Gravitational Apparent Motion Research Articles

Novel Special Orthogonal Group Optimization for Coarse Alignment Method of SINS on a Rocking Base

In order to solve the coarse alignment problem of the strapdown inertial navigation system on a rocking base, a fast coarse alignment method using the Special Orthogonal Group optimization has been proposed in this paper. In this method, based on the alignment idea of tracing gravitational apparent motion in inertial frame, the model of coarse alignment on a rocking base has been established using the Special Orthogonal Group directly. A new attitude error function has been proposed on the basis of the cosines between the measurement vector and predictive vector to describe the error between the estimated attitude and the true one. In order to directly reflect the change in the attitude error in the new innovation term and enable the attitude error to converge to zero as fast as possible, the gradient of the new attitude error function has been selected as the new innovation term to compensate for the attitude in the estimation process. Finally, the stability of the proposed optimization estimation method has been proved by employing the Lyapunov stability theory. Simulation and experiment results show that the method presented in this paper exhibits good performance in terms of alignment accuracy and time and can be applied to coarse alignment under a rocking base under different environments.

A self-alignment method for gravitational apparent acceleration identification and accelerometer bias estimation based on repeated navigation solution.

Estimating inertial measurement unit error without any external reference information has always been a difficult problem. The method based on the reconstruction of the gravitational apparent motion in the inertial frame can estimate the accelerometer bias, but a long identification time is needed to get high alignment accuracy. In order to reduce the convergence time and improve the accuracy of estimation, a fast estimation method based on repetitive navigation under the excitation of swing motion is proposed. Two data processing methods, the forward-forward loop and the backward-forward loop, are studied and compared in this paper. In addition, the influence of data length on the experiment result was analyzed. The simulation and experimental results show that the forward-forward loop calculation cannot solve the contradiction between speed and accuracy, while the backward-forward loop calculation can effectively estimate the accelerometer bias and realize self-alignment, with a short alignment time and high alignment accuracy.

A Newton iterative optimization combined with window loop calculation algorithm for estimating accelerometer bias based on gravitational apparent motion with excitation of swinging motion.

The initial alignment method, including the identification of inertial device error parameters, has always been a key issue in an inertial navigation system (INS). This study focuses on the error caused by the random noise of inertial devices that can be compensated by the reconstruction of gravitational apparent motion in an inertial frame under the condition of swinging motion. Attitude angles and accelerometer bias can also be estimated. However, the analysis and simulation results indicate that the existing methods cannot estimate the gyroscope bias. The accelerometer and the gyroscope bias will change over a long time, which will lead to long-term parameter identification accuracy decline or even failure. In this paper, a parameter identification algorithm based on Newton iterative optimization combined with a window loop calculation is designed to solve these problems. Simulation and turntable tests indicate that the proposed new algorithm can fulfill the initial alignment of strapdown INS under the swinging condition and estimate accelerometer bias effectively. Moreover, the new algorithm improves data utilization, which also has better time sensitivity, and the calculated alignment errors can nearly approach zero.

In-Motion Alignment for a Velocity-Aided SINS With Latitude Uncertainty

For situations where accurate attitude information is needed while the position is not readily available or not necessarily required, such as the attitude heading reference system, this article proposes a velocity-aided in-motion alignment scheme for a strapdown inertial navigation system (SINS) during geographic latitude uncertainty. In the coarse alignment stage, a gravitational apparent motion rebuilding method based on the integral velocity smoothing is designed to roughly determine the attitude and latitude information. Then, the SINS/velocity-integrated navigation method uses the recorded data to complete the fine alignment. Due to the adoption of a well-designed backtracking navigation strategy, the storage space and computation load are reduced to the degree that an ordinary navigation computer can work with. Nine ship tests were carried out and the results show that the proposed method can align the azimuth with an accuracy of 0.04° in a moving environment, which is the same as that of normal in-motion alignment with a known position.

GAM-Based Mooring Alignment for SINS Based on An Improved CEEMD Denoising Method.

To solve the self-alignment problem of the Strapdown Inertial Navigation System (SINS), a novel adaptive filter based on Complementary Ensemble Empirical Mode Decomposition (CEEMD) is proposed. The Gravitational Apparent Motion (GAM) is used in the coarse alignment, and the problem of obtaining the attitude matrix between the body frame and the navigation frame is attributed to obtaining the matrix between the initial body frame and the current navigation frame using two gravitational apparent motion vectors at different moments. However, the accuracy and time of this alignment method always suffer from the measurement noise of sensors. Thus, a novel adaptive filter based on CEEMD using an -norm to calculate the similarity measure between the Probability Density Function (PDF) of each Intrinsic Mode Function (IMF) and the original signal is proposed to denoise the measurements of the accelerometer. Furthermore, the advantage of this filter is verified by comparing with other conventional denoising methods, such as PDF-based EMD (EMD-PDF) and the Finite Impulse Response (FIR) digital low-pass filter method. The results of the simulation and experiments indicate that the proposed method performs better than the conventional methods in both alignment time and alignment accuracy.

