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Spin-valve (SV) sensors are one of the basic elements of modern and prospective spintronics. The sphere of applications of sensors covers almost all areas of industry and activities of daily living. Their advantages are high sensitivity, low energy consumption, low cost, small size, and high spatial and temporal resolution of the magnetic fields of the objects under study. Generally, an SV sensor is a multilayer thin-film structure consisting of two ferromagnetic (F) layers separated by a nonmagnetic layer. The direction of the magnetization vector of one of the F layers (pinned ferromagnetic (PF) layer) is fixed via an exchange interaction with the antiferromagnetic layer (AF). The layer with free magnetization (FF) is a sensitive element in the structure and varies the orientation of its magnetization under the action of an external magnetic field. As a result of noncollinearity of magnetic moments of PF and FF layers, the total resistance of the structure increases. This effect is named giant magnetoresistance (GMR) Wheatstone bridge (WB) configurations of clusters of SV sensors moving in the 3D field of a magnetic label are considered as a sensor of the magnetic field of a label. Potentially, the WB network is a more favorable device than a single SV sensor, offering higher sensitivity to a weak magnetic field and to a weak space variation of the magnetic field. That is an important feature of WB-like sensors in many applications, including the localization and positioning of a moving magnetic object. WB network output signals are considered for different bridge sizes, numbers of sensitive elements, and orientations with respect to the label, see an example in Fig.1. We demonstrate that the WB output signal, as a function of approach distance to the label, strongly depends on several factors. First is the trajectory of the sensor, i.e., the height and width of the signal strongly depend not only on the distance of the nearest approach of the sensor to the label, the so-called impact parameter, but also the position of the line of motion with respect to the geometry and orientation of the label, see examples in Fig.2. The design and parameters of the WB sensor is a second factor. Here we consider WB-like sensors of rectangular design with four SV elements, balanced in a no-field environment, with one-of-four or two-of-four sensitive SV elements and the other SV elements protected from the influence of a magnetic field. We show that the shape and amplitude of the output signal critically depend on the configuration of the sensitive and protected WB arms, the size of the sensor, the number (one or two) of sensitive elements, and spacing between the sensitive arms. A third factor is the orientation of the WB sensor with respect to the label, compare Figs. 2 (a) and (b). In Figs 1 and 2, we demonstrate that the response of the sensor is crucially dependent on the initial orientation of the WB basic plane and magnetic moments of the sensitive elements within the plane. Calculations provided new information on a WB-like SV sensor manifold response to the nonhomogeneous magnetic field of an object. This information can be used to design positioning devices for a variety of applications, including the localization and positioning of a moving magnetic object.