Attitude Update Research Articles

A High-Accuracy Star Centroid Extraction Method Based on Kalman Filter for Multi-Exposure Imaging Star Sensors.

A multi-exposure imaging approach proposed in earlier studies is used to increase star sensors' attitude update rate by N times. Unfortunately, serious noises are also introduced in the star image due to multiple exposures. Therefore, a star centroid extraction method based on Kalman Filter is proposed in this paper. Firstly, star point prediction windows are generated based on centroids' kinematic model. Secondly, the classic centroid method is used to calculate the coarse centroids of the star points within the prediction windows. Lastly, the coarse centroids are, respectively, processed by each Kalman Filter to filter image noises, and thus fine centroids are obtained. Simulations are conducted to verify the Kalman-Filter-based estimation model. Under noises with zero mean and ±0.4, ±1.0, and ±2.5 pixel maximum deviations, the coordinate errors after filtering are reduced to about 37.5%, 26.3%, and 20.7% of the original ones, respectively. In addition, experiments are conducted to verify the star point prediction windows. Among 100 star images, the average proportion of the number of effective star point objects obtained by the star point prediction windows in the total object number of each star image is calculated as only 0.95%. Both the simulated and experimental results demonstrate the feasibility and effectiveness of the proposed method.

A Multiple-Step, Randomly Delayed, Robust Cubature Kalman Filter for Spacecraft-Relative Navigation

This study is focused on addressing the problem of delayed measurements and contaminated Gaussian distributions in navigation systems, which both have a tremendous deleterious effect on the performance of the traditional Kalman filtering. We propose a non-linear, multiple-step, randomly delayed, robust filter, referred to as the multiple-step, randomly delayed, dynamic-covariance-scaling cubature Kalman filter (MRD-DCSCKF). First, Bernoulli random variables are adopted to describe the measurement system in the presence of multiple-step random delays. Then, the MRD-DCSCKF uses the framework of the multiple-step randomly delayed filter, based on a state-augmentation approach, to address the problem of delayed measurements. Meanwhile, it depends on a dynamic-covariance-scaling (DCS) robust kernel to reject the outliers in the measurements. Consequently, the proposed filter can simultaneously address the problem of delayed measurements and inherit the virtue of robustness of the DCS kernel function. The MRD-DCSCKF has been applied to vision-based spacecraft-relative navigation simulations, where quaternions are adopted to represent spacecraft’s attitude kinematics, and the attitude update is completed with quaternions and generalized Rodrigues parameters. Monte Carlo simulations have illustrated that MRD-DCSCKF is superior to other well-known algorithms by providing high-accuracy position and attitude estimations in an environment with different delay probabilities and/or different outlier-contamination probabilities. Therefore, the proposed filter is robust to delayed measurements and can suppress outliers.

Retracted] Motion Control and Tracking Control of UAV Based on Adaptive Sensor

In order to meet the requirements of UAV motion control and tracking control, an adaptive sensor‐based technology is proposed. The main content of the technology is based on the mathematical model of the adaptive sensor, through the quaternion attitude update model, using nonlinear attitude SVDCK filtering and dynamic adaptive adjustment factors and other technologies, and finally through simulation experiments and analysis to build the research means of UAV motion control and tracking control system. The experimental results show that the roll Angle, pitch Angle, and yaw Angle of SVDCKF are 1.703, 1.972, and 1.928, respectively. By adjusting the dynamic adaptive factor, the attitude‐filtering algorithm reduces the error of the attitude solution and improves the robustness of the attitude solution under high dynamic conditions. Conclusion. The technology research based on adaptive sensor can meet the requirements of UAV motion control and tracking control.

