In this paper, we study parameter estimation in multiple-input multiple-output (MIMO) wireless powered sensor networks (WPSN). The sensor nodes are powered exclusively by harvesting the radio frequency signals transmitted from the energy access points. We propose a joint design of the sensor data precoders and energy covariance matrices to minimize the mean square error (MSE) of the parameter estimate. This design also incorporates optimal allocation of the harvested power for data acquisition and data transmission. We employ a zero-forcing precoding based estimation framework and the alternating minimization technique to compute the precoders, power allocation, and energy covariance matrices. Simulation results demonstrate that the proposed method achieves a superior estimation performance in comparison to the conventional energy transfer techniques for estimation in WPSNs.