An Extended Kalman Filter-Based Attitude Tracking Algorithm for Star Sensors

Treatment of Extended Kalman Filter Implementations for the Gyroless Star Tracker

The literature since Apollo contains exhaustive material on attitude filtering, usually treating the problem of two sensors, a combination of state measuring and inertial devices. More recently, it has become popular for a sole attitude determination device to be considered. This is especially the case for a star tracker given its unbiased stellar measurement and recent improvements in optical sensor performance. The state device indirectly estimates the attitude rate using a known dynamic model. In estimation theory, two main attitude filtering approaches are classified, the additive and the multiplicative. Each refers to the nature of the quaternion update in the filter. In this article, these two techniques are implemented for the case of a sole star tracker, using simulated and real night sky image data. Both sets of results are presented and compared with each other, with a baseline established through a basic linear least square estimate. The state approach is more accurate and precise for measuring angular velocity than using the error-based filter. However, no discernible difference is observed between each technique for determining pointing. These results are important not only for sole device attitude determination systems, but also for space situational awareness object localisation, where attitude and rate estimate accuracy are highly important.

Variational Bayesian Iteration-Based Invariant Kalman Filter for Attitude Estimation on Matrix Lie Groups

Motivated by the rapid progress of aerospace and robotics engineering, the navigation and control systems on matrix Lie groups have been actively studied in recent years. For rigid targets, the attitude estimation problem is a benchmark one with its states defined as rotation matrices on Lie groups. Based on the invariance properties of symmetry groups, the invariant Kalman filter (IKF) has been developed by researchers for matrix Lie group systems; however, the limitation of the IKF is that its estimation performance is prone to be degraded if the given knowledge of the noise statistics is not accurate. For the symmetry Lie group attitude estimation problem, this paper proposes a new variational Bayesian iteration-based adaptive invariant Kalman filter (VBIKF). In the proposed VBIKF, the a priori error covariance is not propagated by the conventional steps but directly calibrated in an iterative manner based on the posterior sequences. The main advantage of the VBIKF is that the statistics parameter of the system process noise is no longer required and so the IKF’s hard dependency on accurate process noise statistics can be reduced significantly. The mathematical foundation for the new VBIKF is presented and its superior performance in adaptability and simplicity is further demonstrated by numerical simulations.

A SLIC-DBSCAN Based Algorithm for Extracting Effective Sky Region from a Single Star Image

The star tracker is widely used for high-accuracy missions due to its high accuracy position high autonomy and low power consumption. On the other hand, the ability of interference suppression of the star tracker has always been a hot issue of concern. A SLIC-DBSCAN-based algorithm for extracting effective information from a single image with strong interference has been developed in this paper to remove interferences. Firstly, the restricted LC (luminance-based contrast) transformation is utilized to enhance the contrast between background noise and the large-area interference. Then, SLIC (the simple linear iterative clustering) algorithm is adopted to segment the saliency map and in this process, optimized parameters are harnessed. Finally, from these segments, features are extracted and superpixels with similar features are combined by using DBSCAN (density-based spatial clustering of applications with noise). The proposed algorithm is proved effective by successfully removing large-area interference and extracting star spots from the sky region of the real star image.

Unscented Particle Filter Algorithm Based on Divide-and-Conquer Sampling for Target Tracking

Unscented particle filter (UPF) struggles to completely cover the target state space when handling the maneuvering target tracing problem, and the tracking performance can be affected by the low sample diversity and algorithm redundancy. In order to solve this problem, the method of divide-and-conquer sampling is applied to the UPF tracking algorithm. By decomposing the state space, the descending dimension processing of the target maneuver is realized. When dealing with the maneuvering target, particles are sampled separately in each subspace, which directly prevents particles from degeneracy. Experiments and a comparative analysis were carried out to comprehensively analyze the performance of the divide-and-conquer sampling unscented particle filter (DCS-UPF). The simulation result demonstrates that the proposed algorithm can improve the diversity of particles and obtain higher tracking accuracy in less time than the particle swarm algorithm and intelligent adaptive filtering algorithm. This algorithm can be used in complex maneuvering conditions.

INS/CNS Deeply Integrated Navigation Method of Near Space Vehicles

Celestial navigation is required to improve the long-term accuracy preservation capability of near space vehicles. However, it takes a long time for traditional celestial navigation methods to identify the star map, which limits the improvement of the dynamic response ability. Meanwhile, the aero-optical effects caused by the near space environment can lead to the colorization of measurement noise, which affects the accuracy of the integrated navigation filter. In this paper, an INS/CNS deeply integrated navigation method, which includes a deeply integrated model and a second-order state augmented H-infinity filter, is proposed to solve these problems. The INS/CNS deeply integrated navigation model optimizes the attitude based on the gray image error function, which can estimate the attitude without star identification. The second-order state augmented H-infinity filter uses the state augmentation algorithm to whiten the measurement noise caused by the aero-optical effect, which can effectively improve the estimation accuracy of the H-infinity filter in the near space environment. Simulation results show that the proposed INS/CNS deeply integrated navigation method can reduce the computational cost by 50%, while the attitude accuracy is kept within 10” (3 σ). The attitude root mean square of the second-order state augmented H-infinity filter does not exceed 5”, even when the parameter error increases to 50%, in the near space environment. Therefore, the INS/CNS deeply integrated navigation method can effectively improve the rapid response ability of the navigation system and the filtering accuracy in the near space environment, providing a reference for the future design of near space vehicle navigation systems.

