###### Abstract
The particular use of Doppler for anti-spoofing applications is explored in [11]. In any case, the most common use of the Doppler shift in the GNSS context is for velocity estimation [1; 12]. CP measurements are used for precise positioning; the higher precision and accuracy are obtained at the cost of increasing the navigation engine complexity due to the intrinsically ambiguous nature of CP observables [1; 12]. In addition, the loss of lock and cycle slip are additional problems in the usage of this type of measurement. By exploiting the difference between two consecutive CP measurements, TDCP removes the problem of the unknown ambiguity (in the absence of cycle slips) [3], making this technique very powerful due to its reachable accuracy. Several research studies have focused on TDCP; it has been used to estimate the velocity of a standalone GPS receiver [2], but it has also been successfully applied to other constellation cases such as BeiDou in the static case, where mm/s accuracy was obtained, and in the kinematic case, where only a cm/s accuracy level was achieved due to the sudden acceleration of the vehicle [13], revealing a possible weakness of this technique. Moreover, the performance of TDCP using Galileo in the static case and on different signal frequencies is analyzed in [14]. One of the main limitations of TDCP is the usage of two consecutive measurements, which are referred to as different epochs. If between the two epochs a new navigation message is received, two different sets of ephemerides are used, resulting in a discontinuity of the TDCP measurement; this problem has been addressed in [15], where a method that considers the same ephemerides set for every couple of epochs is proposed. In 2015, the Leica Geosystems company published a white paper on the Velocity And Displacement Autonomous Solution Engine (VADASE) algorithm [16], which exploits the difference between two consecutive phase measurements, i.e., TDCP, for a precise velocity estimation. In the sector of inertial and integrated navigation, TDCP also garnered considerable interest due to its capability to improve the accuracy of an integrated solution; in [17], this technique was used to enhance Inertial Navigation System (INS) with an iterative extended Kalman filter (EKF); in [18], a novel TDCP-GNSS/INS integration was designed for a low-cost GNSS receiver and low-accuracy INS, where the role of TDCP was in cycle slip detection and handling. The TDCP technique has been investigated for several applications: for automotive applications in [19], where TDCP is used for the computation of the heading and pitch angles of an antenna mounted on a vehicle; for critical infrastructural monitoring in [20]; and for seismic motion detection in [21]. Low-cost GNSS devices include mass-market receivers and smartphones. These devices are exploited by billions of users in different operational conditions. Currently, few studies have been performed to analyze the performance of TDCP using such devices, which are usually characterized by noisy and discontinuous measurements. The measurement quality of such devices was analyzed and assessed in several studies; in [22; 23; 24], exhaustive assessments of several smartphones' observations are provided in terms of different aspects: carrier-to-noise density power ratio (C/N0), multipath error, positioning performance, and so on. The TDCP potentialities of such devices are also revealed; in [25], a static analysis considering only GPS data was conducted by comparing receivers of different grades, confirming mm/s level accuracies for all the adopted devices, i.e., for the smartphone as well. The GNSS market is evolving very fast, and the capability of low-cost devices is increasing; several manufacturers have enhanced their products, for example, by tracking new constellations and adding different frequencies. These evolutions have led to the wider adoption of low-cost devices (including smartphones) for several applications.