept of operations. The proposed lunar nanospacecraft concept is designed without a deep space network, typically used for lunar and deep space operations. Instead, radio telescopes are being repurposed for communications and radio frequency ranging, and celestial optical navigation is developed for on-board orbit determination.

Guidance and Control for Safe Contactless Plume Impingement Operations to Detumble an Uncooperative Spacecraft

In recent years, the interest in proximity operations to uncooperative and non-collaborative objects has been growing and and demanding for specific technology advances to tackle these challenging cases of in-orbit servicing and removal missions. Indeed, these architectures hold a crucial role in guaranteeing future sustainable and efficient space operations. One of the main challenges of conducting robotic operations with a chaser in close proximity to an uncooperative object stems from its rotational motion. A tumbling motion of a large target object may require a costly and complex synchronisation of the servicer relative trajectory to the capture point and hinder the safety of operations due to rotating appendages. In this paper, the plume impingement strategy is employed to control the target’s tumbling motion in a contactless fashion, thus guaranteeing feasible approach and capture operations. Specifically, guidance and control strategies to be employed during this delicate and complex operation are devised, focusing on improving the safety of the trajectory while maximising the efficiency of the impingement effect during proximity flight. Simulations discuss the detumbling of a satellite of a large constellation, critically comparing delta-v cost, trajectory safety and overall time of operations.

Trajectory Generation Method for Serial Robots in Hybrid Space Operations

The hybrid space of robots is divided into task space and joint space, with task space focused on trajectory-tracking accuracy, while joint space considers dynamic responsiveness and synchronization. Therefore, the robot-motion control systems need to effectively integrate both aspects, ensuring precision in task trajectory while promptly responding to unforeseen environmental events. Hence, this paper proposes an online trajectory-generation method for robots in both joint and task spaces. In task space, a planning approach is presented for high-precision NURBS curves. The global NURBS curve is segmented into several rational Bezier curves, establishing local coordinate systems for control points. This ensures that all local control points meet the chord error constraint, guaranteeing trajectory accuracy. To address the feed rate dynamic planning issue for segmented curves, an improved online S-shape feed-rate scheduling framework is introduced. This framework dynamically adjusts the current execution speed to meet task requirements. In joint space, an offline velocity planning based on a time synchronization scheme and a multi-dimensional synchronization technique based on the principle of spatial-coordinate system projection are proposed. Building upon the offline scheme, it allows for the modification of the target state for any sub-dimension during the motion process, with the remaining dimensions adapting accordingly. Simulation and experimentation demonstrate that the two proposed online trajectory generations for robot motion spaces, while ensuring task trajectory accuracy, effectively handle external unexpected events. They ensure joint synchronization and smoothness, carrying significant practical implications and application value for the stability of robot systems.

Deep learning‐based space debris detection for space situational awareness: A feasibility study applied to the radar processing

AbstractThe increasing number of space objects (SO), debris, and constellation of satellites in Low Earth Orbit poses a significant threat to the sustainability and safety of space operations, which must be carefully and efficiently addressed to avoid mutual collisions. The space situational awareness is currently addressed by an ensemble of radar and radio‐telescopes that detect and track SO. However, a large part of space debris is composed of very small and tiny metallic objects, very difficult to detect. The authors demonstrate the benefits of using deep learning (DL) architectures for small space object detection by radar observations. TIRA radio telescope has been simulated to generate range‐Doppler maps, then used as inputs for object detection exploiting You‐Only‐Look‐Once (YOLO) frameworks. The results demonstrate that the object detection by using YOLO algorithms outperform conventional target detection approaches, thus indicating the potential benefits of using DL techniques for space surveillance applications.

Between Sea and Sky: Understanding Liability for Private and Commercial Space Operations

The legal framework for commercial space activities has been an emerging issue in recent decades. Understanding and addressing liability in space activities is crucial for the sustainable and responsible development of the commercial space industry, analogous to laying the foundation for a sturdy structure that can withstand the challenges of the ever-evolving space frontier. This article explores the concept of liability for private and commercial space launches and its importance in ensuring the safe and responsible operation of activities in space. Examining liability in lex maritima and commercial space law involves drawing parallels between the regulations governing both domains and uncovering potential opportunities for learning from existing legal frameworks. The analysis considers liability in various maritime zones, such as the territorial sea, high sea, and deep-sea bed, and draws comparisons to liability in the territory, space, and celestial body. It discusses the challenges and implications of addressing liability in space activities, including the allocation of liability, the protection of public safety, and the preservation of space as a shared resource.