Attitude Angle Compensation for a Synchronous Acquisition Method Based on an MEMS Sensor

As a new type of micro-electro-mechanical systems (MEMS) inertial sensor, the Quartz Vibrating Beam Accelerometer (QVBA) is widely used in intelligent sweeping robots, small aircraft, navigation systems, etc. For these applications, correcting and compensating the attitude angle with the result of acceleration plays an important role to improve the measurement accuracy. The synchronization error between the measurement of the accelerometer and gyroscope attitude angle has an adverse impact on the accuracy of the attitude angle. In this paper, a synchronous acquisition scheme of the accelerometer and gyroscope attitude angle in a strapdown inertial navigation system (SINS) is proposed. At the same time, to improve the sampling accuracy and the conversion speed of QVBA, an improved equal-precision frequency measuring method is also implemented in this paper. The hardware float point unit (FPU) is used to accelerate the calculation of the frequency measurement value. The long-term cumulative error of the frequency measurement value is less than 10−4. The calculation process time from sampling to attitude angle compensation calculation is reduced by 40.8%. This work has played a very good role in improving the measurement accuracy and speed of the SINS.

Motion Blurred Star Image Restoration Based on MEMS Gyroscope Aid and Blur Kernel Correction

Under dynamic conditions, motion blur is introduced to star images obtained by a star sensor. Motion blur affects the accuracy of the star centroid extraction and the identification of stars, further reducing the performance of the star sensor. In this paper, a star image restoration algorithm is investigated to reduce the effect of motion blur on the star image. The algorithm includes a blur kernel calculation aided by a MEMS gyroscope, blur kernel correction based on the structure of the star strip, and a star image reconstruction method based on scaled gradient projection (SGP). Firstly, the motion trajectory of the star spot is deduced, aided by a MEMS gyroscope. Moreover, the initial blur kernel is calculated by using the motion trajectory. Then, the structure information star strip is extracted by Delaunay triangulation. Based on the structure information, a blur kernel correction method is presented by utilizing the preconditioned conjugate gradient interior point algorithm to reduce the influence of bias and installation deviation of the gyroscope on the blur kernel. Furthermore, a speed-up image reconstruction method based on SGP is presented for time-saving. Simulated experiment results demonstrate that both the blur kernel determination and star image reconstruction methods are effective. A real star image experiment shows that the accuracy of the star centroid extraction and the number of identified stars increase after restoration by the proposed algorithm.

Adaptive Square-Root Unscented Particle Filtering Algorithm for Dynamic Navigation

This paper presents a new adaptive square-root unscented particle filtering algorithm by combining the adaptive filtering and square-root filtering into the unscented particle filter to inhibit the disturbance of kinematic model noise and the instability of filtering data in the process of nonlinear filtering. To prevent particles from degeneracy, the proposed algorithm adaptively adjusts the adaptive factor, which is constructed from predicted residuals, to refrain from the disturbance of abnormal observation and the kinematic model noise. Cholesky factorization is also applied to suppress the negative definiteness of the covariance matrices of the predicted state vector and observation vector. Experiments and comparison analysis were conducted to comprehensively evaluate the performance of the proposed algorithm. The results demonstrate that the proposed algorithm exhibits a strong overall performance for integrated navigation systems.

A New Polar Transfer Alignment Algorithm with the Aid of a Star Sensor and Based on an Adaptive Unscented Kalman Filter

Because of the harsh polar environment, the master strapdown inertial navigation system (SINS) has low accuracy and the system model information becomes abnormal. In this case, existing polar transfer alignment (TA) algorithms which use the measurement information provided by master SINS would lose their effectiveness. In this paper, a new polar TA algorithm with the aid of a star sensor and based on an adaptive unscented Kalman filter (AUKF) is proposed to deal with the problems. Since the measurement information provided by master SINS is inaccurate, the accurate information provided by the star sensor is chosen as the measurement. With the compensation of lever-arm effect and the model of star sensor, the nonlinear navigation equations are derived. Combined with the attitude matching method, the filter models for polar TA are designed. An AUKF is introduced to solve the abnormal information of system model. Then, the AUKF is used to estimate the states of TA. Results have demonstrated that the performance of the new polar TA algorithm is better than the state-of-the-art polar TA algorithms. Therefore, the new polar TA algorithm proposed in this paper is effectively to ensure and improve the accuracy of TA in the harsh polar environment.