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This paper presents a modified Sage-Husa adaptive Kalman filter-based SINS/DVL integrated navigation system for the autonomous underwater vehicle (AUV), where DVL is employed to correct the navigation errors of SINS that accumulate over time. When negative definite items are large enough, different from the positive definiteness of noise matrices which cannot be guaranteed for the conventional Sage-Husa adaptive Kalman filter, the proposed modified Sage-Husa adaptive Kalman filter deletes the negative definite items of adaptive update laws of the noise matrix to ensure the convergence of the Sage-Husa adaptive Kalman filter. In other words, this method sacrifices some filtering precision to ensure the stability of the filter. The simulation tests are implemented to verify that expected navigation accuracy for AUV can be obtained using the proposed modified Sage-Husa adaptive Kalman filter.

Autonomous underwater vehicle (AUV) has been widely used in ocean exploration, where accurate navigation and positioning ability are essential to ensure the long voyage operation of AUV. Considering the underwater environment, various navigation methods cannot be applied to the AUV, such as optical navigation, radio navigation, and satellite navigation. In response to this problem, a lot of novel navigation methods are studied in [

Since the strapdown inertial navigation (SINS) is with the advantages of strong autonomy, high precision, and full navigation parameters, it is widely used in the navigation system of AUV. However, the navigation error of SINS is accumulated over time, which results in low navigation accuracy. In view of this problem, the Doppler velocimeter (DVL) is combined with SINS in [

For the SINS/DVL integrated navigation system, how to integrate the output information of SINS and DVL to obtain high-precision navigation information is the core issue. Since the Kalman filter is able to estimate the system states in the presence of noises, it is widely applied in the SINS/DVL integrated navigation system. However, the inaccurate measurement model under the time-varying measurement noise results in substantial estimation errors or even filter divergence. To solve this problem, the interacting multiple model algorithm which uses more than one model is proposed in [

In this paper, a modified Sage-Husa adaptive Kalman filter-based SINS/DVL integrated navigation system is proposed to provide the AUV with accurate navigation parameters, where the adaptive update laws of the noise matrix are modified by deleting the negative definite items. Therefore, the filtering convergence can be guaranteed, while the expected filtering accuracy can be obtained.

The rest of this paper is organized as follows. The error equations of SINS and DVL are given in Section

When the AUV moves on the water surface, considering the drift of the gyroscopes and accelerometer, the error equations of SINS are presented.

Define the longitude and latitude as

The horizontal position error equation of SINS is calculated as

The horizontal velocity error equation of SINS is calculated as

The drift of the gyroscope in the navigation coordinate system can be described as

For the four-beam Doppler velocimeter, the calibration coefficient error is defined as

Since

Since the navigation error of SINS is accumulated over time, the four-beam Doppler velocimeter is used to correct the navigation information of SINS. Define the state vector as

Since the velocity is selected as the measurement, the measurement equation is presented as

From equations (

Thus, equation (

By discretizing the state (equation (

Due to the fact that the measurement noises of the Kalman filter equation are usually time-varying and difficult to be accurately predicted in the practical environment, the filter accuracy of the conventional Kalman filter is easy to be decreased and even be divergent. In response to this problem, the Sage-Husa adaptive Kalman filter is proposed to improve the filter performance by estimating the unknown noises, whose calculation loop is presented in Figure

Calculation loop of the modified Sage-Husa adaptive Kalman filter.

with the forgetting factor

To suppress filter divergence,

Thus,

From equation (

In this section, numerical simulations are investigated to verify that expected navigation accuracy can be obtained under the proposed modified Sage-Husa adaptive Kalman filter-based SINS/DVL integrated navigation system for AUV.

The forgetting factor of the modified Sage-Husa adaptive Kalman filter is set as

The simulations are presented in Figures

System states of the Kalman filter for the SINS/DVL integrated navigation system.

Velocities of the SINS and SINS/DVL integrated navigation system.

Velocity errors of the SINS and SINS/DVL integrated navigation system.

Positions of the SINS and SINS/DVL integrated navigation system.

Position errors of the SINS and SINS/DVL integrated navigation system.

For AUV, a modified Sage-Husa adaptive Kalman filter-based SINS/DVL integrated navigation system is designed in this paper to obtain expected navigation accuracy. The negative definite items of adaptive update laws of the noise matrix are deleted to guarantee the positive definiteness of noise matrices, such that the filter stability can be ensured. Simulations are presented to verify that expected navigation accuracy for AUV can be obtained using the proposed filter method.

The data supporting the findings of this study are available within the article.

The authors declare that they have no conflicts of interest.