This paper presents a novel high-resolution signal processing technique for non-intrusive detection of broken bar fault condition in induction machine rotor. The technique is based on parametric spectral estimation of stator current waveform recorded while a machine is running. The frequency components that are related to broken rotor bar condition are very close to the fundamental frequency, and this combined with low signal to noise ratio makes the task of detecting a broken rotor bar condition difficult. The method proposed is based on the least squares fit of the predefined parametric signal model. The problem is nonlinear with a number of local minimum values in the feasible region. Classical nonlinear least squares methods, like Levenberg-Marquardt or Nelder-Mead algorithms, can converge to a local minimum giving inaccurate spectral estimation parameters. To overcome this problem we employed the global optimization algorithm based on grid search. The grid on which the search for optimum is performed is constructed using the Hyperbolic Cross Points (HCP). The global search on the HCP grid is complemented with the Nelder-Mead local search algorithm, to refine the result. We are able to estimate broken rotor bar frequencies and the associated amplitudes with high accuracy for wide range of motor operating conditions and severities of broken rotor bar faults. The results presented in the paper show that HCP algorithm can be used to diagnose broken bar fault in induction motor using very short current signal segments and during light motor loadings.