[問題] 最小自乘法求解五個球的交點已回收
我用最小自乘法模擬了GPS衛星定位的方法
五個球的球心為衛星所在位置 五個球的交點則是GPS user的位置
觀測方程式如下所示:
sqrt((x_I-a_1)^2 + (y_I-b_1)^2 + (z_I-c_1)^2)+cdt-r^2
總共有五個類似的球的方程式
所以五個式子共有四個未知數(x_I,y_I,z_I,cdt)
在式子最後面的cdt則是一個我要求的未知數(接收儀的時鐘誤差)
理論上 五個式子利用最小自乘法求四個未知數應該可以求解
但奇怪的是
他每執行一次迭代就出現一次以下錯誤訊息:
Warning: Matrix is close to singular or badly scaled.
Results may be inaccurate. RCOND = 3.883246e-017.
Warning: Matrix is close to singular or badly scaled.
Results may be inaccurate. RCOND = 1.985238e-018.
Warning: Matrix is close to singular or badly scaled.
Results may be inaccurate. RCOND = 5.081079e-020.
Warning: Matrix is close to singular or badly scaled.
Results may be inaccurate. RCOND = 4.440271e-017.
Warning: Matrix is close to singular or badly scaled.
Results may be inaccurate. RCOND = 5.776448e-018.
Warning: Matrix is close to singular or badly scaled.
Results may be inaccurate. RCOND = 4.422662e-017.
Warning: Matrix is close to singular or badly scaled.
Results may be inaccurate. RCOND = 1.325433e-024.
Warning: Matrix is close to singular or badly scaled.
Results may be inaccurate. RCOND = 8.270576e-026.
Warning: Matrix is singular to working precision.
我的解發散掉了!
可是若是我拿掉未知數cdt 使得只剩三個未知數 一樣用五個式子去求解
就可以正確求解 也證明我的最小二乘法矩陣排列無誤
想了很久 想破頭了都還是不知道到底為什麼
不知道板上有沒有強者可以為我解答 我真的感激不盡>"<~~
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◆ From: 61.66.130.37
※ 編輯: tingyili 來自: 61.66.130.37 (01/06 21:58)
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