Fig. 1. Measurement residuals of CKF and MKF.

Fig. 2. Equalization model and state estimation process of MKF.

Fig. 3. (a) Variance of process noise versus the measurement error; (b) variance of measurement noise versus the process noise.

Fig. 4. Variance rate of measurement errors versus SNR.

Fig. 5. BER of the recovered signal versus OSNR. The scrambling rate is (a) 10 MHz and (b) 20 MHz. The reference curves (gray dashed lines) are under the back-to-back (B2B) case without RSOP.

Fig. 6. (a) Signal qualities versus scrambling rates at the OSNR of 24 dB; (b) signal qualities versus scrambling rates at the OSNR of 20 dB.

Fig. 7. Initialization tolerance of Q/R parameter for linear CKF and MKF at the OSNR of 30 dB and 10 MHz scrambling rate. (a) CKF without Q/R adaptive algorithm; (b) CKF with Q/R adaptive algorithm; (c) MKF without Q/R adaptive algorithm; (d) MKF with Q/R adaptive algorithm.