In this study, an algebraic closed-form method for jointly locating the target and refining the antenna positions in multiple-input–multiple-output radar systems is proposed. First, a set of linear equations is formed by non-linear transformation and nuisance parameters elimination, and then, an estimate of the target position is obtained by employing a weighted least-squares estimator. To jointly refine the target and antenna positions, the associated error terms are estimated in the sequence. The proposed method is shown analytically and confirmed by simulations to attain the Cramér–Rao lower bound performance under small-error conditions. Numerical simulations are given to support the theoretical developments.