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A data assimilation approach is coined that enables the discovery of forcing functions in Lagrangian, point-particle models from limited measurements of trajectory coordinates. Central to the proposed formulation of this inverse problem is the expression of the forcing function in terms of modal basis functions that are dependent on the relative velocity difference between a known carrier flow and the particle solution weighted with coefficients that are known within confidence intervals. The probability density function of the random forcing coefficients is inferred using a combination of the forward, particle model and its adjoint dynamics, which calculates the gradient of the cost function defined as the distance between the measured and predicted particle locations. To ensure convergence of the gradient-based optimization, multiple measurements may be required. If the measurements are noisy, samples of the forcing model within an assumed Gaussian distribution of the confidence interval of the measurement are computed using a Hamiltonian Monte Carlo method. The method is verified to correctly infer the forcing function of particles traced in the Arnold–Beltrami–Childress flow and a homogeneous isotropic turbulence. The confidence interval of the inferred forcing function with respect to a flow condition is improved if the particle is exposed more frequently to the flow condition. The forcing coefficients adapt the model to flow conditions that are outside of the limited range for which the point-particle models are typically known only empirically or within confidence intervals.