Signal detection of rotational processes and frequency demodulation

A signal detection problem for continuous rotational processes is formulated by using H. P. McKean\´s trick of "injection." Both the sensor and the signal dynamics are described by bilinear 3 ?? 3-matrix Ito differential equations, where noise can be viewed as entering multiplicatively. The injection is shown to be bijective. This facilitates the derivation of a likelihood ratio formula in terms of updated observation. The least-squares estimation required in the formula can be solved analogously. These results are then applied to signal detection from frequency-modulated carriers. In particular, the likelihood ratio for the frequency-shift-keyed binary communication is evaluated.