## 1 Introduction
The integral action has also been commented in [14] and is demonstrated to be a useful technique to achieve zero steady-state errors for systems with disturbances. Moreover, Kalman filter or EKF [15; 16] is also commonly used for filtering general disturbances and estimating the motion states of marine robots. The estimated states can then be used for controller design assuming the \"separation\" principle holds so that the controller and observer could be designed separately. With the information on localization and ocean current, the controller computes the input to the AUV system so as to achieve certain tasks. The most widely implemented controller is proportional-integral-derivative (PID) [13] due to its simplicity. More recent PID variants are usually equipped with gain scheduling [17] or fuzzy logic [18] designs to deal with nonlinearities. Lyapunov-based techniques such as backstepping [19] and sliding mode control [20] are also frequently used in AUV control to handle nonlinearities and guarantee convergence. However, these methods are often associated with tedious tuning procedures, and the control performance differs when the environment, load, or tasks change. Besides, control metrics and system constraints cannot be handled. In addition to systematically handling system constraints and optimizing performance, model predictive control (MPC) is inherently robust to disturbances to a certain degree [21]. MPC is applied to the AUV docking scenario in [22]. In [23], a series of MPC controllers are proposed to the AUV path following problem, and closed-loop system stability is guaranteed theoretically. A sliding mode control, a filtered Smith predictor, and an MPC controller are integrated in [24] to deal with disturbances, dead time, and constraints, respectively. However, most of the control problems assume the availability of the localization information of AUV, which is not practical. In this paper, we consider the localization and control problem of AUVs simultaneously. In the absence of GPS signals, an acoustic localization method based on three surface buoys is first proposed. The three buoys emit acoustic signals periodically from the surface. The different times of arrivals of these signals at the AUV can then determine an estimated position of the AUV upon the receiving of the third signal in a localization cycle. Regarding the noises in the estimated positions, the unavailability of the velocity states, and the uncertainties due to the ocean current, an EKF approach is proposed to provide an estimate of the system's full state. With the estimated system states, MPC is applied to track a reference trajectory. System physical constraints and control performance are explicitly considered. Since the localization and control have different sampling times, the dead-reckoning technique is utilized with detailed AUV dynamics. In the MPC controller design, to relieve the possible computational burden, the AUV dynamics are simplified through successive linearizations. Briefly, this paper contributes to the state of the art in the following aspects:  
1. a novel integrated acoustic localization and predictive tracking control approach is proposed for AUVs;
2. the uncertainties in localization and ocean currents are handled together systematically using EKF;
3. the approach of successive linearizations is applied to AUVs for computational efficiency. Simulation results demonstrate the effectiveness of the proposed algorithms for AUVs. The remainder of the paper is organized as follows. Section 2 presents the AUV dynamic model and the tracking control problem statement. Then in Section 3, the acoustic localization method is proposed. The tracking control based on successively linearized prediction models, state estimation with EKF and MPC are further proposed in Section 4. Section 5 presents simulation results and discussions, followed by concluding remarks and future research considerations in Section 6.