This paper shapes the periodic cycling of a lithium-ion battery to maximize the battery's parameter identifiability. The paper is motivated by the need for faster and more accurate lithium-ion battery diagnostics, especially for transportation. Poor battery parameter identifiability makes diagnostics challenging. The existing literature addresses this challenge by using Fisher information to quantify battery parameter identifia-bility, and showing that test trajectory optimization can improve identifiability. One limitation is this literature's focus on offline estimation of battery model parameters from multi-cell laboratory cycling tests. This paper is motivated, in contrast, by online health estimation for a target battery or cell. The paper examines this "targeted estimation" problem for both linear and nonlinear second-order equivalent-circuit battery models. The simplicity of these models leads to analytic optimal solutions in the linear case, providing insights to guide the setup of the optimization problem for the nonlinear case. Parameter estimation accuracy improves significantly as a result of this optimization. The paper demonstrates this improvement for multiple electrified vehicle configurations.