Different kinds of quaternion signal detection problems in continuous-time by using a widely linear processing are dealt with. The suggested solutions are based on an extension of the Karhunen-Loève expansion to the quaternion domain which provides uncorrelated scalar real-valued random coefficients. This expansion presents the notable advantage of transforming the original four-dimensional eigen problem to a one-dimensional problem. Firstly, we address the problem of detecting a quaternion deterministic signal in quaternion Gaussian noise and a version of Pitcher's Theorem is given. Also the particular case of a general quaternion Wiener noise is studied and an extension of the Cameron-Martin formula is presented. Finally, the problem of detecting a quaternion random signal in quaternion white Gaussian noise is tackled. In such a case, it is shown that the detector depends on the quaternion widely linear estimator of the signal. © 2012 Navarro-Moreno et al.; licensee Springer.
CITATION STYLE
Navarro-Moreno, J., Ruiz-Molina, J. C., Oya, A., & Quesada-Rubio, J. M. (2012). Detection of continuous-time quaternion signals in additive noise. Eurasip Journal on Advances in Signal Processing, 2012(1). https://doi.org/10.1186/1687-6180-2012-234
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