A Maximum Likelihood Approach for Signal Estimation and Data Quality Assessment for High-Energy Calorimeter Systems

Abstract

In high-energy calorimetry, energy estimation is typically performed using digital linear filters, from which the amplitude of a conditioned signal is inferred. The linear approach is justified when electronic noise can be approximated by a Gaussian distribution. However, calorimeters operating at high event rates and under high-luminosity conditions—such as those in modern particle colliders—are affected by non-Gaussian noise sources, notably signal tails from adjacent collisions that do not carry relevant physical information about the event of interest. Despite this, the true noise probability density function (pdf) is often neglected, and only second-order statistics are considered to preserve the linear model.This work presents a novel approach based on the full characterization of the noise distribution using maximum likelihood estimators (MLE). An iterative optimization algorithm is proposed to determine the parameter values that maximize a non-Gaussian multivariate distribution. Additionally, the study evaluates the use of maximum likelihood estimates for data quality assessment, enabling the rejection of signals with poor estimation quality. Simulation results comparing the proposed method with conventional linear approaches show that the non-Gaussian MLE achieves superior performance in terms of estimation error across a wide range of cell occupancy conditions. Furthermore, the final likelihood value can be used as a performance metric for signal reconstruction, providing a robust quality factor (QF) for discriminating signals in physics analyses when compared to traditional strategies.