Slave Inertial Navigation System Research Articles

A high-accuracy system model and accuracy evaluation method for transfer alignment

With the increasing demand for high-accuracy navigation, distributed payloads put forward higher requirements for the initial alignment accuracy of their equipped slave inertial navigation systems (INSs). However, the existing transfer alignment models have poor compensation effect on flexible deformation, resulting in low alignment accuracy. Moreover, these models cannot accurately evaluate the accuracy of transfer alignment due to ignoring the errors of the master INS. To address these two problems, a new high-accuracy transfer alignment system model is established by comprehensively considering errors of the master and slave INSs. Further, the propagation characteristics of the master and slave inertial sensor errors in transfer alignment are analyzed, and the relationship expression between the master and slave inertial sensor accuracy and the transfer alignment accuracy is derived. Thus, the accuracy of transfer alignment can be pre-evaluated according to the master and slave inertial sensor accuracy. The experiment results show that the alignment accuracy of the proposed method is improved by more than 71.56% compared with the traditional methods, and the relative errors between the proposed accuracy evaluation method and the Monte Carlo simulations are less than 9.14%. Thus, the correctness, effectiveness and superiority of the proposed method are verified.

Estimation algorithm of pod installation angles based on cubature Kalman filter

To estimate the installation angles of the pod, a detailed derivation of the attitude transformation relationship between the pod, aircraft, and inertial navigation systems is performed. Based on this, a cubature Kalman filtering algorithm is proposed to estimate the pod’s installation angles. The algorithm architecture integrates the time update part of the Kalman filter and measurement update part of the cubature Kalman filter. This algorithm has been validated through a flight test, demonstrating its effectiveness in estimating the installation angles of the master inertial navigation system relative to the aircraft wing, as well as the slave inertial navigation system relative to the pod frame. After compensating for the installation angles, the standard deviations of roll, pitch, and azimuth between the two inertial systems have significantly improved: roll angle from 0.1414° to 0.0282°, pitch angle from 0.0803° to 0.0335°, and azimuth angle from 0.2629° to 0.0490°.

A fast and accurate transfer alignment method without relying on the empirical model of angular deformation

AbstractThis paper, in allusion to the limitations of traditional transfer alignment methods based on the external measurement equipment or the empirical model of angular deformation, proposes a rapid and accurate transfer alignment method without relying on the empirical angular deformation model. Firstly, the relationship between the actual angular deformation and the angular velocities measured by the gyroscopes in the master and slave inertial navigation systems (INSs) is derived to roughly estimate the angular deformation. Secondly, according to the error characteristics of gyroscopes, the error model of angular deformation is established. Thirdly, expanding the angular deformation error instead of the installation error angle, flexure angle and flexure angle rate into the state vector, a low-order transfer alignment filtering model independent of the empirical angular deformation model is established. The proposed method not only gets rid of the dependence on an empirical angular deformation model, but also realises the rapid and accurate initial alignment of the slave INS without adding any external measurement equipment. The simulations and experiments evidence the validity of the proposed transfer alignment method.

Applied singular value decomposition method in transfer alignment and bias calibration

The transfer alignment accuracy between the master inertial navigation system (MINS), the slave inertial navigation system (SINS) and the online calibration capability of SINS are the important factors that affect the system performance. The traditional Kalman filtering-based transfer alignment method greatly depends on the prior information. The alignment and calibration based on optimisation-based alignment are preliminarily achieved without the prior information, but many deductions are required to achieve an optimal solution. In this study, a novel method aimed at transfer alignment and bias calibration is proposed, which is based on singular value decomposition by the inertial measurement vector matching equation to construct the least-squares solution. The performance of the system is analysed from the transfer alignment accuracy and the inertial instrument error estimation, respectively. The simulation and flight experiment results demonstrate that the proposed method is concise and effective without complex deduction and calculation. The relative attitude angle between MINS and SINS can be estimated accurately as well as the bias of SINS.

