This paper presents a simple DFT-based golden section searching algorithm (DGSSA) for the single tone frequency estimation. Because of truncation and discreteness in signal samples, Fast Fourier Transform (FFT) and Discrete Fourier Transform (DFT) are inevitable to cause the spectrum leakage and fence effect which lead to a low estimation accuracy. This method can improve the estimation accuracy under conditions of a low signal-to-noise ratio (SNR) and a low resolution. This method firstly uses three FFT samples to determine the frequency searching scope, then – besides the frequency – the estimated values of amplitude, phase and dc component are obtained by minimizing the least square (LS) fitting error of three-parameter sine fitting. By setting reasonable stop conditions or the number of iterations, the accurate frequency estimation can be realized. The accuracy of this method, when applied to observed single-tone sinusoid samples corrupted by white Gaussian noise, is investigated by different methods with respect to the unbiased Cramer-Rao Low Bound (CRLB). The simulation results show that the root mean square error (RMSE) of the frequency estimation curve is consistent with the tendency of CRLB as SNR increases, even in the case of a small number of samples. The average RMSE of the frequency estimation is less than 1.5 times the CRLB with SNR = 20 dB and N = 512.

Localization is one of the oldest mathematical and technical problems that have been at the forefront of research and development for decades. In a wireless sensor network (WSN), nodes are not able to recognize their position. To solve this problem, studies have been done on algorithms to achieve accurate estimation of nodes in WSNs. In this paper, we present an improvement of a localization algorithm namely Gaussian mixture semi-definite programming (GM-SDP-2). GMSDP is based on the received signal strength (RSS) to achieve a maximum likelihood location estimator. The improvement lies in the placement of anchors through the Fuzzy C-Means clustering method where the cluster centers represent the anchors’ positions. The simulation of the algorithm is done in Matlab and is based on two evaluation metrics, namely normalized root-mean-squared error (RMSE) and cumulative distribution function (CDF). Simulation results show that our improved algorithm achieves better performance compared to those using a predetermined placement of anchors.