We propose a sensor placement method for spatio-temporal field estimation based on a kriged Kalman filter (KKF) using a network of static or mobile sensors. The developed framework dynamically designs the optimal constellation to place the sensors. We combine the estimation error (for the stationary as well as non-stationary component of the field) minimization problem with a sparsity-enforcing penalty to design the optimal sensor constellation in an economic manner. The developed sensor placement method can be directly used for a general class of covariance matrices (ill-conditioned or well-conditioned) modelling the spatial variability of the stationary component of the field, which acts as a correlated observation noise, while estimating the non-stationary component of the field. Finally, a KKF estimator is used to estimate the field using the measurements from the selected sensing locations. Numerical results are provided to exhibit the feasibility of the proposed dynamic sensor placement followed by the KKF estimation method.