X Sx y y Sy z z 5z

£ S ^ g S g Jig g in (6), and repeat the computation to get a new estimate of P0=[x y z]T. The iterations will have converged when S x, S y, S z are essentially zero, and the position of AUV is achieved via the iterative refinement scheme. The solution derived above can be easily simplified to the case where the target undergoes motions in two dimensional space with fixed depth z. Considering the noise covariance matrix R= a21 (i.e., the noise terms ei are independent with the same variance ), the covariance matrix of the LS estimation errors in the corresponding position can be calculated as

The system is computationally simple requiring inversion of n (sonobuoys as reference stations) by 3 matrix and it usually converges in several iterations, but the linearized estimator is sensitive to the geometry of the situation. For instance, sonobuoys were placed very clear each other and the AUV is in very deep depth, then even small measurement errors of TOA will lead to large position estimation errors due to the occurred ill-conditioned matrix.

On the other hand, the solved depth of the underwater target is very inaccurate when depth is small compared to the distance between transponders. In this case, a pressure sensor integrated in the mobile's pinger is one solution, and the telemetry technique used is of an external freedom for depth accuracy as the time delay between two pulses is proportional to the depth.

Within different time slots, all of the dedicated AUVs in the coordinated team can be calculated with this high precise navigation algorithm based on intelligent sonobuoys with DGPS. Benefited from all of the vehicle positions, The ASV can generate and allocate the waypoints to the AUVs as well as providing the navigation information so that the coordinated control of heterogenous vehicles including the ASV and AUVs could be possible. At the same time, the ASV with the collected AUV positions will follow the AUVs and move above the central of mass of the underwater vehicles to keep the heterogenous team as a whole (Xianga et al., 2007).

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