Use when you must estimate the in-flight magnetometer bias vector with scalar-checking batch least squares: expand |m_k - b|^2 = B_k^2 over the measured body-frame samples m_k and the known field magnitudes B_k, build the 4-unknown rows [-2 m_k, 1] with right sides B_k^2 - |m_k|^2, solve the normal equations A^T A x = A^T y by partial-pivot Gaussian elimination, and recover the bias from the first three unknowns with the fourth unknown |b|^2 as the consistency check.
