Parameter Estimation of Frequency-Modulated Sinusoids with the Distribution Derivative Method
Frequency-modulated (FM) sinusoids are commonly used to model signals in several engineering applications, such as radar, sonar, communications, acoustics, and optics. The estimation of the parameters of FM sinusoids is a challenging problem with a long history in the literature. In this article, we use the distribution derivative method (DDM) to estimate the parameters of FM sinusoids in additive white Gaussian noise. Firstly, we derive the estimation of parameters of the model with DDM. Then, we compare the results of Monte-Carlo simulations (MCS) of DDM estimation of FM signals in additive white Gaussian noise against the state of the art (SOTA) and the Cramér-Rao lower bound (CRLB). DDM estimation of FM sinusoids showed performance comparable to the SOTA with less estimation bias. Additionally, DDM estimation of FM sinusoids is simple and straightforward to implement with the fast Fourier transform (FFT) relative to other approaches in the literature. Finally, DDM estimation has effectively the same computational complexity as the FFT.