State estimation and control are often addressed separately, leading to unsafe execution due to sensing noise, execution errors, and discrepancies between the planning model and reality. Simultaneous control and trajectory estimation using probabilistic graphical models has been proposed as a unified solution to these challenges. Previous work, however, relies heavily on appropriate Gaussian priors and is limited to holonomic robots with linear time-varying models. The current research extends graphical optimization methods to vehicles with arbitrary dynamical models via Simultaneous Trajectory Estimation and Local Adaptation (STELA). The overall approach initializes feasible trajectories using a kinodynamic, sampling-based motion planner. Then, it simultaneously: (i) estimates the past trajectory based on noisy observations, and (ii) adapts the controls to be executed to minimize deviations from the planned, feasible trajectory, while avoiding collisions. The proposed factor graph representation of trajectories in STELA can be applied for any dynamical system given access to first or second-order state update equations, and introduces the duration of execution between two states in the trajectory discretization as an optimization variable. These features provide both generalization and flexibility in trajectory following. In addition to targeting computational efficiency, the proposed strategy performs incremental updates of the factor graph using the iSAM algorithm and introduces a time-window mechanism. This mechanism allows the factor graph to be dynamically updated to operate over a limited history and forward horizon of the planned trajectory. This enables online updates of controls at a minimum of 10Hz. Experiments demonstrate that STELA achieves at least comparable performance to previous frameworks on idealized vehicles with linear dynamics.[...]