A high-accuracy SINS attitude update algorithm based on Legendre polynomial

The large-acceleration motion of HFV (hypersonic flight vehicle), the high-speed rolling of spinning missile, and the large-maneuver flight of fighter aircraft has put forward higher performance demand for SINS (strapdown inertial navigation system). The high-accuracy positing will be realized under the high-dynamic maneuver environment after decreasing measurement error of IMU (inertial measurement unit), meanwhile the algorithm of SINS must be improved. The conventional algorithm calculates the flight attitude with determining the compensation term of coning error, after ignoring the high-order term of the Bortz equation. To improve the algorithm accuracy of SINS under high-dynamic maneuver environment, a high-accuracy algorithm, which uses Legendre polynomial to complete angular velocity function approximation and takes the numerical method of quaternion differential equation as core, is proposed herein. The high-order coning error is compensated in the numerical solving period in the proposed novel algorithm, because no approximation exists in deducing process. The attitude calculating simulations are finished in coning motion condition and high-dynamic maneuver condition respectively. Compared with the quadruple-cross-product compensation algorithm which has the highest accuracy at present, the attitude error of proposed algorithm is less than its 1/3 in coning motion condition. And algorithm accuracy is raised an order of magnitude under the high-dynamic maneuver environment. The high-accuracy algorithm based on Legendre polynomial has reference significance for accurate positing of future HFV, atomic gyroscope INS research and high-accuracy algorithm design of SINS.

Implementation of a real-time star centroid extraction algorithm with high speed and superior denoising ability.

Star tracker is the most precise attitude measuring device, and its advantages include a high resolution and high update rate. Star centroid extraction, which is a very time-consuming process, has great influence on the attitude update rate. This paper proposes a real-time star centroid extraction algorithm based on a field programmable gate array. First, a 1D top-hat filter is used for star segmentation, which is suitable for both uniform and nonuniform background conditions. Second, multichannel image data is reorganized together into a complete frame through image stitching, which prevents the star spots on the channel boundary from being divided into different parts. Finally, star coordinates are extracted by the center-of-mass algorithm. For an image sensor with a resolution of 2048×2048 pixels, simulation results conducted by a ModelSim simulator show that the star centroid processing time of a single frame is roughly 5.2 ms. Real night experiments demonstrate that the standard deviation of a star centroid error is within 10-2 pixel and the standard deviation of attitude is (2.6 2.2 12.0) arcseconds, which proves that the proposed star centroid extraction algorithm can work continuously and stably.

A 3D Attitude Estimation Method Based on Attitude Angular Partial Feedback for Polarization-Based Integrated Navigation System.

Polarization (POL) navigation is inspired by insects’ behavior of precepting celestial polarization patterns to orient themselves. It has the advantages of being autonomous and having no accumulative error, which allows it to be used to correct the errors of the inertial navigation system (INS). The integrated navigation system of the POL-based solar vector with INS is capable of 3D attitude determination. However, the commonly used POL-based integrated navigation system generally implements the attitude update procedure without considering the performance difference with different magnitudes of the angles between the solar-vector and body-axes of the platform (S-B angles). When one of the S-B angles is small enough, the estimated accuracy of the attitude angle by the INS/POL is worse than that of the strapdown inertial navigation system. To minimize the negative impact of POL in this situation, an attitude angular adaptive partial feedback method is proposed. The S-B angles are used to construct a partial feedback factor matrix to adaptively adjust the degree of error correction for INS. The results of simulation and real-world experiments demonstrate that the proposed method can improve the accuracy of 3D attitude estimation compared with the conventional all-feedback method for small S-B angles especially for yaw angle estimation.

Compensation Filtering for Spacecraft Attitude Estimation Using Error-Covariance Reconstruction

Traditional spacecraft attitude estimation algorithms normally require the assumption that the true quaternion approximates to the estimated value. Otherwise, it may lead to a large truncation error. However, this assumption is difficult to be always satisfied during practical applications. To alleviate it, this article proposes a new scheme to reconstruct the error covariance matrix to minimize this truncation error. Specifically, the recursive formulas of measurement updates used in traditional algorithms are recalculated with the quaternion derived from the attitude update, which can reduce the influence caused by the initial conditional errors and inaccurate attitude estimations. This new scheme is then applied to the quaternion attitude estimators. It is shown that the error covariances of the proposed algorithms are theoretically bounded. Simulations for a low-earth-orbit spacecraft state estimation are performed. Through updating the estimated quaternion and then reconstructing the error covariance, the comparison results show that the proposed algorithms thus reduce the introduction of truncation error and thus achieve better performance than traditional algorithms in terms of robustness and convergence rate.

