Strapdown Inertial Navigation System Error Model Research Articles

A novel adaptive nonlinear Kalman filter scheme for DVL-aided SINS alignment in underwater vehicles

The rapid and accurate initial alignment of a strapdown inertial navigation system (SINS) aided by a Doppler velocity logger (DVL) still poses a significant challenge in unmanned underwater vehicle navigation. In this study, a novel adaptive nonlinear filtering alignment scheme is developed for a SINS with a large misalignment angle. In previous studies, the frame-inconsistency problem of the nonlinear SINS error model was neglected. Thus, a modified nonlinear error model of a SINS is derived here rigorously as the process model of the nonlinear Kalman filter. In addition, the noise amplification of applying Sage-Husa adaptive Kalman filter (SHAKF) in alignment is analyzed, and a novel arctangent fading memorial factor is introduced to dynamically adjust the weight of current measurements. Simulations and field experiments indicate that the proposed algorithm is efficient in underwater DVL/SINS in-motion alignment. The alignment accuracy and convergence rate of the modified model are significantly improved compared to those of the traditional model. The arctangent fading memorial SHAKF can reliably estimate the measurement noise and improve the performance of alignment.

Analysis of Deflection of Vertical Compensation for Inertial Navigation System

With the development of high-precision inertial navigation systems, the deflection of vertical (DOV), gravity disturbance, is still one of the main error sources that restrict navigation accuracy. For the DOV compensation of the Strapdown Inertial Navigation System (SINS) problem, the influences of the calculation degree of the spherical harmonic coefficient and the calculation error of the DOV on the compensation effect were studied. Based on the SINS error model, the error propagation characteristics of the DOV in SINS were analyzed. In addition, the high-precision global gravity field spherical harmonic model EIGEN-6C4 was established and the influence comparative analysis of the calculation degree of the spherical harmonic coefficient on the DOV compensation of SINS in different regions was carried out. Besides, the influence of the calculation error of the DOV on the compensation was emphatically analyzed. Finally, the vehicle experiment verified the feasibility of compensation in SINS based on the gravity field spherical harmonic model. The simulation and experiment results show that it is necessary to consider the influence of the calculation degree and the calculation error of the DOV on the compensation for long-time high-precision SINS with the position accuracy of 0.3 nm/h, while the SINS with general requirements for position accuracy can ignore the impact.

An Improved MCMC-Based Particle Filter for GPS-Aided SINS In-Motion Initial Alignment

In many practical applications, the initial alignment of the strapdown inertial navigation system (SINS) must be performed under large misalignment angles. However, the error model of SINS in this situation is nonlinear, making it hard to obtain an accurate initial alignment result. Aiming at solving this problem via nonlinear filtering, an improved Markov chain Monte Carlo (MCMC)-based particle filter (PF) algorithm is designed in this article, which uses a square-root cubature Kalman filter (SCKF), PF, and MCMC algorithm synthetically. The algorithm is dedicated to extract particles from the posterior distribution of the state by the improved MCMC algorithm and avoid the particle degeneration and the particle impoverishment in a PF. This can effectively improve the performance of particle filtering for nonlinear systems. Furthermore, to solve the problem caused by the fixed number of iterations in the typical MCMC algorithm, a novel adaptive approach is introduced according to the maximum mean discrepancy. The simulation and experimental results of GPS-aided SINS in-motion initial alignment show that the proposed algorithm can provide good filtering accuracy and have good real-time performance.

Damping Rotating Grid SINS Based on a Kalman Filter for Shipborne Application

The measurement error of the inertial measurement unit (IMU) significantly affects the navigation accuracy of the grid strap-down inertial navigation system (SINS) applied in polar regions. In this paper, the single-axis rotation modulation grid SINS is designed to suppress the navigation error caused by IMU constant error. Then on the basis of rotation modulation scheme, a novel external horizontal damping algorithm based on a Kalman filter is conducted to further suppress the 84.4 min Schuler oscillation caused by IMU random error. The Kalman filter is established based on the error model of shipborne grid SINS. When the reference velocity provided by Doppler velocity log is usable, the Schuler oscillation can be restrained through feedback calibration by calibrating the grid horizontal attitude errors and grid horizontal velocity errors. The simulation results demonstrate that the proposed external horizontal damping algorithm can efficiently suppress the Schuler oscillation, meanwhile compared with traditional external horizontal damping algorithm based on damping network, the proposed algorithm has the advantage of reducing the overshoot errors in the process of state switching.

Application of improved fifth-degree cubature Kalman filter in the nonlinear initial alignment of strapdown inertial navigation system.

