The in-flight alignment is a critical stage for airborne inertial navigation system/Global Positioning System (INS/GPS) applications. The alignment task is usually carried out by the Kalman filtering technique that necessitates a good initial attitude to obtain a satisfying performance. Due to the airborne dynamics, the in-flight alignment is much more difficult than the alignment on the ground. An optimization-based coarse alignment approach that uses GPS position/velocity as input, founded on the newly-derived velocity/position integration formulae is proposed. Simulation and flight test results show that, with the GPS lever arm well handled, it is potentially able to yield the initial heading up to 1 deg accuracy in 10 s. It can serve as a nice coarse in-flight alignment without any prior attitude information for the subsequent fine Kalman alignment. The approach can also be applied to other applications that require aligning the INS on the run.

Velocity/Position Integration Formula Part I: Application to In-Flight Coarse Alignment

Adetailed survey ispresentedoftheliteratureonattituderepresentationdatingfromtheearlyworkofEulerand Hamilton to recent publications in e elds such as navigation and control. The scope is limited to the development of the aircraft kinematic transformation equations in terms of four different attitude representations, including the well-known Euler angles, the Euler-axis rotation parameters, the direction cosines, and the Euler ‐Rodrigues quaternion.Theemphasisisdirectedattheapplicationofthequaternionformulationtoaircraftkinematics.Results are presented that reinforce observations that the quaternion formulation, typically implemented to eliminate singularities associated with the Euler angle formulation, is far superior to the other commonly used formulations based on computational efe ciency alone. A development of quaternion constraints necessary to independently constrain roll, pitch, yaw, bank angle, elevation angle, and/or azimuth angle is presented. For verie cation of simulation codes, a general closed-form solution to the quaternion formulation, for the case of constant rotation, is also presented. Additionally, a discussion is provided of numerical integration methods and numerical errors for the quaternion formulation. This discussion is especially important for simulations that may still utilize a common error reduction scheme originally developed for analog computers.

Review of Attitude Representations Used for Aircraft Kinematics

This paper deals with the problem of state estimation for the integration of an inertial navigation system (INS) and Global Positioning System (GPS). For a nonlinear system that has the model error and white Gaussian noise, a predictive filter (PF) is used to estimate the model error, and based on this, a modified iterated extended Kalman filter (IEKF) is proposed and is called predictive iterated Kalman filter (PIKF). The basic idea of the PIKF is to compensate the state estimate by the estimated model error. An INS/GPS integration system is implemented using the PIKF and applied to synthetic aperture radar (SAR) motion compensation. Through flight tests, it is shown that the PIKF has an obvious accuracy advantage over the IEKF and unscented Kalman filter (UKF) in velocity.

Predictive Iterated Kalman Filter for INS/GPS Integration and Its Application to SAR Motion Compensation

The inertial navigation system (INS)/GPS integration system is designed by employing an adaptive filter that can estimate measurement noise variance using the residual of the measurement To verify the efficiency of the proposed loosely-coupled INS/GPS integration system, simulations were performed by assuming that GPS information has large position errors The simulation results show that the proposed integration system with the adaptive filter is more effective in estimating the position and attitude errors than a system that uses the extended Kalman filter

INS/GPS Integration System using Adaptive Filter for Estimating Measurement Noise Variance

INS algorithm using quaternion model for low cost IMU

The psi-angle model and the equivalent tilt (ET) model have been widely used for in-flight alignment (IFA) to align and to calibrate a strapdown inertial navigation system (SDINS) on a moving base. However, these models are not effective for a system with large attitude errors because the neglected error terms in the models degrade the performance of a designed filter. In this paper, with an odometer as an external aid, a velocity-aided SDINS is designed for IFA. Equivalent error models applicable to IFA with large attitude errors are derived in terms of rotation vector error and additive and multiplicative quaternion errors. It is found that error models in terms of additive quaternion error (AQE) become linear. Thus the proposed error models reduce unmodeled error terms for a linear filter. From a number of van tests, it is shown that the proposed error models effectively improve the performance of IFA.

Comparison of SDINS in-flight alignment using equivalent error models

The conventional linearized error models of strapdown inertial navigation system( SDINS ) are found not to be effective to represent the nonlinear characteristics of navigation error propagation in case of the system which causes the large navigation errors. To represent the large attitude error of the SDINS, the rotation vector error is introduced and the relationship between the rotation vector error and the quaternion error is derived. Using this relationship the nonlinear error models of the SDINS are presented with the rotation vector error and the quaternion error, respectively. And it is shown that the nonlinear SDINS error models presented here are equivalent to each other. In addition it is shown that in the case of the system with the small enough attitude error, the nonlinear error models can be reduced to the conventional linearized error models.

Equivalent nonlinear error models of strapdown inertial navigation system

This paper addresses the performance comparisons of the GPS pseudorange and pseudorange rate measurements in the tightly coupled INS/GPS Navigation systems Even though the two measurements have the same ability in estimating level attitude errors, pseudorange rate has an advantage in improving estimating heading attitude error performance The performance of pseudorange and pseudorange rate measurements is compared in numerical simulations and van test

An Attitude Error Estimation Performance Comparison of Tightly Coupled INS/GPS Navigation System using Different Measurements

In guided missile systems, reducing terminal-position error is the primary objective of the inertial navigation system. As a seeker is used to sense and track a target, the critical function of the inertial navigation system is to provide the seeker with accurate missile attitude information and help the seeker to keep tracking a target continuously. As inertial sensor body and missile body alignment errors are taken into account, it is desirable to minimize the alignment errors between the missile seeker and the attitude of inertial navigation system. Among the alignment errors, this paper addresses the methods of measuring and compensating misalignment between inertial sensor body and housing frame and shows test results of several experiments.

http://www.ndsl.kr/soc_img/society/kimst/GSGGBW/2012/v15n4/GSGGBW_2012_v15n4_374.pdf

A Study on Methods of Measuring and Compensating Misalignment between Inertial Sensor Body and Housing Frame

An approach to improve the performance of SDINS and GPS integrated system for bank-to-turn flight vehicles is described. Then, it is shown through the simulation that a specific gyro misalignment error results in an increased heading error of SDINS. A new modelling method is presented herein for identifying of sensor and attitude error. The main advantage of the proposed method is that it not only estimates the gyro misalignment error of SDINS, but also improves estimate performance of heading error of SDINS in the presence of the gyro misalignments.

Heung-Won Park

Papers

Comparison of SDINS in-flight alignment using equivalent error models

Equivalent nonlinear error models of strapdown inertial navigation system

An Attitude Error Estimation Performance Comparison of Tightly Coupled INS/GPS Navigation System using Different Measurements

A Study on Methods of Measuring and Compensating Misalignment between Inertial Sensor Body and Housing Frame

Performance improvement of SDINS attitude error estimation using GPS for bank-to-turn flight vehicle