Safety analysis of evaluation and acceptance processes for space systems and operations based on system-theoretic approach

The proposed analysis consists of identifying systemic aspects that can influence safety and mission fulfillment in the Evaluation and Acceptance Processes of Space Systems and Operations for Launch through the application of System-Theoretic Process Analysis, a technique capable of identifying potential hazardous design and operational flaws, including system design errors and unsafe interactions among multiple procedures and system components. This research identifies losses, hazards, system-level safety constraints, the control structure of the general system, unsafe control actions, loss scenarios that could occur and related causal factors, detecting improvement possibilities for future verifications, evaluations, approvals, and acceptances of space systems and launch operations. These findings can promote safety in space system designs and operations, supporting the activities conducted by launch vehicle and payload developers, certification authorities, and launch centers management, enabling means to proactively act in order to mitigate risks, avoiding unsafe actions and undesired system behaviors, or even to mitigating their consequences. The practical applications of this work can result in safety and mission fulfillment improvements for safety management systems, launch approval regulations and standards; launch operation procedures; space systems design; vehicle, payload, and ground support equipment productions; systems testing; and launch authorization processes.

An introductory review of swarm technology for spacecraft on‐orbit servicing

AbstractThis review paper presents a comprehensive evaluation and forward‐looking perspective on the underexplored topic of servicing target objects using spacecraft swarms. Such targets can be known or unknown, cooperative or uncooperative, and pose significant challenges in modern space operations due to their inherent complexity and unpredictability. Successfully servicing space objects is vital for active debris removal and broader on‐orbit servicing tasks such as satellite maintenance, repair, refueling, orbital assembly, and construction. Significant effort has been invested in the literature to explore the servicing of targets using a single spacecraft. Given its advantages and benefits, this paper expands the discussion to encompass a swarm approach to the problem. This review covers various single‐spacecraft approaches and presents a critical examination of the existing, although limited, body of work dedicated to servicing orbital objects using multiple spacecraft. The focus is also broadened to include some influential studies concerning the characterization, capture, and manipulation of physical objects by general multiagent systems, a subject with significant parallels to the core interest of this manuscript. Furthermore, this article also delves into the realm of simultaneous localization and mapping, highlighting its application within close‐proximity operations in space, especially when dealing with unknown uncooperative targets. Special attention is paid to the benefits that this field can receive from distributed multiagent architectures. Finally, an exploration of the promising field of swarm robotics is presented, with an emphasis on its potential to revolutionize the servicing of orbital target objects. Concurrently, a survey of general research directly engaging swarms in the orbital context is conducted. This review aims to bridge the knowledge gap and stimulate further research in the underexplored domain of servicing space targets with spacecraft swarms.

Berthing proximity maneuvers and trajectory planning of a space manipulator via Kane’s formulation

On-orbit servicing is one of the most challenging tasks of the recent space era. Space Manipulator Systems (SMS) can represent viable technological solutions for several space operations, such as in-situ refueling, repairing of operating spacecraft, or debris grappling. Regardless of the specific task, SMS must approach the target object and then establish a physical connection with it using a single or more robotic arms. This work considers a space vehicle equipped with a pair of two-link robotic arms, with the intent of efficiently designing and simulating the overall spacecraft dynamics until contact takes place. The links that compose each arm are modeled as rigid bodies, assuming relatively slow dynamics. Instead, flexibility is introduced in the model of the rotary joints. The overall dynamics is investigated using Kane's methodology, which is general, highly systematic, and joins the advantages of both the Newton/Euler and the Lagrange formulation. Both SMS and the target, assumed as noncooperative, are placed in low Earth orbit, in close proximity. Trajectory planning of the robotic arm is investigated, while considering the effect of the arm motion on the overall attitude dynamics. Precise attitude maneuvering is mandatory in order that grappling be successfully completed. To do this, a quaternion-based, globally stable attitude feedback law is designed, implemented, and tested. Actuation is demanded to an arrangement of control momentum gyroscopes. These devices are modeled with the inclusion of gyroscopic coupling effects, and are driven by means of suitable steering laws, for the purpose of pursuing the desired attitude control action. Accurate modeling of SMS, with also the inclusion of disturbances due to joint flexibility, in conjunction with the use of suitable feedback attitude control and steering laws for both the robotic arms and the actuation devices, allows obtaining the desired variables, i.e. (i) the motor torques (for steering both the joints and the attitude devices) and (ii) the constraint actions (forces and torques). A Monte Carlo analysis points out effectiveness of the control architecture proposed in this study in the challenging mission scenario of interest.

