Parameter Estimation from Flight Data of a missile using Maximum Likelihood and Neural Network Method

[Abstract] Parameter estimation from flight data as applied to aircraft, missile in the linear flight regime is currently being used on routine basis. However, the linear aerodynamic models used successfully upto this time seem to be inadequate for newly introduced short range, highly maneuverable missile, rockets etc. The aerodynamics is required throughout the design process of any flight vehicle. Rapid progress has been made in the use of the so-called output error method, such as the modified Newton-Raphson method and maximum likelihood (ML) methods. Several requirements have been introduced to improve accuracy and reliability of estimates. The presence of measurement and process noise and this, in general, has resulted in relatively increased complexity and computational time. Application of these methods requires a priori postulations of the aerodynamic model. The application of the Delta method and ML method on flight data of a typical tactical missile faces one main difficulty. Due to operational reasons, it might not be possible to excite the missile with a multistep efficient control input and that might result in having flight data with inadequate information content for the purpose of parameter estimation. The present study makes an attempt to estimate aerodynamic parameters from a typical flight data of a short range missile. Since ML method requires a priori postulation of the model, exhaustive wind tunnel testing were conducted to generate longitudinal force and moment coefficients. Identification methods were applied on the selected wind tunnel data to capture the general form of the aerodynamic model. During the application of ML method, the estimation algorithm assumed this wind tunnel identified aerodynamic model to be exact. To avoid any requirement of postulation of aerodynamic model, the Delta method was applied to estimate the aerodynamic parameters. The Delta method used measured aircraft motion and control variables as the inputs to the Feed Forward Neural Network and the aerodynamic force or moment coefficient was the output for training the Feed Forward Neural Network. The application of the Delta method results in large scatters in the estimated parameters. To overcome this problem of large scatter, the Delta method was modified by changing the training strategy. The Delta method with new training strategy will be referred as the Modified Delta method. It is expected that the proposed Modified Delta method would result in estimates with less uncertainties. Further to check the robustness of the both ML and Delta as the Modified delta methods, the estimation was also carried out with flight data having known measurement noise. The effect of control input form in the accuracy of estimates obtained by ML and the Delta as the Modified Delta methods are also studied. It is observed that the Modified Delta method can advantageously be applied on the flight data of a tactical missile to estimate aerodynamic parameters. The paper progresses with the description of the generation of wind tunnel data and aerodynamic model identification using selected wind tunnel data. Finally it concludes by demonstrating applicability of ML and the Delta as the Modified Delta methods on simulated flight data of a typical short range tactical missile configuration.