# A Local Search Maximum Likelihood Parameter Estimator of Chirp Signal
###### Abstract  
A local search Maximum Likelihood (ML) parameter estimator for mono-component chirp signal in low Signal-to-Noise Ratio (SNR) conditions is proposed in this paper. The approach combines a deep learning denoising method with a two-step parameter estimator. The denoiser utilizes residual learning assisted Denoising Convolutional Neural Network (DrCNN) to recover the structured signal component, which is used to denoise the original observations. Following the denoising step, we employ a coarse parameter estimator, which is based on the Time-Frequency (TF) distribution, to the denoised signal for approximate estimation of parameters. Then around the coarse results, we do a local search by using the ML technique to achieve fine estimation. Numerical results show that the proposed approach outperforms several methods in terms of parameter estimation accuracy and efficiency. chirp parameter estimation; signal denoising; time-frequency analysis; maximum likelihood +
Footnote †: journal: Medical  
The FRFT is also shown to correspond to a representation of the signal on an orthonormal basis formed by chirps, which are essentially shifted versions of one another [14]. So, FrFT have a good property of energy concentration for chirp signal on a proper transform order. After the FrFT transform of a chirp signal, we can estimate the parameters by searching the peak position in the FrFT domain. Although FrFT performs very well in chirp signal detection, however, in terms of parameter estimation, it is highly influenced by signal length, sample rate, and searching step size. It has been proved that the ML estimator [21; 22] obtains the best performance for finite data samples and is asymptotically optimal in the sense that it achieves the Cramer-Rao Lower Bound (CRLB) [23; 24]. Directly use ML estimator to chirp parameters estimation involves a two-dimensional grid search of compressed likelihood function that is limited by computational consideration for high estimation accuracy. Another approach to chirp parameter estimation is based on deep learning. Data-driven and deep learning-based methods in the digital signal processing area have been of significant interest in recent years. [PERSON] applies Convolutional Neural Network (CNN) for replacing the Fourier transform and FrFT, uses it for single frequency signal and LFM signal detection and estimation [25], it has proved that the CNN based method can achieve good recognition performance in low SNR conditions. [PERSON] addresses the problem of estimating the parameters of constant-amplitude chirp signals that have single or multiple components and are embedded in noise based on a Complex-Valued Deep Neural Network (CV-DNN) [5]. Simulation results indicate that the CV-DNN outperforms conventional processors. And it is more accurate and faster than the WHT, which will enable real-time signal processing with fewer computational resources. Furthermore, they demonstrate that the CV-DNN shows strong robustness to the changes in modulation parameters and the number of components of a chirp signal. Besides chirp signals, [PERSON] proposes a deep learning denoising based approach for line spectral estimation [26], by using CNN to preprocess sinusoidal signals in the time domain and offers a substantial improvement in line spectral estimation. As for denoising, [PERSON] proposes a CNN method to remove noises from speech signals for enhancing the quality and intelligibility of speech [27], the training date and validation data set are the STFT amplitude spectra of the noisy and clean audio signals respectively and then transform back to the time domain by using inverse STFT with amplitude spectra of CNN output and the phase spectrum of the noisy signal. Deep learning also plays an active role in the field of signal detection and classification.