Parameter Estimation

We consider a simple mathematical model of a communication network involving 3 interacting nodes. The dynamic behavior (i.e. observable information) of the overall system is described by the following difference equation system: y(k) = θ1y(k − 1) + θ2u(k − 1), yneighbor1(k) = θ4yneighbor1(k − 1) + θ5y(k − 1), yneighbor2(k) = θ7yneighbor2(k − 1) + θ8y(k − 1) + θ9yneighbor1 (k − 1), where y(k), yneighbor1(k) and yneighbor2(k) characterize the observed output information (dynamical behavior) at the respective nodes for k ≥ 0. An input excitation u(k) is also fed to the system at y(k). The system is assumed to be perturbed with zero-mean Gaussian noise at certain nodes. The communication network is static in space, i.e. all the nodes are of some fixed local position. We can assume that the communicating nodes are located close to each other in space, hence it is possible that the same perturbation (ε(k)) affects all of them with some time-delay. Estimate the system parameters using simple LSQ approach and quantify the predictive performance of the resulting model! Next identify the parameters by taking into account the possibility of correlated noise! Compare the performance with the simple LSQ case.