State filtering and parameter estimation for state space systems with scarce measurements

•State and parameter estimation problems are studied for state space systems.•A least squares based and an observer based estimation algorithms are developed.•A combined parameter estimation and state filtering algorithm is presented.

This paper considers the state filtering and parameter estimation problems for state space systems with scarce output availability. When the scarce states are available, a least squares based algorithm and an observer based parameter estimation algorithm are developed to estimate the system parameter matrices and states. For the case with unknown states, a combined parameter estimation and state filtering algorithm is presented for canonical state space models, using the reconstructed states for the parameter estimation. Finally, an example is provided to test the effectiveness of the proposed algorithms.