最小二乗法を行うことで、三辺測量の精度を向上させようとしました。初期推定では、クラスター ポイントの平均値を取得します。この値は、次の推定までの距離が十分に小さくなるまで増加します。増分値は、次の式を使用して計算されます。
私の質問は、ほとんどの場合、最終的な答えが本来あるべきものから非常に重要な点をそらすのはなぜですか? それほど正確ではありませんが、最初の見積もりはさらに優れています。ここで何かが恋しいですか？
編集
式はここで説明した通りです。この写真の方が分かりやすいと思いますが、
最終点が交差領域の外側にあることも確認してください。
I think I have a clear enough idea of the problem to offer an answer.
Basically the three-cornered region's interior consists entirely of points that undershoot the three estimated distances (inaccurate circle radii). So it is not surprising that an iterative improvement to the solution, seeking a minimum squared error approximation, will move the point outside that three-cornered region.
More about why the points inside the region give distances that are below the given estimates: These points are exactly those that are inside all three circles (if such an arrangement holds). Therefore the three distances from such a point to the circles' centers are all below their respective radii.
Using the average of the three corner points (is this what is meant by cluster points in the question?) is probably a pretty good way to start. If there is a simple place to improve the calculation, it might lie in using a weighted least squares criterion rather than an absolute least squares criterion.
What I mean by this is that if one radius is 10 yards, and the other two radii are much larger (say 200 and 300 yards for the sake of discussion), it probably doesn't make sense to assume the estimated distances all have errors of about equal size (which is what an absolute least squares fit looks for). Instead assuming the error in the estimated distances is roughly proportion to each distance (a relative error criterion) is more likely to produce a better solution, e.g. giving a greater weight to the shorter distance (because a proportional error in that would be less in absolute magnitude than the proportional error in the longer distances).
This is just a sketch of one idea you might want to incorporate in your solution. I take you have only the three data to work with (locations known to fairly good accuracy as centers of circles, greater uncertainty in the three radii). So it doesn't make sense to try and apply methods that are sophisticated in respect of accuracy, but rather to prefer methods that give a robust solution. I think the relative error criterion would move you in that direction.
最小二乗法は誤差の全体的な二乗を最小化しますが、個々の点が真の値にどれだけ近いかについては何も言いません。係数は、いくつかのポイントだけでなく、すべてのポイントの影響を受けます。