Apparatus for estimating phase by processing sensor signals from a set of sensors , the sensor signals collectively conveying a sensed phase for a periodically varying state of an object, the sensed phase including an error component due to non-ideal arrangement or performance of the sensors , comprising: a phase estimation processor operative to apply a first correlation calculation to simultaneously collected samples of the sensor signals to generate first quadrature values for the sensor signals, the first correlation calculation employing calibration coefficients, and apply a phase calculation to the first quadrature values to generate an estimated phase indicative of the periodically varying state of the object; and a pre-quadrature calibration circuit operative to apply respective second correlation calculations to respective sequences of samples of the sensor signals individually to generate respective sets of second quadrature values for each of the sensor signals, apply phase and/or magnitude calculations to the sets of second quadrature values to generate the calibration coefficients for the first correlation calculation and thereby compensate for the error component and improve accuracy of the estimated phase, wherein the pre-quadrature calibration circuit is further operative to record successive sets of samples into digital memory along with respective estimated phases of the periodically varying state of the object when the respective sets were generated, and to select from among the recorded samples to form the sequences of samples used in the second correlation calculations to generate the sets of second quadrature values to which the phase and/or magnitude calculations are applied, recorded samples being selected at different phase points over one period of the sensor signal as indicated by respective stored estimated phases. a phase estimation processor operative to apply a first correlation calculation to simultaneously collected samples of the sensor signals to generate first quadrature values for the sensor signals, the first correlation calculation employing calibration coefficients, and apply a phase calculation to the first quadrature values to generate an estimated phase indicative of the periodically varying state of the object; and a pre-quadrature calibration circuit operative to apply respective second correlation calculations to respective sequences of samples of the sensor signals individually to generate respective sets of second quadrature values for each of the sensor signals, apply phase and/or magnitude calculations to the sets of second quadrature values to generate the calibration coefficients for the first correlation calculation and thereby compensate for the error component and improve accuracy of the estimated phase, wherein the pre-quadrature calibration circuit is further operative to record successive sets of samples into digital memory along with respective estimated phases of the periodically varying state of the object when the respective sets were generated, and to select from among the recorded samples to form the sequences of samples used in the second correlation calculations to generate the sets of second quadrature values to which the phase and/or magnitude calculations are applied, recorded samples being selected at different phase points over one period of the sensor signal as indicated by respective stored estimated phases. <EOS>