In this paper we propose an algorithm for formant estimation using a data-driven approach. The vocal tract is typically modeled as an all-pole filter, whose spectral peaks are taken as the formant estimates. Estimating the filter parameters by minimizing the ℓ2-norm of the residual signal leads to pitch-locking tendency. This is avoided if the ℓ1-norm criterion is used, but the solution is computationally burdensome. Minimizing the weighted ℓ2-norm provides a good compromise between the pitch-locking tendency and computation, but requires the knowledge of the Glottal Closure Instants (GCIs). In our method knowledge of the GCI is not required; instead, we adjust the weighting sequence parameters in a data-driven manner. Our results on both synthetic as well as natural voiced-speech show that our method is superior to LPC; when compared with SWLP, our method gives estimates with lower variance. © 2020 IEEE.