This paper addresses the state estimation of the nonlinear initial alignment of the strapdown inertial navigation system (SINS), which mainly focuses on the initial alignment on the swaying base and under the in-motion condition with the measurement uncertainties. In order to achieve a higher alignment precision, stronger numerical stability, and lower computational cost for the initial alignment of SINS on the swaying base, a new discrete large azimuth misalignment error model of SINS is established, and an improved fifth-degree cubature Kalman filter (5th-CKF) algorithm is proposed, which combines the 5th-CKF and a simplified dimensionality reduction filtering algorithm. The 5th-CKF is introduced to solve the nonlinear filtering problem, a simplified dimensionality reduction algorithm is derived to reduce the large calculation values of 5th-CKF. Furthermore, under the Bayesian framework, a novel filtering approach named the fifth-degree variational Bayesian (VB) adaptive cubature Kalman filter is deduced for the in-motion alignment with a large azimuth misalignment angle and unknown and time-varying measurement noise statistics, which combines the iterative VB approach and 5th-CKF. The 5th-CKF is exploited to handle the nonlinear initial alignment model, and the VB approach is utilized to iteratively estimate the sufficient statistics of the measurement noise. Mathematical simulation, turntable, and vehicle experiments are performed to demonstrate the effectiveness and the superiority of the proposed approaches.

A Novel Adaptive H∞ Filtering Method with Delay Compensation for the Transfer Alignment of Strapdown Inertial Navigation Systems.

Transfer alignment is always a key technology in a strapdown inertial navigation system (SINS) because of its rapidity and accuracy. In this paper a transfer alignment model is established, which contains the SINS error model and the measurement model. The time delay in the process of transfer alignment is analyzed, and an H∞ filtering method with delay compensation is presented. Then the H∞ filtering theory and the robust mechanism of H∞ filter are deduced and analyzed in detail. In order to improve the transfer alignment accuracy in SINS with time delay, an adaptive H∞ filtering method with delay compensation is proposed. Since the robustness factor plays an important role in the filtering process and has effect on the filtering accuracy, the adaptive H∞ filter with delay compensation can adjust the value of robustness factor adaptively according to the dynamic external environment. The vehicle transfer alignment experiment indicates that by using the adaptive H∞ filtering method with delay compensation, the transfer alignment accuracy and the pure inertial navigation accuracy can be dramatically improved, which demonstrates the superiority of the proposed filtering method.

A Damping Grid Strapdown Inertial Navigation System Based on a Kalman Filter for Ships in Polar Regions.

The grid strapdown inertial navigation system (SINS) used in polar navigation also includes three kinds of periodic oscillation errors as common SINS are based on a geographic coordinate system. Aiming ships which have the external information to conduct a system reset regularly, suppressing the Schuler periodic oscillation is an effective way to enhance navigation accuracy. The Kalman filter based on the grid SINS error model which applies to the ship is established in this paper. The errors of grid-level attitude angles can be accurately estimated when the external velocity contains constant error, and then correcting the errors of the grid-level attitude angles through feedback correction can effectively dampen the Schuler periodic oscillation. The simulation results show that with the aid of external reference velocity, the proposed external level damping algorithm based on the Kalman filter can suppress the Schuler periodic oscillation effectively. Compared with the traditional external level damping algorithm based on the damping network, the algorithm proposed in this paper can reduce the overshoot errors when the state of grid SINS is switched from the non-damping state to the damping state, and this effectively improves the navigation accuracy of the system.

Autonomous integrated navigation method based on the strapdown inertial navigation system and Lidar

An integrated navigation method based on the strapdown inertial navigation system (SINS) and Doppler Lidar was presented and its validity is demonstrated by practical experiments. A very effective and independent integrated navigation mode is realized that both an inertial navigation system (INS) and Lidar are not interfered with or screened by electromagnetic waves. In our work, the SINS error model was first introduced, and the velocity error model was transformed into body reference coordinates. Then the expression for measurement model of SINS/Lidar integrated navigation was deduced under Lidar reference coordinates. For application of land or vehicle navigation, the expression for the measurement model was simplified, and observation analysis was carried out. Finally, numerical simulation and vehicle test results were carried out to validate the availability and utility of the proposed SINS/Lidar integrated navigation method for land navigation.

Application of Nonlinear H∞ Filtering Algorithm for Initial Alignment of the Missile-borne SINS

The H∞ filtering and Unscented Transformation(UT) algorithm are introduced to deal with the initial alignment error of missile-borne Strapdown Inertial Navigation System(SINS), which is caused by the nonlinear error model and the uncertainty of the disturbance noise. Firstly, on the basis of additional quaternion error, the error model of SINS is built up. Secondly, the nonlinear H∞ filter based on UT and H∞ filtering is constructed, which is with nonlinear approximation ability and strong robustness. Finally, simulations are made compared with UKF and the nonlinear H∞ filter under the conditions of disturbance model of strong wind. The result shows that nonlinear H∞ filter is more stable and faster than UKF under the disturbance conditions of strong wind and can effectively improve the accuracy of initial alignment and robustness of the algorithm.