High Update Rate Attitude Measurement Method of Star Sensors Based on Star Point Correction of Rolling Shutter Exposure.

Attitude update rate is one of the important indicators of star sensor performance. In order to resolve the problem of the low attitude update rate of star sensors, this paper proposes a star sensor attitude update method based on star point correction of rolling shutter exposure. Based on the characteristics of the asynchronous exposure of the rolling shutter, recursive estimation of the motion attitude and the corrected star point information were combined to realize multiple updates of the attitude in a single frame of the star map. Simulation and experimental results proved that the proposed method could increase the attitude update rate of a star sensor by 15 times, up to 150 Hz.

Fast Star Matching Method Based on Double K-Vector Lookup Tables for Multi-Exposure Star Trackers.

A high update rate is always one of the vital indices of star trackers. By recording star positions at N moments within a single star image, the multi-exposure imaging approach (MEIA) proposed in an earlier study can improve the attitude update rate of star trackers by N times. Unfortunately, when the existing star matching method is adopted to match the observed and predicted stars in MEIA, the matching time is significantly increased with the increase in multi-exposure times, N, or the number of navigation stars, M, which sharply affects the MEIA’s performance. Therefore, a fast star matching method based on double K-vector lookup tables (DKVLUTs) is proposed to address the above issue. In this method, the information of all predicted stars is used to establish the DKVLUT, and thus, the speed of the whole matching process between observed and predicted stars would be increased effectively by means of the DKVLUT. Both simulations and experiments are conducted to verify the performance of the proposed method. The results both show that the matching time of the proposed method is reduced by nearly one order of magnitude compared with that of the existing method, which demonstrates the feasibility and effectiveness of the proposed method.

Node Attitude Aware Information Dissemination Model Based on Evolutionary Game in Social Networks

The information dissemination in social networks is affected by many factors. However, node attitude which is an important influence factor of information dissemination in social network have not been fully considered in the previous works. Aiming at the problem of the influence of node attitude on information dissemination, this paper proposes an information propagation model based on evolutionary game. Firstly, from the individual point of view, the node’s attitude update rules are defined according to non-Bayesian social learning rules. Secondly, an inter-node game matrix based on attitude value is established. Based on the evolution analysis paradigm, an information dissemination model based on node attitude is established. The equilibrium solution of dynamic equations is replicated for both positive and negative attitudes, and the corresponding equilibrium points are stabilized. The validity of the proposed model is verified by numerical analysis and simulation experiments. They all show that the different attitudes of nodes play an important role in information dissemination.

Attitude Output of Strapdown Inertial Navigation System Based on Laser Gyro

Aiming at the real-time problems of signal acquisition, attitude calculation and data exchange of strapdown inertial navigation system, the data exchange between the core device of three-axis screw instrument and three-axis accelerometer sensor inertial unit (IMU) is analyzed. The RS-232 serial interface and can bus interface are adopted, which can not meet the requirements of high-speed sampling and real-time data transmission of each sensor. A new method based on FPGA dual port RAM and dual DSP is proposed Speed data access mode, through the main control CPU clock synchronization, can effectively solve the bottleneck problem of data communication between IMU attitude data and core equipment, and realize the rapid response ability of vehicle navigation system. Experiments and simulations show that the highest frequency attitude update rate of the method can reach 2000kHz, which can effectively solve the input and output data and navigation calculation ability, and improve the maneuverability of the carrier.

