Tone and color reproduction functions (TRC or CRC) characterize how a printer maps a desired tone or color into the actual output. Ideally, the TRC/CRC should be identity maps. Sensing the TRC/CRC is needed for closed loop feedback control. Currently, sensing of the high dimensional TRC/CRC is limited since only a small number of tone/color sensor patches can be printed and measured at a time. Time-sequential sampling is proposed to alleviate this difficulty by sampling different tones/colors at different times. A Kalman filtering approach is proposed to reconstruct the TRC/CRC from the time-sequential samples. The effect of two sampling strategies - lexicographical and bit-reversed strategies are analyzed. It is shown that the periodic Kalman reconstruction filter is effective, and that it can be interpreted to consist of cascade of modulation, low pass and demodulation processes.