In this paper, an estimator for underwater DOA estimation is proposed by using a cross-linear nested array with arbitrary cross angle. The estimator excludes the variation acoustic velocity by deriving the geometric relation of the cross-linear array on the proposed algorithm. Therefore, compared with traditional DOA estimation algorithms via linear array, this estimator eliminates systematic errors caused by the uncertainty factor of the acoustic velocity in the underwater environment. Compared with the traditional acoustic velocity independent algorithm, this estimator uses the nested array and improves the performance of DOA estimation. In addition, the estimator is based on arbitrary angle of the cross-linear array, so it is more flexible in practical applications. Numerical simulations are provided to validate the analytical derivations and corroborate the improved performance in underwater environments where the actual acoustic velocity is not accurate.

This paper focuses on a low-complexity one-dimensional (1D) direction-of-arrival (DOA) algorithm with an arbitrary cross-linear array. This algorithm is highly accurate without the performance error usually caused by the uncertainty factor of the wave velocity in the underwater environment. The geometric relationship between two crossed linear arrays is employed to derive the expression of DOA estimation with the finding that this algorithm is capable of excluding the wave velocity variable in the DOA estimation expression. A method without parameter pairing is also proposed to reduce the complexity of this algorithm. Additionally, the influence of wave velocity is analyzed in terms of RMSE c and the Cramer-Rao bound (CRB) for 1D DOA with the arbitrary cross-linear array is established. The simulation results demonstrate that the proposed algorithm can achieve better performance than the traditional algorithm under the condition of an inaccurate estimate of wave velocity. Compared with the velocity-independent DOA algorithm, it exhibits the feature of low complexity.

In this paper, an estimator for underwater DOA estimation is proposed by using a cross-linear nested array with arbitrary cross angle. The estimator excludes the variation acoustic velocity by deriving the geometric relation of the cross-linear array on the proposed algorithm. Therefore, compared with traditional DOA estimation algorithms via linear array, this estimator eliminates systematic errors caused by the uncertainty factor of the acoustic velocity in the underwater environment. Compared with the traditional acoustic velocity independent algorithm, this estimator uses the nested array and improves the performance of DOA estimation. In addition, the estimator is based on arbitrary angle of the cross-linear array, so it is more flexible in practical applications. Numerical simulations are provided to validate the analytical derivations and corroborate the improved performance in underwater environments where the actual acoustic velocity is not accurate.

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