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Optimal detection of liquid ionization calorimeter signal in experimental particle physics is considered. A few linear and nonlinear approaches for amplitude and arrival time estimation based on the χ2 function are compared in simulation considering the noise sample correlation introduced by the analog pulse shaper. The estimation bias of the first-order approximation, a.k.a linear optimal filtering, is studied and contrasted to those of the second-order as well as the exhaustive search. A gradient-descent technique is presented as an alternative to the exhaustive search with significantly reduced search time and computation complexity. Results from various pulse shapers including the CR-RC2, CR-RC3, and CR2-RC2 are also compared.