Dual Frequency Estimation in Sinusoidal Signals Embedded in Additive White Gaussian Noise

In this project, we designed and implemented a method for estimating dual frequencies in sinusoids embedded in additive white Gaussian noise. Our implementation involved deriving the Cramér-Rao Lower Bound (CRLB) for the signal model and developing a nonlinear least squares frequency estimator. The algorithm implementation includes numerical optimization techniques for frequency parameter estimation, utilizing gradient-based methods to minimize the squared error between observed and modeled signals. We evaluated the estimator through comprehensive numerical examples, implementing Monte Carlo simulations to assess statistical performance. Additionally, we conducted extensive experiments to validate the estimator's robustness, testing scenarios with varying signal-to-noise ratios and frequency separation conditions. The experimental framework included computational efficiency analysis and convergence testing of the optimization algorithm. Our implementation demonstrates that the method achieves excellent performance and reliability in dual-frequency estimation, with the numerical results closely approaching the theoretical CRLB under optimal conditions. The algorithm effectively handles the nonlinear nature of frequency estimation while maintaining computational efficiency through appropriate initialization and iterative refinement techniques.