An iterative optimization method for estimating accelerometer bias based on gravitational apparent motion with excitation of swinging motion.

Field calibration is an important method to guarantee the accuracy of a strapdown inertial navigation system. Zero velocity update based on the zero-velocity constraint when the carrier is without translational motion is a typical system-level calibration method. In zero velocity update, there is a coupling between biases and horizontal misalignment angles. The accuracy of horizontal misalignment angles is determined by the equivalent accelerometer biases in horizontal directions, which means that improving the accuracy of horizontal angles needs accurate calibration of accelerometer biases. Meanwhile, alignment with gravitational apparent motion is widely used taking advantages of its alignment ability in a swinging condition. But it is an analytical method and cannot calibrate sensor biases and is always dealt as a coarse alignment method. In order to calibrate accelerometer biases and utilize advantages of the alignment method with gravitational motion, a method to estimate accelerometer biases based on an iterative optimization method and gravitational apparent motion is presented in this paper. First, accelerometer biases are introduced to calculate apparent acceleration and an objective function is constructed. Then, Newton's iteration is applied to iteratively optimize the parameters describing gravitational apparent motion and accelerometer biases. As revealed by the theoretical analysis and experimental results, different patterns of gravity and accelerometer biases will be generated when the carrier exhibits a swinging motion; thus, the convergence of the proposed algorithm will be ensured. After accelerometer biases are removed, initial alignment performed with the gravitational apparent motion reconstructed by the estimated parameters gives nearly zero horizontal misalignment angles.

Gravitational Apparent Motion-Based SINS Self-Alignment Method for Underwater Vehicles

To solve the self-alignment problem of strapdown inertial navigation system (SINS) for underwater vehicles, a novel gravitational apparent motion (GAM)-based method is proposed. Different from conventional GAM methods, the proposed GAM method can complete SINS self-alignment under swaying conditions without using the a priori local latitude information. First, we determine the gravity vector in the earth frame and the local latitude by using the gradient descent optimization and certain geometry constraints. Then, the self-alignment process is formulated as an optimization-based alignment quaternion determination problem by constructing an objective function with the estimated gravity vector. We employ gradient descent optimization to achieve the least square solution of the objective function. Thus, the attitude quaternion can be determined according to the quaternion product chain rule. The simulation and experiments results demonstrate the proposed GAM method without using the local latitude achieves an alignment accuracy close to conventional GAM methods during the coarse alignment process.

In-Motion Filter-QUEST Alignment for Strapdown Inertial Navigation Systems

By analyzing the error models of the measured vectors of the gravitational apparent motion, an in-motion filter-QUEST alignment method only with the inertial measurement unit is presented in this paper. The contribution of the proposed method lies in constructing the in-motion model of the measured vectors of the gravitational apparent motion and developing the extracted method to reconstruct the measured vectors. Furthermore, the relationship between the noise characteristic and the moving state of the vehicle is analyzed in detail. Different from the several current techniques, the presented method can be carried out without any other external additional equipment, when the vehicle is in-motion. With the designed real-time wavelet denoising (RWD) method, the high-frequency noises of the measured vectors are filtered. Based on the constructed parameter recognition model of the measured vectors, a robust adaptive Kalman filter is devised to estimate the optimal parameters, which are used to calculate the reconstructed observation vectors. Moreover, the gross outliers, which are contained in the filtered vectors of the RWD, are eliminated effectively. The simulation and the field trial results demonstrate that the presented method is applicable to the in-motion initial alignment, and it can serve as a nice initial alignment method in the follow-on fine alignment process and navigation process.

A Kalman Filter for SINS Self-Alignment Based on Vector Observation.

In this paper, a self-alignment method for strapdown inertial navigation systems based on the q-method is studied. In addition, an improved method based on integrating gravitational apparent motion to form apparent velocity is designed, which can reduce the random noises of the observation vectors. For further analysis, a novel self-alignment method using a Kalman filter based on adaptive filter technology is proposed, which transforms the self-alignment procedure into an attitude estimation using the observation vectors. In the proposed method, a linear psuedo-measurement equation is adopted by employing the transfer method between the quaternion and the observation vectors. Analysis and simulation indicate that the accuracy of the self-alignment is improved. Meanwhile, to improve the convergence rate of the proposed method, a new method based on parameter recognition and a reconstruction algorithm for apparent gravitation is devised, which can reduce the influence of the random noises of the observation vectors. Simulations and turntable tests are carried out, and the results indicate that the proposed method can acquire sound alignment results with lower standard variances, and can obtain higher alignment accuracy and a faster convergence rate.

