This paper proposes a state observer design method for tensegrity structures based on joint use of non-minimal representation of the structure’s model and orthogonal decomposition method. Tensegrity structures have a number of potential applications in robotics, from drones to planetary probes, and at the same time their use poses a number of open research problems. Effective state observer design is one of them. As evident by success of model-based state estimator design methods in various areas of robotics, computational problems posed by complex dynamics can be overcome; often they are overcome with the use of simplifications, projections and appropriate choices of state variables. The use of so-called node-distance coordinates can simplify the dynamics equations of tensegrity structures. The resulting model (and its linearized form) will include explicit constraints, which can be dealt with using orthogonal decomposition methods. Resulting linear equations can be used to design state observer by solving Riccati equation. The paper presents simulation results illustrating the work of the proposed observer.