## 1 Introduction  
In many sensing technologies, object localization and tracking with range measurements have received significant attention because of their importance in many applications, such as obstacles avoidance, smart surveillance, human-computer interaction, safe sensing in factories, and autonomous navigation [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. Aiming at the problem of object localization and tracking, this paper focuses on the construction of an object localization and tracking system based on an ultrasonic array. The system can locate the target by calculating the distances of ultrasonic echo signals between the sensors and the target. In this system, envelope extraction, TOF estimation, and object localization are three key issues. Several methods for envelope extraction and TOF estimation are presented in the literature. A sensing system is designed in [11], which uses the waveform of reflected ultrasonic signals to obtain additional information about the environment, and constructs a signal classification system for objects of different materials. The Hilbert transform is used to extract the envelope of the echo signal of ultrasonic, and the traditional threshold detector is used to estimate the TOF, which can capture the echo shape reliably and accurately. However, the Hilbert transform method is not effective because it uses fast Fourier transform (FFT) and FFT inverse. The threshold method [12; 13] is the simplest method to measure TOF, where TOF is determined when the echo amplitude exceeds the threshold value for the first time. Aiming at the situation where a single threshold is not robust enough to noise, a dual-threshold method [14] is proposed, which uses a parabolic approximation method to fit two points to the rising edge of the ultrasonic echo envelope. In [15], an analytic model of an ultrasonic envelope is proposed to estimate TOF with a dual-threshold method. The dual-threshold-based method [16] is also implemented in the microprocessor for dynamic distance estimation and is applied in the application of a human body. Both methods use two-level verification to correct the TOF estimation in the envelope signal. However, due to the deformation of the echo signal, the threshold-based method is often not robust. To solve the problem of threshold-based methods, the optimal correlation detection method [14; 17] provides unbiased estimation using a matched filter containing a copied echo waveform that is used to determine the most likely position of the received echo signal. However, due to the variation of the echo waveform, it is necessary to store a large number of desired signal templates for correlation calculations, which consumes a large amount of computing. In [18; 19; 20], the cross-correlation method of transmitting and receiving signals is proposed. The sine fitting method for determining the phase shift is further mentioned in [20] as the second technique for estimating TOF with higher accuracy. To solve the problem that the frequency of noise is close to that of the desired signals and the amplitude of received signal is small and unstable, an improved energy genetic-ant colony optimization-three-cycle algorithm [21] is presented to estimate the TOF by judging the maximum energy position of the signal. However, these methods can only be applied to the standard shape of the envelope signal, but not to the envelope deformation caused by signal attenuation during the ultrasonic propagation process and the change of orientation, position, size, and material of the detected object. Object localization is also a critical issue in this study. In general, the measurement methods in the localization problem can be classified into four categories [22], that is, time of arrival (TOA) [23], time difference of arrival (TDOA) [24], angle of arrival (AOA) [25], and received signal strengths (RSS) [26]. Several approaches are applied to the localization problem, and least-squares-based (LS) methods are widely developed in this field [27; 28; 29; 30; 31].