A single chip Z-axis linear magnetoresistive sensor assembly comprising a single chip Z-axis linear magnetoresistive sensor, and a first coil, wherein the single chip Z-axis linear magnetoresistive sensor comprises a soft ferromagnetic flux concentrator and a magnetoresistive sensing unit array that are located on a substrate, the soft ferromagnetic flux concentrator is elongated, and has a long axis along a Y direction and a short axis along an X direction, all the magnetoresistive sensing units are TMR sensing units, magnetization directions of pinned layers are all along the X direction, magnetization directions of free layers thereof are all along the Y direction; the magnetoresistive sensing units are electrically connected to form a push magnetoresistive sensing unit string and a pull magnetoresistive sensing unit string along the Y direction, which are respectively located on two sides of a Y-axis center line above or below the surface of a corresponding soft ferromagnetic flux concentrator, and have a same distance from the Y-axis center line; and the push magnetoresistive sensing unit string and the pull magnetoresistive sensing unit string are electrically connected to form a push-pull magnetoresistive sensor, when a Z-direction external magnetic field is measured, the soft ferromagnetic flux concentrator distorts the Z-direction external magnetic field into two magnetic field components that are parallel and anti-parallel to the magnetization direction of the pinned layer, have identical amplitudes, and are applied to the push magnetoresistive sensing unit string and the pull magnetoresistive sensing unit string respectively; characterized by further comprising a second coil, wherein one of the first and second coils is a calibration coil (101, 102) that comprises straight wires (10, 11, 12, 13) parallel to the push magnetoresistive sensing unit string and the pull magnetoresistive sensing unit string, and is configured to generate calibration magnetic fields at the push magnetoresistive sensing unit string and the pull magnetoresistive sensing unit string respectively, the calibration magnetic field having magnetic field components that have identical intensity but are respectively parallel and anti-parallel to the magnetization direction of the pinned layer; and wherein the other of the first and second coils is an initialization coil (104, 105) that comprises straight wires (18, 19, 20) parallel to the magnetization direction of the pinned layer of the magnetoresistive sensing unit, and is configured to generate a uniform initializing magnetic field having magnetic field components parallel to the magnetization direction of the free layer at all the magnetoresistive sensing units, wherein either: (i) the initialization coil is a planar initialization coil, the planar initialization coil comprises a plurality of straight wires perpendicular to the Y-axis center line of the soft ferromagnetic flux concentrator and electrically connected in series, wherein the straight wires are located right above or right below a magnetoresistive sensing unit row of the Z-axis linear sensor along the X-axis direction, and have identical current directions; or (ii) the initialization coil is a three-dimensional initialization coil, the three-dimensional initialization coil comprises an upper, first group having a plurality of straight wires and a lower, second group having a plurality of straight wires that are parallel to a magnetoresistive sensing unit row of the magnetoresistive sensing unit array along the X-axis direction, the first group of straight wires and the second group of straight wires are respectively located on the surfaces of the soft ferromagnetic flux concentrators and the magnetoresistive sensing units, and the first group of straight wires and the second group of straight wires have opposite current directions, and are connected to form a solenoid coil. (i) the initialization coil is a planar initialization coil, the planar initialization coil comprises a plurality of straight wires perpendicular to the Y-axis center line of the soft ferromagnetic flux concentrator and electrically connected in series, wherein the straight wires are located right above or right below a magnetoresistive sensing unit row of the Z-axis linear sensor along the X-axis direction, and have identical current directions; or (ii) the initialization coil is a three-dimensional initialization coil, the three-dimensional initialization coil comprises an upper, first group having a plurality of straight wires and a lower, second group having a plurality of straight wires that are parallel to a magnetoresistive sensing unit row of the magnetoresistive sensing unit array along the X-axis direction, the first group of straight wires and the second group of straight wires are respectively located on the surfaces of the soft ferromagnetic flux concentrators and the magnetoresistive sensing units, and the first group of straight wires and the second group of straight wires have opposite current directions, and are connected to form a solenoid coil.