Airborne Distributed Position and Orientation System Transfer Alignment Method Based on Fiber Bragg Grating.

With the demand for high resolution remote sensing, load array technology has gradually become an effective measure to improve imaging resolution. However, the external flow and internal engine vibration disturbance may lead to the flexible deformation of wings. The traditional rigid baseline error compensation method cannot solve the problem of serious coupling movement error caused by flexible deformation. To address the problem, a transfer alignment model based on fiber Bragg grating for distributed position and orientation system is proposed in this paper. Firstly, based on the multidimensional requirements of flexible deformation information, the layout scheme of fiber Bragg grating was designed, then the continuous strain in the wing surface was obtained after the quadratic fitting of strain measured by fiber Bragg gratings, and the deformation displacement and angle are calculated. Thirdly, flexible deformation compensation for distributed position and orientation system based on fiber Bragg grating was studied. The state equation including position error, velocity error, misalignment angle, and inertial device error was established. The position and attitude information compensated by the flexible lever arm was used as the quantitative measurement. The filtering estimation improved the measurement accuracy of the slave inertial navigation systems. At last, the experiment was carried out and showed that the accuracy of the transfer alignment has been improved significantly.

Hull Deformation Measurement With Large Angles Based on Inertial Sensors

The partial reference is used in large ships to measure the hull deformation, which is normally realized through the transfer alignment between the master inertial navigation system and the slave inertial navigation system. In recent years, the matching methods based on several inertial measurement units has become the development trend to avoid the initial alignment of the slave system. However, these methods always require that the deformation angle is small and the system model can be regarded as a linear model. The purpose of this article is to solve the large deformation problem through coarse estimation based on the optimized attitude determination and propose an improved transfer alignment method based on the attitude matching in the inertial frame. The coarse estimation does not rely on the deformation model and can decrease the deformation error to a small angle in a short time. Then the system model and the measurement model are built to carry out the attitude matching in the inertial frame, which is stable and can avoid initial alignment. The swing table test show that the proposed method can estimate the large deformation between the two IMUs rapidly and precisely.

회전익항공기에 장착되는 종속 관성항법장치의 초기정렬기법

회전익항공기에 장착되는 종속 관성항법장치의 초기정렬기법

쿼터니언 정합 기반 전달정렬 필터

Transfer alignment, which has been widely researched, is the main process of finding the attitude information of a slave inertial navigation system by using navigation information of a master inertial navigation system (MINS). Transfer alignment algorithms can be classified according to the information of the MINS, such as velocity matching, attitude matching, angular rate matching, and acceleration matching. In this paper, we only consider the attitude matching algorithm and propose a new transfer alignment algorithm based on quaternion information. Moreover, we prove that the proposed algorithm is equivalent to the transfer alignment algorithm based on direction cosine matrix information, which has been used for attitude matching.

Lever Arm Compensation of Autonomous Underwater Vehicle for Fast Transfer Alignment

Transfer alignment is used to initialize SINS (Strapdown Inertial Navigation System) in motion. Lever-arm effect compensation is studied existing in an AUV (Autonomous Underwater Vehicle) before launched from the mother ship. The AUV is equipped with SINS, Doppler Velocity Log, depth sensor and other navigation sensors. The lever arm will cause large error on the transfer alignment between master inertial navigation system and slave inertial navigation system, especially in big ship situations. This paper presents a novel method that can effectively estimate and compensate the flexural lever arm between the main inertial navigation system mounted on the mother ship and the slave inertial navigation system equipped on the AUV. The nonlinear measurement equation of angular rate is derived based on three successive rotations of the body frame of the master inertial navigation system. Nonlinear filter is utilized as the nonlinear estimator for its capability of non-linear approximation. Observability analysis was conducted on the SINS state vector based on singular value decomposition method. State equation of SINS was adopted as the system state equation. Simulation experiments were conducted and results showed that the proposed method can estimate the flexural lever arm more accurately, the precision of transfer alignment was improved and alignment time was shortened accordingly.

