Precise　and　rapid　extraction　of　spherical　target　features　from　laser　point　clouds　is　critical　for　achieving　high-precision　registration　of　multiple　point　clouds.　Existing　methods　often　use　linear　models　to　represent　spherical　target　characteristics,　which　have　several　drawbacks.　This　paper　proposes　a　rigorous　estimation　algorithm　for　spherical　target　features　based　on　least　squares　configurations,　in　which　the　point-cloud　data　error　is　used　as　a　random　parameter,　while　the　spherical　center　coordinates　and　radius　are　used　as　nonrandom　parameters,　emphasizing　correlation　between　spherical　parameters.　The　implementation　details　of　this　algorithm　are　illustrated　by　deriving　calculation　formulas　for　three　variance-covariance　matrices:　variance-covariance　matrices　of　the　new　observations,　variance-covariance　matrices　of　the　new　observation　noise,　and　variance-covariance　matrices　of　random　parameters　and　the　new　observation　noise.　Experiments　show　that　the　estimation　accuracy　of　sphere　centers　using　our　method　is　improved　by　at　least　5.7%　compared　to　classical　algorithms,　such　as　least　squares,　total　least　squares,　and　robust　weighted　total　least　squares.