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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

In-motion alignment of Strapdown Inertial Navigation Systems (SINS) without any geodetic-frame observations is one of the toughest challenges for Autonomous Underwater Vehicles (AUV). This paper presents a novel scheme for Doppler Velocity Log (DVL) aided SINS alignment using Unscented Kalman Filter (UKF) which allows large initial misalignments. With the proposed mechanism, a nonlinear SINS error model is presented and the measurement model is derived under the assumption that large misalignments may exist. Since

With the development of high-frequency, multi-beam Doppler sonar, which can provide bottom velocity measurements with a precision of 0.3% or less with a update rate of up to 5Hz, a wide variety of Doppler-based navigation techniques have been developed [

Due to the random wave motions as well as the dynamics of the vehicle, it is difficult to estimate the attitude to the accuracy of within a few degrees in a short period with the existing coarse alignment methods [

The other main effort to deal with the large misalignments problem is based on such nonlinear filtering methods as the so-called extended Kalman filter (EKF), unscented Kalman filter (UKF), and particle filter (PF). Among these nonlinear filtering methods, the UKF is wildly used due to its elimination of the cumbersome derivation and low computational complexity [

The rest of this paper is organized as follows: Section 2 is devoted to the presentation of the nonlinear DVL-aided IMU alignment model which can tolerate large misalignments. Section 3 presents the mathematical formulas of the UKF and adaptive UKF techniques. In Section 4, the performance of the proposed algorithms are evaluated and compared with real experimental data. The conclusions are drawn in Section 5.

The nonlinear SINS error model proposed in [^{c}^{b}^{b}^{b}^{c}_{ie}_{n}_{m}

Define:

In the error model presented above, all the three misalignment angles are assumed to be large. For real time applications, it is often the case that there are a large uncertainty in heading angle and low uncertainties in leveling angles [

The velocity of Doppler in the local level frame
_{d}

Inserting

Differentiating the velocity of INS and DVL, the measurement model is given below:

The considered nonlinear discrete-time system with additive noise is presented as follows [_{k}^{n}_{k}^{m}_{k}_{k}

With a view of reducing the computational burden, the non-augmented UKF is widely used in such additive noise cases [

Initialization:

Time-updating:

Measurement-updating:

The parameters for calculating the sigma-points are given as follows:
^{(}^{m}^{)} and ^{(}^{c}^{)} represent the mean weight and covariance weight, respectively [_{k}_{∣}_{k}_{−1};

The innovation sequence _{k}_{k}_{k}_{∣}_{k}_{−1} is given as follows:
_{k}_{∣}_{k}_{−1} is obtained from _{ẑkẑk}

As can be seen from _{k}

The residual sequence could also be used with the purpose of obtaining a realistic estimator of the measurement noise covariance. The residual sequence _{k}_{k}_{k}_{k}_{|}_{k}_{−1}) by an extra UT:
_{k}

It can be used in the computation of epoch _{k}

The ship-mounted experimental data were collected to evaluate the performance of the in-motion alignment. The experiment was carried out in Yangzi River. The equipped sensors are listed as follows:

IMU: Consists of three ring laser gyroscopes with drift rate 0.01° / ^{−5}

Bottom-lock Doppler: Provides three-axis transformation velocities with accuracy ±5‰ of speed and update rates up to 1 Hz.

GPS receiver: Provides velocity with precision of about 0.1m/s, position with precision of about 10 m, and update rates up to 1 Hz.

In the experiment, the IMU and the GPS receiver were set up on a vessel. The DVL module was put beneath 1m underwater. The fixing and level arm parameters of devices are shown in

A test is done by intentionally adding large initial attitude errors (100 degrees for heading, 1 degree for roll and pitch). ^{2}/s^{2}). It can also be seen from the figures that the estimation oscillation becomes obvious when shorter window sizes are used. It illustrates that a short window size may lead to unstable estimation. This is similar to the conclusions of AKF [

A test is done by intentionally adding large initial attitude errors (100 degrees for heading, 1 degree for roll and pitch). ^{2}/s^{2}). It can also be seen from the figures that the estimation oscillation becomes obvious when shorter window sizes are used. It illustrates that a short window size may lead to unstable estimation. This is similar to the conclusions of AKF [

A test was designed to evaluate the performance of the estimated measurement noise covariance. The initial attitude error was 100 degrees for heading, 1 degree for roll and pitch, respectively. As can be seen from ^{2}/s^{2}). Therefore, this value was applied in the alignment [^{2}/s^{2})]. In addition, the alignment was also executed with a larger ^{2}/s^{2})] and a smaller ^{2}/s^{2})]. ^{2}/s^{2}) converged more rapidly than that with the value of 0.1 (m^{2}/s^{2}) and 0.001 (m^{2}/s^{2}).As shown in ^{2}/s^{2}) while the convergence time for ^{2}/s^{2}) and 0.001 (m^{2}/s^{2}) were 766 s and 800 s respectively. In a sense, the estimated measurement noise covariance is proved to be realistic. Furthermore, it's clearly shown that the measurement noise covariance plays an important part in the performance of the UKF. Once the

The tests were designed to compare the performance of the UKF and AUKF techniques for their applications in the DVL-aided SINS alignment problem. An example is shown in ^{2}/s^{2}). The window size for both the innovation-based and residual-based AUKF was 100. As can be seen from ^{2}/s^{2})] given for the UKF was very close to the optimal values obtained from the above tests, the trends of the error curves obtained by the UKF and the AUKF methods are similar. Partial magnification of the heading errors are shown in ^{2}/s^{2})] is applied. However, in the case of underwater vehicles, it's very difficult to obtain a prior knowledge of the measurement noise covariance due to unstable Doppler measurements. Though a proper

Regarding the attitude obtained from a high precision INS/GPS integration as reference,

This paper has presented a new alignment scheme for the DVL-aided SINS in-motion alignment which allows large initial misalignments. From the experimental data, it has been clearly shown that the proposed alignment model can be applied for the DVL-aided SINS in-motion alignment with any initial heading errors. As the measurement noise covariance is of great importance to the performance of the UKF, the covariance-matching methods applied in AKF have been extended for use in the Adaptive UKF. By using innovation-based and residual-based AUKF techniques, the measurement noise covariance can be estimated reliably and hence can improve the performance of the UKF. Its performance has been demonstrated with field experimental data.

The first author is sponsored by China Scholarship Council (CSC) for his joint Ph.D. research training at the University of New South Wales, Sydney, Australia.

DVL-aided IMU alignment scheme.

Fixing of experimental devices.

Alignment flowchart.

Heading error comparison with different initial heading errors.

Convergence time comparison with different initial heading errors.

Heading error comparison with extra large initial heading errors.

Estimation of measurement noise covariance with different window sizes by innovation-based AUKF.

Estimation of measurement noise covariance with different window sizes by residual-based AUKF.

Estimation of measurement noise covariance with different initial

Estimation of measurement noise covariance with different initial

Heading error comparisons with different

Attitude error comparison between UKF and AUKFs with initial attitude error of [1°, 100°, 1°].

Partial magnification of the heading error.

Heading accuracy comparison with different window sizes.

Performance comparisons with different

^{2}/s^{2}) |
||
---|---|---|

1e-1 | 0.0629 | 766 |

1e-2 | 0.0282 | 676 |

1e-3 | 0.0367 | 800 |