Maximum Likelihood Method with Gaussian Colored Noise (GCN)

This text discusses the maximum likelihood method and Gaussian colored noise. The maximum likelihood method is a widely used parameter estimation technique that utilizes observed data to estimate model parameters by maximizing the probability of observing the data under the given model. In computational implementations, this typically involves formulating a likelihood function and applying optimization algorithms like gradient descent or Newton-Raphson methods for parameter estimation. Gaussian colored noise represents a common noise model that shares similarities with Gaussian white noise but exhibits different noise power across frequencies. Key implementation differences include their spectral characteristics: while white noise has a flat power spectrum, colored noise requires modeling frequency-dependent power spectral density (PSD) using techniques like autoregressive models or spectral estimation algorithms. The distinction between these concepts primarily lies in their noise power spectrum characteristics and spectral coloration properties. Although these concepts may appear distinct, they can interact in practical scenarios - for instance, when implementing maximum likelihood estimators that must account for colored noise characteristics in signal processing applications. Proper implementation often involves incorporating noise covariance matrix estimation or spectral shaping filters in the likelihood function formulation.