Conditional equivalence between Extended Kalman filter and complementary filter for two-vector gyro-aided attitude determination

Extended Kalman Filter (EKF) and Complementary Filter (CF) are the two most commonly-used attitude determination algorithms in inertial and magnetic measurement units. It is known that the only difference between the a posterior attitude estimates provided by EKF and CF respectively is the gain matrix (GM) assigned to innovation for attitude update. Through mathematical derivation, it is concluded that the GM of EKF can be simplified to the one of CF, which means that CF is an approximation to EKF. Monte Carlo simulations were done to validate what influence of these simplifications is put on the performance of EKF. The main finding is EKF is more stable than CF in condition of low sampling rate, and hence CF must rely more on the measurements of gyroscope for attitude determination to improve its stability.

A correlational inference-based unscented total Kalman filter for integrated navigation

An unscented total Kalman filter (UTKF) estimator with nonlinear dynamic errors-in-variables (DEIV) model is derived based on correlational inference. The proposed UTKF considers all random errors in both system and observation equations and is a Jacobian matrix free alternative to the existing TKF estimators. In particular, this estimator is applied to the inertial navigation system (INS)/ultra-wideband (UWB) integration, in which the marginalised unscented transformation (MUT) as well as the use of generalised Rodrigues parameter (GRP) for attitude updates are embedded into the UTKF to improve the computational efficiency and deal with the dimensional mismatching problems. Furthermore, a theoretical analysis to the effects of DEIV model on total Kalman filter is given. Simulation test has been conducted to compare the performance of UTKF and standard unscented Kalman filter (UKF) in terms of attitude, velocity and position errors. The results demonstrate the feasibility and effectiveness of the proposed estimator.

High‐precision attitude determination and control system design and real‐time verification for CubeSats

SummaryThis paper presents the design and real‐time verification of a high‐precision and low‐cost attitude determination and control system (ADCS) for CubeSat based on a micro‐electro‐mechanical (MEMS) gyroscope. The CubeSat new missions require accurate and sophisticated ADCS with attitude drift adjustment. Moreover, designing an effective ADCS for the CubeSat poses a difficult challenge. The satellite comprises of a two‐unit CubeSat, which denotes that the ADCS is designed with small size, tight mass, and energy limitations. The ADCS has been enhanced in the former few years from fairly small resolution of 10 to around 0.6 m. This attitude drift, if not properly compensated, will cause a slow attitude information loss as the error in attitude rises between the actual and estimated. To correct the attitude adrift, the proposed system utilizes a MEMS gyroscope sensor which offers a comparative attitude to the Kalman filter for estimated attitude update. Real‐time verification and validation for the ADCS are performed through Matlab/Simulink environment and lab testing to prove the efficacy of the proposed system. Simulation of the ADCS shows accurate results with error of no more than 1°.

Systems Engineering Challenges in Realizations of Spinning Satellite Versus Rotating Payload to Improve Systems Reliability

AbstractSatellites are playing vital role in the astronomical study by scientific community. Whereas making a bigger satellite, catering complex mission requirement for scientific study is not viable due to huge realization duration and launch cost. Configurations of astronomical study satellites are quite different compared to earth observation satellites, in such a way that payloads of former may demand rotating mechanisms. A cost effective spinning satellite configuration is studied to meet the payload rotation requirement for space astronomy exploration. On the other hand, accomplishing the essential requirements is a challenge viz. power generation, stringent payload pointing, attitude updates, telecommand establishment, telemetry links, visibility to data reception ground station for a spinning satellite. This paper is intended to bring out the complexity involved and the systems engineering concepts adopted to achieve the mission goal, mainframe elements redundancy, positive energy balance and high systems reliability to build a cost effective spinning small satellite.

