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

This paper derives a novel initial alignment method for the strapdown inertial navigation system (SINS), which transforms the attitude alignment into an attitude estimation problem. The process model of the proposed initial alignment method by attitude estimation is established by decomposition of the attitude matrix. The measurement model is constructed based on a generalized velocity integration formula that can integrate the inertial measurements over certain fixed time intervals. The contributions of the work presented here are twofold. First, the attitude estimation-based structure enables the proposed method to estimate the gyroscope biases other than the attitude quaternion, which is celebrated for the low-cost SINS. The second is the application of the proposed generalized velocity integration formula to attenuate the accumulated errors in vector observations caused by the traditional velocity integration formula. Experimental road tests are performed with a low-cost SINS, which validate the efficacy of the proposed method.

Initial Alignment by Attitude Estimation for Strapdown Inertial Navigation Systems

This paper proposes an ingenious alignment scheme for a Doppler velocity log-aided strapdown inertial navigation system with only the initial velocity and position information. The proposed scheme decomposes the task into two tightly coupled subproblems. First, an optimization-based coarse alignment (OBCA) method is developed to derive the constant attitude at the very start of the alignment. During the OBCA process, the required velocity and position are all approximated using their initial values. Second, a nonlinear-filtering-based fine alignment (NFFA) is developed to refine the attitude and calculate the real-time velocity and position. In an NFFA, the standard inertial navigation equations are used directly as the process model, which, therefore, can track the vehicle maneuverability during the alignment period. The NFFA is carried out again from the very start, initialized with the roughly known attitude by OBCA and the known initial velocity and position information. This scheme necessitates the recording of the sensor data during the OBCA. The experimental results show that the proposed method can not only align the attitude to high precision within very short time, but also determine the velocity and position with satisfied accuracy.

Initial Alignment for a Doppler Velocity Log-Aided Strapdown Inertial Navigation System With Limited Information

In this paper, the in-motion coarse alignment (IMCA) for odometer-aided strap-down inertial navigation system (SINS) is investigated with the main focus on compensating for the dynamic errors of gyroscope induced by severe maneuvering. A new Kalman-filtering-based IMCA method for an odometer-aided SINS is presented. A novel closed-loop approach to estimating the attitude matrix from the current body frame to the initial body frame is proposed, in which the attitude error between the closed-loop calculation and the true attitude matrix is first estimated, and then, the estimated attitude matrix is obtained by refining the closed-loop calculation with the estimated attitude error. A linear state-space model for the attitude error is derived, and then, a Kalman filter is employed to track the attitude error. Experimental results illustrate that the proposed closed-loop approach can estimate the attitude matrix from the current body frame to the initial body frame better than the existing open-loop approach, which results in improved alignment accuracy as compared with the existing optimization-based alignment method for the odometer-aided SINS when the vehicle maneuvers severely.

Kalman-Filtering-Based In-Motion Coarse Alignment for Odometer-Aided SINS

To enhance the performance of the navigation system under the complex underwater environment, a hybrid interacting multiple model (HIMM) aided inertial navigation system (INS)/Doppler velocity logs (DVL) integration solution is proposed. First, to employ the acoustic Doppler current profiler mode of DVL, a novel INS/DVL mechanism is constructed where the water current velocity is estimated in real time and both bottom-track and water-track velocity measurements of DVL are involved in the observation vector. Meanwhile, to deal with the outliers and observation noises in the DVL's measurements, a HIMM algorithm is proposed to adaptively select the proper models to describe the changing environment. Simulations and field test are conducted to evaluate the effectiveness of the proposed algorithm, where the interacting multiple model (IMM) algorithm is employed for comparison. The results indicate that the proposed HIMM-aided INS/DVL integration solution shows superiority than the traditional IMM method when the observation noises and outliers exist. Meanwhile, the proposed integration scheme can successfully bridge the DVL's bottom-track outages.