PMI based nonlinear H∞ estimation of unknown sensor error for INS/GPS integrated system

This paper deals with the problem of robust estimation for time-varying sensor errors of inertial navigation system (INS) and global positioning system integration. A nonlinear strapdown INS error model is established to describe the behavior of the the integrated system. Under assumptions of time-varying bias and noise being L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm bounded, a robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> nonlinear estimator by Krein space theory is proposed and, based on this, a proportional and multi-integral H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> estimator is developed for simultaneous estimation of the navigation states and sensor errors. Finally, a flight experiment is implemented to show the effectiveness of the proposed method.

Robust aspects in dependable filter design for alignment of a submarine inertial navigation system

The strapdown inertial navigation system (SINS) is able to provide continuous estimates of a vehicle’s velocity, position and attitude. As a rule, the SIMS component known as a high accuracy strapdown inertial measurement unit (SIMU) is an exceptionally expensive system. Less expensive SIMUs comprised of low cost sensors suffer from degraded performance, but this can be compensated for, in part, by addition of a velocity data recorder (VDR) to accompany the SINS. In this configuration, the need frequently arises to align the SINS of a submarine to in order to avoid a long run-up of the inertial system before a start command is issued. This in-motion alignment (IMA) can be accomplished by integrating SINS data with some external aiding source, such as the VDR, by using some form of measurement matching method. Accordingly, this paper demonstrates a consistent IMA scheme for a low-cost SIMU using a robust Kalman/\( H_{\infty } \) filter structure. An error model of the SINS is derived in which the state vector includes attitude, velocity, position and sensor errors. Velocity information from the VDR is used as a measurement to the proposed filter. All significant equations concerning navigation are presented in conjunction with argument. Results show the advantages of the approach and emphasize diverse aspects of the SINS.

A theoretical approach to observability analysis of the SDINS/GPS in maneuvering with horizontal constant velocity

A theoretical method for analyzing the observability of a strapdown inertial navigation system (SDINS) integrated with the global positioning system (GPS) is proposed. The analysis is performed based on two types of maneuvers for a vehicle on a horizontal trajectory: level flight with constant north velocity and level flight with constant east velocity. The observability also is analyzed using the convergence theorem, stationary state observability analysis results, and Kalman filter measurement information to rearrange the SDINS error model equation. The state variables are divided into observable and unobservable parts, and determine which state variables are observable and estimable with some errors from the relationship of observable and unobservable state variables. Our results have shown that the north and east axes accelerometer bias errors were unobservable, and that attitude errors, and east and down axes gyro bias errors were estimable with some unknown bias errors. It has been shown that horizontal maneuvering improves the observability of down axis gyro bias error compared with the stationary state, and the estimation errors of the heading error state and east axis gyro bias error are dependent on the magnitude of north velocity. The results of the theoretical observability analysis are confirmed through computer simulation.

Calibration and Initial Alignment of Low Cost MEMS Inertial Navigation Sensors for UAV Application

This work deals with an simple approach to calibrate low cost six degree of freedom MEMS inertial Navigation system to be used in Unmanned Air Vehicle (UAV). The accelerometer and gyroscope are modelled with inter axis misalignment correction. To determine calibration parameters of a tri axis accelerometer at least nine equations will be required to solve for nine unknowns (3 scale factor, 3 zero bias, 3 misalignment angles). In this simple approach three new linear equations were formulated to determine the calibration parameters thereby reducing number of positions needed in multi position test. The formulated methodology for accelerometer is validated by conducting twelve position tests. All combination of positions were attempted iteratively. After identifying the singularities, the study on the results suggests that only six positions are enough to solve nine unknowns. Similar methodology was applied to calibrate tri axial Gyroscope in rate test. Rate test results were studied and analysed with standard values provided my sensor manufacturer. A strap down inertial navigation system (SINS) error model is introduced, and the observability of the SINS error model is analyzed. Then on the basis of this SINS error model and a kalman filter is used to estimate the states of the error models. Based on the analysis of computer simulation results, a fast and precision initial alignment method is proposed for SINS on stationary base.

Study on SRUKF Applied in Initial Alignment with Large Misalignment Angle on Stationary Base of SINS

The initial alignment error model of SINS (Strap-down Inertial Navigation System) with large misalignment angle is nonlinear. The traditional EKF (Extended Kalman Filter) was used to linearization a nonlinear system, but its performance is limited. In this paper we use the SRUKF (Square Root Unscented Kalman Filter) to process this nonlinear system and the results indicate that SRUKF is better than EKF in convergence speed and estimation accuracy.

