python - 在 Python 上编写代码：从嘈杂的测量中恢复正弦曲线

Question

我需要计算平面坐标（x，y）。有变化的轨迹，需要计算后续坐标。有一个改变坐标的近似公式，它取决于两个系数k1和k2随机噪声：

x = k2cos(k1t) + noise
y = k1sin(k2t) + noise

在输入中给出了 1000 对坐标 xy 前一千秒（从 0 到 999）的列表：

[(0.8990863593574939, 8.475387292276096e-07), (0.8089593833113505, 0. 3534820061950688), (0.5566465706027002, 0.4399620826711653), (0.19273411906364982, 0.19411748737324), (-0. 20981822525965102, -0.19835273653070376), (-0.5703058016775612, -0.44099688186601116), (-0.8164537877967621, -0. 35053466833726243), (-0.8989145629777989, 0.004703700279075586), … (-0.801155143314037, 0. 35638955826565816), (-0.5427749453575453, 0.43887713883486584), (-0.17557562076019273, 0.18985994842390025), (0. 22682425709951057, -0.20256735021079741), (0.5837487993279974, -0.4419853288796921), (0.8236405373374047, -0. 3475501356746985), (0.8984026035824828, 0.009406628459256976), (0.7930484451922395, 0.3592589441057791)]

作为响应，预计第二千秒（从 1000 到 1999）的 1000 对数组，例如：

[(0.8990863593574939, 8.475387292276096e-07), (0. 8089593833113505, 0.3534820061950688), (0.5566465706027002, 0.4399620826711653), (0.19273411906364982, 0. 19411748737324), (-0.20981822525965102, -0.19835273653070376), (-0.5703058016775612, -0.44099688186601116), (-0. 8164537877967621, -0.35053466833726243), (-0.8989145629777989, 0.004703700279075586), … (-0.801155143314037, 0. 35638955826565816), (-0.5427749453575453, 0.43887713883486584), (-0.17557562076019273, 0.18985994842390025), (0. 22682425709951057, -0.20256735021079741), (0.5837487993279974, -0.4419853288796921), (0.8236405373374047, -0. 3475501356746985), (0.8984026035824828, 0.009406628459256976), (0.7930484451922395, 0.3592589441057791)]

标签： pythonmath