Anti-Disturbance Initial Alignment Method Based on Quadratic Integral for Airborne Distributed POS

Airborne distributed position and orientation system (POS) is playing an important role in the high-resolution aerial survey and a remote sensing system. It is composed of a master inertial navigation system (INS), the global navigation satellite system, and several slave INSs. However, the high-frequency vibration disturbance of aircraft engine and the flexure deformation disturbance of lever arm could lead to serious initial alignment errors of slave INSs. In order to solve the problem, an anti-disturbance initial alignment method based on quadratic integral for airborne distributed POS is proposed. A coarse alignment based on quadratic integral in inertial frame is proposed to reduce the disturbances of high-frequency vibration and flexure deformation. Furthermore, the disturbance of flexure deformation is considered as the first-order Markov process, and is added into the fine transfer alignment model. The experimental results verified that the proposed method can effectively improve the initial alignment of the distributed POS, especially the azimuth precision of two slave INSs which are improved by 0.0260° and 0.0167°, respectively.

A unified model for transfer alignment at random misalignment angles based on second-order EKF

In the transfer alignment process of inertial navigation systems (INSs), the conventional linear error model based on the small misalignment angle assumption cannot be applied to large misalignment situations. Furthermore, the nonlinear model based on the large misalignment angle suffers from redundant computation with nonlinear filters. This paper presents a unified model for transfer alignment suitable for arbitrary misalignment angles. The alignment problem is transformed into an estimation of the relative attitude between the master INS (MINS) and the slave INS (SINS), by decomposing the attitude matrix of the latter. Based on the Rodriguez parameters, a unified alignment model in the inertial frame with the linear state-space equation and a second order nonlinear measurement equation are established, without making any assumptions about the misalignment angles. Furthermore, we employ the Taylor series expansions on the second-order nonlinear measurement equation to implement the second-order extended Kalman filter (EKF2). Monte-Carlo simulations demonstrate that the initial alignment can be fulfilled within 10 s, with higher accuracy and much smaller computational cost compared with the traditional unscented Kalman filter (UKF) at large misalignment angles.

Non‐linear estimation of the flexural lever arm for transfer alignment of airborne distributed position and orientation system

As the development of aerial mapping, obtaining the motion parameters of the mapping sensors mounted under the flexural wing of the aircraft is necessary to accomplish the mission. Airborne distributed position and orientation system (DPOS) could be applicable which is composed of master inertial navigation system (INS), several slave INSs and the global positioning system. The slave INS is mounted on the mapping sensor for measuring the motion parameters. However, the flexural deformation of the wing will impose critical influence on the transfer alignment between master and slave INSs. The formed flexural lever arm should be compensated precisely. A non-linear relation between the flexural angle and flexural lever arm variation is proposed, and a novel 27-state non-linear model is established for transfer alignment of airborne DPOS. The non-linear measurement equation of angular rate is derived based on three successive rotations of the body frame of the master INS. Unscented Kalman filter is utilised as the non-linear estimator for its capability of non-linear approximation. It is shown from the simulation results that the proposed method can estimate the flexural angles and flexural lever arm variations more accurately, and the attitude and position accuracy of slave INS is also improved correspondingly.

Research on shipborne transfer alignment under the influence of the uncertain disturbance based on the extended state observer

The process of the transfer alignment for the shipborne inertial navigation system is greatly affected by its external environment. Under the entire influence of its external environment, the structure of the ship will be deformated. First of all, the flexural deformation is analyzed in the environment of the engine vibration and the impact of waves, taking the lever arm effect into consideration. Secondly, the specific force integration matching scheme which is suitable to the moving of carriers in the environment of the low speed is adopted in order to accomplish transfer alignment between master and slave inertial navigation system. Thirdly, a method has been well designed to improve the Kalman filter techniques based on the extended state observer. The usage of the method makes it possible to estimate the disturbance of the uncertain model and realizes dynamic feedback linearization in the inertial navigation system for ship during the process of transfer alignment. Finally, the above theoretical analyses are verified through simulation.