Initial Alignment for SINS based on Low-cost IMU

The initial alignment is vital to the strapdown inertial navigation system (SINS). In this work, an efficient initial alignment method for SINS based on a six-degree of freedom inertial measurements unit (IMU) is proposed. The three dimensional linear accelerations and angular rates are acquired from a data acquisition board which contains a low-cost IMU. Preprocess the gyro data and modeling the SINS error model for initial alignment. Analysis the observability of this SINS error model and then simplify the model based on the observability. A kalman filter is conducted to estimate the misalignment angle. The results show that the initial alignment method proposed in this paper is advisable for a SINS based on low-cost IMU on a stationary base.

Error Analysis of Strapdown Inertia Navigation System in Tactical Missiles

To clarify the navigation error of strapdown inertial navigation system(SINS) with low navigation accuracy, short working period, and fickle operating environment that installed in tactical missiles, a new navigation error model of SINS was established. Founded by a six dimensional kinematic model of tactical missile and a three dimensional target model, the paper rebuilt the whole course of tactical missile attacking the moving target, where correlative output parameters were used to calculate the navigation error model of SINS simultaneously. Experiment result revealed the influence of different error sources to navigation errors of SINS, which is constructive to the improvement of navigation accuracy of SINS.

SINS/ANS integration for augmented performance navigation solution using unscented Kalman filtering

The fundamental concept of the multisensor integrated navigation system is the utilization of a medium precision INS in conjunction with one or more auxiliary sensors which perform as error bounding sources. Strapdown inertial navigation system (SINS) integrated with astronavigation system (ANS) yields reliable mission capability and enhanced navigational accuracy for spacecrafts. The theory and characteristics of integrated system based on unscented Kalman filtering is investigated in this paper. This Kalman filter structure uses unscented transform to approximate the result of applying a specified nonlinear transformation to a given mean and covariance estimate. The filter implementation subsumed here is in a direct feedback mode. Axes misalignment angles of the SINS are observation to the filter. A simple approach for simulation of axes misalignments using stars observation is presented. The SINS error model required for the filtering algorithm is derived in space-stabilized mechanization. Simulation results of the integrated navigation system using a medium accuracy SINS demonstrates the validity of this method on improving the navigation system accuracy with the estimation and compensation for gyros drift, and the position and velocity errors that occur due to the axes misalignments.

A fast and accurate initial alignment method for strapdown inertial navigation system on stationary base

In this work, a fist and accurate stationary alignment method for strapdown inertial navigation system (SINS) is proposed. It has been demonstrated that the stationary alignment of SINS can be improved by employing the multiposition technique, but the alignment time of the azimuth error is relatively longer. Over here, the two-position alignment principle is presented. On the basis of this SINS error model, a fist estimation algorithm of the azimuth error for the initial alignment of SINS on stationary base is derived fully from the horizontal velocity outputs and the output rates, and the novel azimuth error estimation algorithm is used for the two-position alignment. Consequently, the speed and accuracy of the SINS’s initial alignment is enhanced greatly. The computer simulation results illustrate the efficiency of this alignment method.

Modeling Inertial Sensor Errors Using Autoregressive (AR) Models

The accelerometer and gyro sensor errors of a Strapdown Inertial Navigation System (SINS) consist of two parts: a deterministic part and a random part. The deterministic part includes biases and scale factors, which are determined by calibration and then removed from the raw measurements. The random part is correlated over time and is basically due to the variations in the SINS sensor bias terms. Therefore, these errors are modeled stochastically so that they can be included in the SINS error model. For most of the navigation-grade SINS systems, a first-order Gauss-Markov model with a fairly large correlation time is usually used to describe the random errors associated with inertial sensors. By studying the autocorrelation sequences of the noise components at the outputs of inertial sensors, we have determined that a first-order Gauss-Markov is not adequate to model such noise behavior. This paper offers a new method to model the inertial sensor noise as a higher order autoregressive (AR) process and adaptively estimates the AR model parameters. Three different methods of determining the AR model parameters are investigated, namely: the Yule-Walker (autocorrelation) method, the covariance method and the Burg’s method. The three algorithms were tested with different AR model orders with real SINS static data. The results showed that the Burg’s method gives the minimum prediction mean square estimation error and hence this method was used for generating the applied AR models. In this paper, the current algorithms for modeling inertial sensor errors are introduced. The different algorithms for AR modeling are discussed and their results are presented. The results after applying the Burg’s AR models with different orders are also analyzed.

A fast initial alignment method for strapdown inertial navigation system on stationary base

In this paper a strapdown inertial navigation system (SINS) error model is introduced, and the observability of the SINS error model is analyzed. Then, on the basis of this SINS error model and the analysis of computer simulation results, a fast estimation method of the azimuth error /spl Phi//sub D/ is proposed for the initial alignment of SINS on stationary base. Consequently, the time of initial alignment is reduced greatly. The computer simulation results illustrate the efficiency of this fast initial alignment method.