The objective of navigation is to determine the instantaneous location of a moving vehicle. Historically, sailors estimated the speed of a ship by dropping a log into the water and observing the time for it to float from the bow to the stern [1, pp. 21-38]. Combining this speed information with directional data from a compass yields a velocity estimate. Finally, integrating the velocity estimate with respect to time and using the known initial position yields a position estimate at each instant of time. This procedure is called dead reckoning [2, p. 30], [3] or, when performed by animals without the benefit of calculus and digital computation, path integration [4]. Although not all navigation is based on dead reckoning-for example, celestial navigation uses the stars for position fixing-it is widely used due to its ability to utilize speed, direction, and time data from a variety of sensors. By computing position from velocity data, dead reckoning is an integration process. It is important to stress, however, that, because of the lack of observability, dead reckoning cannot take advantage of an observer and, thus, cannot stabilize the integrator dynamics. Therefore, dead reckoning is an inherently unstable process, regardless of how the velocity and direction data are acquired.

中文翻译：

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从状态估计角度介绍惯性导航【聚焦教育】


导航的目的是确定移动车辆的瞬时位置。历史上，水手们通过将一根圆木放入水中并观察它从船头漂浮到船尾的时间来估计船的速度[1，第 21-38 页]。将此速度信息与罗盘的方向数据相结合即可得出速度估计值。最后，将速度估计相对于时间积分并使用已知的初始位置产生每个时刻的位置估计。这个过程称为航位推算 [2, p. 11]。 30]、[3]，或者，当由动物在没有微积分和数字计算的情况下执行时，路径积分[4]。尽管并非所有导航都基于航位推算（例如，天体导航使用星星进行位置固定），但由于其能够利用来自各种传感器的速度、方向和时间数据，因此得到了广泛的应用。通过根据速度数据计算位置，航位推算是一个集成过程。然而，需要强调的是，由于缺乏可观察性，航位推算无法利用观察者，因此无法稳定积分器动态。因此，无论如何获取速度和方向数据，航位推算本质上都是不稳定的过程。