Optimisation-based Transfer Alignment and Calibration Method for Inertial Measurement Vector Integration Matching

The traditional Kalman filtering-based transfer alignment methods largely depend on prior information for initialisation. However, the initialisation process is hard to fulfil on a moving base. In this paper, a type of inertial measurement vector integration matching for optimisation-based transfer alignment and calibration is proposed to estimate the misalignment between the Master Inertial Navigation System (MINS) and Slave Inertial Navigation System (SINS), and main inertial sensor error parameters of SINS, including bias and scale factor error. In contrast to filter techniques, the proposed method has the capability of self-initialisation and provides a new idea to solve the alignment and calibration problem. No prior information is needed. Moreover, the integration time interval for the matching inertial measurement vector is selected by considering both the observation degree of inertial sensor error parameters and the noise effect. Simulation results demonstrate that the proposed method has faster convergence and is more accurate than Kalman filter techniques.

Analytic Coarse Transfer Alignment Based on Inertial Measurement Vector Matching and Real-Time Precision Evaluation

This paper presents an analytic coarse transfer alignment method based on inertial measurement vector matching for the inertial navigation system (INS) on vertically launched missiles from the ground. The alignment problem is transformed into the estimation of the relative attitude between the master INS (MINS) and slave INS (SINS) by decomposing the attitude matrix of SINS. As inspired by the ideology of the traditional analytic alignment method, the measurements from the accelerometers and gyroscopes of MINS and SINS are utilized to construct matching vectors to estimate the relative attitude between them without any initial information. Furthermore, the sensitivity of Euler angles with respect to the inertial sensor errors is analyzed according to the presented coarse transfer alignment principle. An algebraic expression for alignment error estimation is given, and thus the real-time precision evaluation for the presented coarse alignment method is achieved. It allows the system to switch to fine alignment in a timely and accurate manner. The simulation and flight test demonstrate that, compared with the quaternion-optimization-based alignment method proposed by Kang et al. , the presented method has a smaller calculation cost and satisfactory convergence. The corresponding precision evaluation algorithm can describe the trend of true alignment error accurately, and is good enough to judge the moment for switching to the fine alignment.

H∞ filter for flexure deformation and lever arm effect compensation in M/S INS integration

On ship, especially on large ship, the flexure deformation between Master (M)/Slave (S) Inertial Navigation System (INS) is a key factor which determines the accuracy of the integrated system of M/S INS. In engineering this flexure deformation will be increased with the added ship size. In the M/S INS integrated system, the attitude error between MINS and SINS cannot really reflect the misalignment angle change of SINS due to the flexure deformation. At the same time, the flexure deformation will bring the change of the lever arm size, which further induces the uncertainty of lever arm velocity, resulting in the velocity matching error. To solve this problem, a H ∞ algorithm is proposed, in which the attitude and velocity matching error caused by deformation is considered as measurement noise with limited energy, and measurement noise will be restrained by the robustness of H ∞ filter. Based on the classical “attitude plus velocity” matching method, the progress of M/S INS information fusion is simulated and compared by using three kinds of schemes, which are known and unknown flexure deformation with standard Kalman filter, and unknown flexure deformation with H ∞ filter, respectively. Simulation results indicate that H ∞ filter can effectively improve the accuracy of information fusion when flexure deformation is unknown but non-ignorable.

In-situ Bias Estimation of Low Grade Gyroscopes for Ship Launched Flight Vehicles

