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Photonics-assisted instantaneous microwave frequency measurement (IFM) has been a topic of interest recently. To perform IFM, an amplitude comparison function (ACF) that relates the microwave frequency to the microwave powers by which the microwave frequency can be estimated by measuring the microwave powers should be established. In this letter, a two-tap photonic microwave filter pair with complementary frequency responses is employed for achieving IFM. Thanks to the complementary nature of the transfer functions of the filter pair, a quasi-linear monotonically decreasing ACF over a large frequency band is obtained, which ensures an improved measurement range and accuracy. An experiment is performed. A microwave frequency measurement range as large as 36 GHz with a measurement accuracy better than ±0.2 GHz is experimentally demonstrated.