A Hybrid IMM Based INS/DVL Integration Solution for Underwater Vehicles

The in-flight alignment is a critical stage for airborne INS/GPS applications. The alignment task is usually carried out by the Kalman filtering technique that necessitates a good initial attitude to obtain satisfying performance. Due to the airborne dynamics, the in-flight alignment is much difficult than alignment on the ground. This paper proposes an optimization-based coarse alignment approach using GPS position/velocity as input, founded on the newly-derived velocity/position integration formulae. 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 one degree accuracy in ten seconds. 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 (I): Application to In-flight Alignment

Inertial navigation applications are usually referenced to a rotating frame. Consideration of the navigation reference frame rotation in the inertial navigation algorithm design is an important but so far less seriously treated issue, especially for super high-speed flying vehicles or the future ultraprecision navigation system of several meters per hour. A rigorous approach is proposed to tackle the issue of navigation frame rotation in velocity/position computation by use of the newly-devised velocity/position integration formulae in the Part I companion paper. The two integration formulae set a well-founded cornerstone for the velocity/position algorithms' design that makes the comprehension of the inertial navigation computation principle more accessible to practitioners, and different approximations to the integrals involved give birth to various velocity/position update algorithms. Two-sample velocity and position algorithms are derived to exemplify the design process. In the context of level-flight airplane examples, the derived algorithm is analytically and numerically compared with the typical algorithms that exist in the literature. The results throw light on the problems in existing algorithms and the potential benefits of the derived algorithm.

Velocity/Position Integration Formula Part II: Application to Strapdown Inertial Navigation Computation

With the development of high-accuracy inertial navigation system inertial sensors, such as ring laser gyroscopes and atomic spin gyroscopes, it is increasingly important to improve the strapdown inertial navigation algorithms to match such high-accuracy inertial sensors. For example, the existing inertial navigation algorithms have not taken into account the triple-cross-product term of noncommutativity error. However, theoretical analysis demonstrates that the ignored triple-cross-product term is nonignorable under coning motion with constant angular rate precession environments. In this paper, a new high-accuracy rotation vector algorithm is proposed for strapdown inertial navigation. The Taylor series about time is used for error analysis and optimization of the new algorithm. General maneuvers and coning motion with constant angular rate precession environments are considered in establishing the coefficient equations in the proposed algorithm. Error drift equations are given after the error compensation. Normalized quaternion under coning motion with constant angular rate precession environments and Savage’s severe integrated angular-rate profiles are used to numerically verify the new algorithm. The results indicate that the new high-order attitude updating algorithm can improve inertial navigation accuracy.

High-order attitude compensation in coning and rotation coexisting environment

This paper presents detailed derivations and further explanations of the state transformation extended Kalman filter (ST-EKF) from the common frame error definition perspective. Both the system error and measurement models of strapdown inertial navigation system (SINS)/Odometer (OD) tightly-coupled navigation are derived based on the ST-EKF. Both theoretical analysis and test results indicate the effectiveness of the proposed velocity error definition on mitigating the covariance-inconsistency problem that is caused by the specific force calculation error in the EKF state transition matrix. The excellent covariance-consistency of the ST-EKF makes it not necessary to remove gyro and accelerometer bias errors from the initial alignment Kalman filter states. This phenomenon can ensure the subsequent integrated navigation performance. Single-position ground SINS alignment experiments by using a navigation grade inertial measurement unit (IMU) showed that the estimated yaw angle from the conventional 15-state EKF slowly diverged over time. Furthermore, this phenomenon became more distinct when the initial yaw angle error was larger. In contrast, the estimated yaw angle from the proposed 15-state ST-EKF was significantly more stable and less degraded by large initial yaw angle errors. Long- distance land-vehicle SINS/OD integrated navigation tests also exhibited the ST-EKF's higher positioning and heading accuracy than the EKF.

Xianfei Pan

Papers

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

Velocity/Position Integration Formula (I): Application to In-flight Alignment

Velocity/Position Integration Formula Part II: Application to Strapdown Inertial Navigation Computation

High-order attitude compensation in coning and rotation coexisting environment

Consistent ST-EKF for Long Distance Land Vehicle Navigation Based on SINS/OD Integration