Magnetometer-Based Phase Shifting Ratio Method for High Spinning Projectile’s Attitude Measurement

Accurate measurement of high spinning projectiles' attitude is the basis of guidance and control. In order to reduce the attitude measurement error and improve the attitude update rate, a magnetometer-based phase shifting ratio method is proposed in this paper. This method does not introduce additional installation errors as the existing methods, simplifies the calibration of the extreme value ratio-pitch angle curve, and makes full use of the measurement data of the sensors. The attitude update is synchronized with the magnetometer output without using the local geomagnetic information. Simultaneously, the local geomagnetic errors are avoided. The results of numerical simulation and semi-physical simulation experiments show that compared with the three orthogonal ratio method and the crest and trough method, the proposed algorithm in this paper can increase the attitude update rate by more than 2 times and the attitude calculation accuracy can be enhanced by 30%.

Distributed Parallel Super-Block-Based Star Detection and Centroid Calculation

Due to the inadequacies of the speed of star detection and centroid calculation (SDCC), the applications of high-resolution and high-frame-rate image sensors are greatly limited in star trackers, restricting the performance of the star trackers. To resolve this problem, a novel distributed parallel super-block-based SDCC method is proposed in this paper. In contrast to the previous SDCC methods, the proposed method divides the star images into several sub-images and processes these sub-images in parallel. Then, by using a super-block-based method and a distributed shared memory-based method to process the stars in sub-images (sub-stars) and in adjacent sub-images (boundary stars), respectively, the position information of all the stars are detected during the parallel scan of the sub-images. The proposed method exhibits a speed that is up to $4 \,\, \times $ M times faster than the previous SDCC methods in processing the star images that are divided into M sub-images. Experimental results demonstrate that the proposed method is correct and effective. It is applicable to the use of most high-performance image sensors and resolves the performance limitation of star trackers to achieve better attitude accuracy and attitude update rate.

3 차원 비행 제어를 위한 회전 행렬 자세 갱신 방법

In this research, an attitude update method using rotation matrix is verified and validated. First, a continuous time rotation matrix update formula is derived newly without any assumptions or approximations. The continuous time method is compared with other existing methods that use quaternion or Euler angles, by a computation experiment of a Matlab Simulink program. The discrete time version of the method is derived and implemented on a quadcopter and validated through a real flight. For a more severe experiment condition, the flight control computer is separately rotated quickly multiple times by hand. From the experimental result, the attitude angle difference between this method and the quaternion method is evaluated.

Attitude Determination Algorithm based on Relative Quaternion Geometry of Velocity Incremental Vectors for Cost Efficient AHRS Design

A novel attitude determination method is investigated that is computationally efficient and implementable in low cost sensor and embedded platform. Recent result on attitude reference system design is adapted to further develop a three-dimensional attitude determination algorithm through the relative velocity incremental measurements. For this, velocity incremental vectors, computed respectively from INS and GPS with different update rate, are compared to generate filter measurement for attitude estimation. In the quaternion-based Kalman filter configuration, an Euler-like attitude perturbation angle is uniquely introduced for reducing filter states and simplifying propagation processes. Furthermore, assuming a small angle approximation between attitude update periods, it is shown that the reduced order filter greatly simplifies the propagation processes. For performance verification, both simulation and experimental studies are completed. A low cost MEMS IMU and GPS receiver are employed for system integration, and comparison with the true trajectory or a high-grade navigation system demonstrates the performance of the proposed algorithm.

A Sequential Multiplicative Extended Kalman Filter for Attitude Estimation Using Vector Observations.

In this paper, a sequential multiplicative extended Kalman filter (SMEKF) is proposed for attitude estimation using vector observations. In the proposed SMEKF, each of the vector observations is processed sequentially to update the attitude, which can make the measurement model linearization more accurate for the next vector observation. This is the main difference to Murrell’s variation of the MEKF, which does not update the attitude estimate during the sequential procedure. Meanwhile, the covariance is updated after all the vector observations have been processed, which is used to account for the special characteristics of the reset operation necessary for the attitude update. This is the main difference to the traditional sequential EKF, which updates the state covariance at each step of the sequential procedure. The numerical simulation study demonstrates that the proposed SMEKF has more consistent and accurate performance in a wide range of initial estimate errors compared to the MEKF and its traditional sequential forms.