This letter introduces a new coupled mixture of polynomial phase signal (PPS) and sinusoidal frequency modulated (FM) signal, motivated by real-world applications, for example, contactless linear encoders. Specifically, the coupling is introduced to express the sinusoidal FM frequency as a function of the PPS-related parameters. Given the coupling mixture, it generalizes two existing models: the pure PPS model and the independent mixture model. Performance bounds of parameter estimation for the coupled mixture model are established in terms of the Cramér-Rao bound (CRB). Unlike the pure PPS case, the derived CRB shows its dependence on the PPS-related and sinusoidal FM-related parameters due to the coupling mixture. On the other hand, the derived CRBs for the PPS-related parameters are lower than their counterparts of the independent mixture model, as the sinusoidal FM frequency provides additional information on the PPS parameters.

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independent mixture model parameter estimation ppsrelated and sinusoidal fmrelated parameters sinusoidal frequency modulated fm signal crb pure pps model coupled mixture of polynomial phase signal pps example contactless linear encoders cramex0301rrao bound

Pu Wang, Yoshitsugu Sawa, Wataru Tsujita, Philip V. Orlik, Kota Sadamoto,.Cramér–Rao Bounds for a Coupled Mixture of Polynomial Phase and Sinusoidal FM Signals. 24 (6),746-750.

Pu Wang, et al."Cramér–Rao Bounds for a Coupled Mixture of Polynomial Phase and Sinusoidal FM Signals" 24

Pu Wang, Yoshitsugu Sawa, Wataru Tsujita, Philip V. Orlik, Kota Sadamoto,"Cramér–Rao Bounds for a Coupled Mixture of Polynomial Phase and Sinusoidal FM Signals"