论文标题
用绳索双重迭代求解开普勒方程
Solving Kepler's equation with CORDIC double iterations
论文作者
论文摘要
在先前的工作中，我们开发了一个想法，可以使用类似绳索的算法来求解开普勒的方程，该算法不需要任何划分，但仍会在每次迭代中乘以乘法。在这里，我们仅使用bitshift，添加和一个初始乘法来克服这个主要的缺点并求解开普勒方程。我们以偏心率和尺度校正因子为例。旋转方向是在不改变尺度的情况下决定的。我们发现，在随后的迭代中，双启示性迭代是自我校正的，并补偿了可能的错误旋转。该算法需要75 \％的迭代，并提供偏心异常，其正弦和余弦术语是偏心率的时间。该算法也可以用于双曲线。新的移位算法使开普勒的方程式接近硬件，并允许使用便宜而简单的硬件组件来解决它。
In a previous work, we developed the idea to solve Kepler's equation with a CORDIC-like algorithm, which does not require any division, but still multiplications in each iteration. Here we overcome this major shortcoming and solve Kepler's equation using only bitshifts, additions, and one initial multiplication. We prescale the initial vector with the eccentricity and the scale correction factor. The rotation direction is decided without correction for the changing scale. We find that double CORDIC iterations are self-correcting and compensate possible wrong rotations in subsequent iterations. The algorithm needs 75\% more iterations and delivers the eccentric anomaly and its sine and cosine terms times the eccentricity. The algorithm can be adopted for the hyperbolic case, too. The new shift-and-add algorithm brings Kepler's equation close to hardware and allows to solve it with cheap and simple hardware components.
