This chapter reviews the widely linear estimation for complex numbers, quaternions, and geometric algebras (or Clifford algebras) and their application examples. It was proved effective mathematically to add , the complex conjugate number of , as an explanatory variable in estimation of complex-valued data in 1995. Thereafter, the technique has been extended to higher-dimensional algebras. The widely linear estimation improves the accuracy and the efficiency of estimation, then expands the scalability of the estimation framework, and is applicable and useful for many fields including neural computing with high-dimensional parameters.
