Underwater Inertial Navigation With Long Baseline Transceivers: A Near-Real-Time Approach

Inertial navigation systems for underwater vehicles are often aided by acoustic time-of-flight positioning schemes. One widely implemented long baseline (LBL) approach uses a ping-response protocol resulting in asynchronous measurements that depend on the state of the vehicle at two time instants. Such aiding measurements that depend on the state at multiple time instants do not fit the model format of the standard extended Kalman filter (EKF) framework. This paper proposes a near-real-time (NRT) Bayesian smoothing framework for the LBL-aided inertial navigation system application. Within this NRT framework, the time interval between LBL cycles is divided into two intervals defined by the ping-response cycles of LBL. The time instant when all the LBL responses are received will be referred to as the NRT point. Between the LBL ping and the NRT point, a traditional real-time EKF is implemented using the inertial measurement unit and all aiding measurements. After the NRT point, when all the LBL responses have been received, an optimal Bayesian trajectory estimator executes. This maximum a posteriori (MAP) estimation includes all the measurement information already collected up to the NRT point of the current LBL cycle. The MAP output is a smoothed trajectory estimate for the period of time between the LBL ping and the NRT point. At the conclusion of this smoothing process, the current EKF estimate is corrected to the optimal MAP solution and propagated to the current time, and then the EKF estimation process continues to the NRT point of the next LBL cycle. At all times, the approach maintains a real-time state estimate suitable for use by the control system. This paper presents the theoretical solution, discusses the implementation, and presents implementation results to illustrate the accuracy and reliability of this NRT approach.