Optimal input design for multi UAVs formation anomaly detection

As the input signal must be informative enough, so that the resulting dataset is enough informative to excite the identification experiment for multi UAVs formation anomaly detection. Based on our previous work on multi UAVs formation anomaly detection, the optimal input signals are designed for two identification strategies, i.e. least squares estimation and improved sparse estimation. Using the variance of the asymptotic distribution corresponding to the unknown parameters, the common trace operation is chosen to construct one numerical optimization problem, whose solution is corresponded to the optimal power spectral. After giving the detailed minimization process, we see that the power spectral corresponding to the optimal input signal is a constant. In addition, for the sake of completeness, one dynamic programming technique in multi UAVs formation anomaly detection is added to complete our early research. Finally, one numerical example illustrates the effectiveness of our proposed theories.