Cargo inside cells have motors to drive their movement along a microtubule. Understanding the cargo transport can give important insight into neurodegenerative diseases such as Alzheimer's and Parkinson's disease, where such transport breaks down. In this work, we propose a new model for this movement and we infer parameters from time series data. The model consists of two different states for each motor based on whether it is attached or detached. If attached, the motors have directed motion along the microtubule; if detached, the movement is diffusive. In either case, the motor dynamics are coupled to those of the cargo. We model these state switches as Markovian processes, which may depend on the distance from the motor to the cargo. We predict particle movement based on the observed position of the cargo in DNA origami data. Using a particle filter and an Expectation-Maximization algorithm, we predict the true trajectory of the particles and infer the parameter values via maximum likelihood estimation.