Predicting the chemical and physical processes occurring in Lithium-ion cells with high-fidelity electrochemical models is today a critical requirement to accelerate the design and optimization of battery packs for automotive and aerospace applications. One of the common issues associated with electrochemical models is the complexity of parameter identification, particularly when relying only on experimental data obtained via non-invasive techniques. This paper presents a novel approach to improve the common methods of parameter calibration that consists of matching the predicted terminal voltage to test data via optimization methods. The study is conducted for an nickel-manganese-cobalt (NMC)-graphite cell, modeled using a reduced-order Extended Single Particle Model (ESPM). The proposed approach relies on using a large-scale particle swarm optimization (PSO), modified by including a term that accounts for the parameter sensitivity information, such that the rate of convergence and robustness of the algorithm to obtain a consistent solution in the presence of uncertainties in the initial conditions are significantly improved.