Abstract The paper presents mechanization of an analytical Transfer Alignment (TA) process and a novel scheme on in-situ bias estimation of Low Grade MEMS Gyroscopes based Inertial Navigation System. The objective of the work presented, is to devise a scheme for estimation of initial vector(s) i.e. velocity, attitude and biases of MEMS gyroscopes of inertial navigation system of flight vehicles being launched from moving ships. Inertial Navigation is a dead reckoning system and prior initialization of velocity and attitude is an essential requirement to achieve minimum Circular-Error-Probable (CEP) at the target point. Establishing the initial vector(s) is straight forward for the flight vehicles being launched from static launchers where the Gravity Vector and Earth Rate Vectors are being measured precisely and utilized for analytical Gyro-Compassing (GC) alignment. The same is not true for moving vehicles like ships, where the reference vectors like Earth Rate and Gravity are not known. Hence, an analytical Transfer Alignment (TA) scheme is developed for pre-initialization of Slave Inertial Navigation System (SINS) on-board flight vehicle with Master Inertial Navigation System (MINS) on-board moving ship. A 5–state Extended Kalman Filter based velocity matching technique is designed and an observability study is presented. The MEMS gyroscopes which have gained importance over their mechanical and optical counterparts are highly reliable, miniature in size and available at low cost. On contrary, these sensors have a poorer day-to-day bias repeatability of the order of 20°/hour which will result into degraded navigation performance. Hence, an attempt was made to devise a scheme to estimate the large biases of SINS, in-situ with external aid from MINS. The presented scheme estimates these gyro biases in tandem with the Transfer Alignment to an accuracy of 1.0°/hour, ensuring convergence within 3 minutes, without compromising on alignment accuracy. A suitable system configuration is conceived based on low grade MEMS gyroscopes and Quartz accelerometers. The total scheme is implemented in real time and experimental results are presented.

Online Estimation of Ship Dynamic Flexure Model Parameters for Transfer Alignment

This paper presents an online approach for estimating the dynamic flexure model parameters in shipboard transfer alignment (TA). Traditionally, the application of Kalman filters (KFs) to the TA process is often restricted because of the lack of real-time information on dynamic flexure characteristics, and a KF designed on the basis of inaccurate parameters of the dynamic flexure model will result in a large alignment error. To overcome this difficulty, a parameter estimation algorithm is proposed in this paper, which utilizes the angular increment difference measured by the master inertial navigation system (MINS) and the slave inertial navigation system. Specifically, the Tufts-Kumaresan method is introduced to compute the unknown parameters of the dynamic flexure model from the angular increment correlation function. Our simulation results show that the proposed method can estimate the dynamic flexure parameters with a high degree of accuracy, even in low signal-to-noise ratio conditions. This parameter estimation method does not require a priori knowledge of dynamic flexure characteristics and, therefore, provides the shipboard sensors with an accurate and rapid-response capability for alignment with the MINS.

An Engineering Accuracy Estimation Method for Transfer Alignment

Aimed at characteristics of transfer alignment on a moving base-guided vehicle, a kind of accuracy estimation method was proposed. The navigation accuracy was mostly caused by attitude error and the simplified relation between transfer alignment error and velocity error was derived according to velocity error formula. After transfer alignment, the system entered into the navigation under similar flight and velocity error was measured in short time, further attitude alignment error was anti-derived. The yaw angle error was estimated by calculating reproducibility of the difference between major and slave inertial navigation system. Pitch and roll angle error were estimated by calculating reproducibility of velocity error between major and slave inertial navigation system. Experiments data show that the alignment accuracy meets the target and it is suitable for engineering application.

Application of Attitude Matrix Row Element Sum Matching in Transfer Alignment

To reduce the calculation brought by attitude angle and attitude matrix matching as well as to insure the transfer alignment accuracy, the paper gives a method that uses slave inertial navigation system (SINS) error model as the state-space model. The complexity of the state equation can be simplified by this method, for the lever-arm effect can be compensated in the observables rather than considering it in the equation of state, in which the inputs do not need to be brought in the equation of state; On the basis of element matching of the attitude matrix with SINS and master inertial navigation system (MINS), the paper raises row elements sum matching method of attitude matrix, which has simpler structure of the observation matrix and lower dimension compared to attitude angle matching and element matching of the attitude matrix, so as to decrease filtering computation. Simulation results have proved that the model and matching algorithm in this paper are effective and the system can achieve higher transfer alignment accuracy.