We examine acoustic Doppler current profiler (ADCP) measurements from underwater gliders to determine glider position, glider velocity, and subsurface current. ADCPs, however, do not directly observe the quantities of interest; instead, they measure the relative motion of the vehicle and the water column. We examine the lineage of mathematical innovations that have previously been applied to this problem, discovering an unstated but incorrect assumption of independence. We reframe a recent method to form a joint probability model of current and vehicle navigation, which allows us to correct this assumption and extend the classic Kalman smoothing method. Detailed simulations affirm the efficacy of our approach for computing estimates and their uncertainty. The joint model developed here sets the stage for future work to incorporate constraints, range measurements, and robust statistical modeling.

翻译：我们检查了水下滑翔机的声学多普勒洋流剖面仪(ADCP)测量,以确定滑翔机位置、滑翔机速度和地表下洋流。但是,ADCP并不直接观测利息量;相反,它们测量了车辆和水柱的相对运动量。我们考察了以前用于这一问题的数学创新的线系,发现了一个未说明但错误的假设独立性。我们重新设计了一种最近的方法,以形成一种当前和车辆导航的共同概率模型,从而使我们能够纠正这一假设并推广典型的卡尔曼滑动方法。详细模拟证实了我们计算估计数的方法及其不确定性的功效。在这里开发的联合模型为未来纳入限制因素、范围测量和稳健的统计模型的工作奠定了基础。