Koopman Operator theory applied to Lambert’s problem with a spectral behavior analysis

Lambert’s problem has been long studied in the context of space operations; its solution enables accurate orbit determination and spacecraft guidance. This work presents an approximate-analytical solution to Lambert’s problem using the Koopman Operator (KO). In contrast to previous methods in the literature, the KO provides the analysis of a nonlinear system by seeking a transformation that embeds the nonlinear dynamics into a global linear representation. The new methodology to solve for Lambert solutions proposed in this paper considers the position of the system’s eigenvalues on the phase plane, evaluating accurate state transition polynomial maps for a computationally efficient propagation of the dynamics. The minimum-energy and minimum-Δv solutions to Lambert’s problem are found using the KO. The spectral behavior of the solutions is studied and a deeper understanding of the dynamical system is provided. The methodology and solutions are compared in accuracy and performance with other techniques found in the literature, highlighting the benefits of the newly developed analytical approach over classical numerical methodologies.

Planar soft space robotic manipulators: Dynamic modeling and control

Space robots have proven their ability to accomplish many space missions impossible or dangerous for the human. However, the conventional space robots suffer from the low adaptability, heavy structures, and the low safety. In this regard, the bio-inspired soft robots, composed of the soft material, have been emerged to overcome these shortcomings and to expand the space missions’ diversity. The potential of soft robots for space applications has recently been investigated in the literature. Although the dynamic modeling and control of soft robotic arms are complicated due to their infinite degrees of freedom, soft manipulators are anticipated to provide the adaptive capture of targets, confined space operations, and the long-distance handling of space facilities. In this regard, a general novel dynamic modeling algorithm is presented here for soft space robotic manipulators (SSRM) in a specified orientation based on the generalized Jacobian method. The proposed algorithm could be employed for different numbers of soft manipulator constant-curvature elements and avoids numerical singularities using the Taylor expansion as well. In addition, the generalized Jacobian matrix is defined to compute the velocity of any arbitrary point on the soft manipulator for contact dynamics objectives. Accuracy of the proposed dynamic model has been verified via comparison to the simulation results of the existing fixed-base soft manipulators. Moreover, performance of the proposed model has been more investigated through two numerical simulation case studies. The first case verifies that the dynamic responses of the floating SSRM follows the physical principles. While the second one addresses the configuration tracking problem of the floating SSRM exposing a computed torque control scheme. The obtained results indicate the effectiveness of the presented dynamic modeling algorithm and the proposed control scheme.

A fuzzy adaptive complementary filter for attitude estimation based on norm judgment

Unmanned aerial vehicle (UAV) has great application prospect because of its capability of three-dimensional space operation. The reliability of attitude and heading reference system (AHRS) for UAV attitude estimation is crucial for the application of UAV. When a UAV is subjected to unknown electromagnetic interference and force interference in flight, its attitude detection system can suffer from reduced accuracy or even failure. In this paper, a fuzzy adaptive complementary filter (CF) for attitude estimation based on norm judgment is proposed to solve the problem that the sensor is easily disturbed by the complex flight environment and the fixed filter parameters are difficult to obtain the UAV attitude accurately under different flight states. Firstly, the correction model of the gyroscope, which includes four filter parameters, namely accelerometer weight, magnetometer weight, proportional gain P and integral gain I, is established. Secondly, the influence of the four parameters on the estimation accuracy is analyzed. Finally, the adaptive adjustment rules are designed to adjust the filter parameters online and thus achieve the accurate and reliable measurement of UAV attitude. The feasibility of the proposed algorithm is verified through static, dynamic and interference experiments with the specially designed AHRS test platform. And the results show that the attitude estimation algorithm designed in this paper can ensure the high accuracy of the system in both steady state and high-speed rotation, shield the pitch and roll angles from the acceleration of motion, and keep the yaw angle from the external magnetic field.