A Self-Alignment Algorithm for SINS Based on Gravitational Apparent Motion and Sensor Data Denoising.

Initial alignment is always a key topic and difficult to achieve in an inertial navigation system (INS). In this paper a novel self-initial alignment algorithm is proposed using gravitational apparent motion vectors at three different moments and vector-operation. Simulation and analysis showed that this method easily suffers from the random noise contained in accelerometer measurements which are used to construct apparent motion directly. Aiming to resolve this problem, an online sensor data denoising method based on a Kalman filter is proposed and a novel reconstruction method for apparent motion is designed to avoid the collinearity among vectors participating in the alignment solution. Simulation, turntable tests and vehicle tests indicate that the proposed alignment algorithm can fulfill initial alignment of strapdown INS (SINS) under both static and swinging conditions. The accuracy can either reach or approach the theoretical values determined by sensor precision under static or swinging conditions.

A novel self-alignment method for SINS based on parameter recognition and dual-velocity vectors

In this paper, self-alignment problem for strapdown inertial navigation system based on tracing gravity drift in inertial frame and dual-vector attitude determination is studied. Aiming to further ease, the interference from sensor random errors, especially accelerometer random noise, without adding alignment time, a novel alignment method based on integrating gravitational apparent motion to form apparent velocity is designed, using recursive least squares algorithm to recognize the parameters describing the theoretical apparent velocity from the calculated velocity containing random noise. Analysis and simulation indicate that with this method, random noise can be effectively removed compared with the only operation of integration. Meanwhile, a reconstruction algorithm with current recognized parameters for dual-velocity vectors is devised which can fully utilize all measurement information and completely avoid collinear problem. Simulation and turntable results show that compared with the existing integrating methods, the proposed method can acquire sound alignment results with lower standard variances and can improve alignment accuracy with the same alignment time or shorten alignment time with the same accuracy.

An improved self-alignment method for strapdown inertial navigation system based on gravitational apparent motion and dual-vector.

Analysis and simulation results indicate that two problems should be solved when the self-alignment method based on gravitational apparent motion and dual-vector can be used for Strapdown Inertial Navigation System. The first one is how to identify the apparent motion from accelerometer measurement containing random noise and the second is how to avoid the collinear problem between two vectors used in alignment solution. In this paper, a parameter identification and reconstruction algorithm is proposed to solve the first problem and simulation results indicate that proposed algorithm can identify apparent motion from accelerometer measurements effectively; and reconstruction algorithm based on current identified parameters for dual-vector is designed in detail to solve the second problem which can make full use of newest identification and avoid collinear problem completely. Simulation and turntable results show that the proposed alignment method can fulfill self-alignment in a swinging condition and the alignment accuracy can reach the theoretical values determined by the sensor precision.

A novel self-alignment method for SINS based on three vectors of gravitational apparent motion in inertial frame

Based on the alignment idea of tracing gravitational apparent motion in inertial frame, a novel self-alignment and latitude calculation method for Strapdown Inertial Navigation System (SINS) is designed. In this method, the problem of acquiring attitude matrix between body frame and navigation frame is attributed to acquiring the matrix between initial body frame and current navigation frame, and the gravitational apparent motion vectors at three moments are used to construct corresponding vectors and matrix through vector-operation. Meanwhile, the latitude information can be obtained by virtue of the geometric relationships among gravitational apparent vectors. Furthermore, the validity of the proposed method is proved by mathematical proof, and the theoretical expressions for evaluating accuracies of initial alignment and latitude calculation are deduced detailedly. Simulation and turntable results indicate that the proposed method can fulfill self-alignment and latitude calculation under a swinging condition without translational motion.

An initial alignment method for strapdown gyrocompass based on gravitational apparent motion in inertial frame

Inspired by the alignment mechanism of Octans, an initial alignment method for strapdown gyrocompass is designed based on gravitational apparent motion in inertial frame. In this method, the gyro outputs are used to trace the body frame and the measurement from accelerometers are projected to the inertial frame to form the track of gravitational apparent motion. According to the calculations on the vectors involved in this track, the attitude matrix between the inertial frame and navigation frame can be obtained and further alignment can be finished. In order to identify the true gravitational apparent motion from the accelerometer measurement containing random noise as well as to avoid the collinear of vectors in vector operation, a reconstruction algorithm concerning parameter identification and reconstruction of apparent motion is devised and simulated. Simulation and turntable test show that the proposed alignment method can realize self-alignment in a swinging condition. The alignment accuracy is able to reach the theoretical one determined by sensor errors and no external information is needed.