State Estimation Of An Unmanned Helicopter

This thesis tries to give a systemic research on the state estimation of an unmanned helicopter(UH), which is heavily required for almost all real tasks, such as stably automatic control, navigation, self positioning, and target tracking.One of foundations for the state estimation is the dynamic model of the UH which is used as an experimental platform. A theoretic approach was adopted to build the model. Some reasonable assumptions were introduced to make a balance between model's complexities and accuracy. Forces and moments of the main rotor, the Bell-Hiller flybar, the tail rotor, and the engine were highlighted. Meanwhile, the precession effect to external moments on the UH was analyzed, and the flybar stabilizing equation was built. At last, a simplified UH dynamic model was obtained after adding noise.Since the UH model is stochastic and nonlinear, only nonlinear filters can be adopted to estimate its state. In this thesis, the estimation accuracy of the Sigma-points Kalman filter(SPKF) and the extended Kalman filter(EKF) was thoroughly analyzed. Theoretic analysis indicates that the SPKF presents the same estimation accuracy as the EKF. Because deriving Jacobians is eliminated in the SPKF, the SPKF is more suitable to be used to estimate the state of the UH than the EKF. At last, we applied the SPKF to estimate the state of the UH by simulations. The simulation results showed the SPKF could successfully estimate the state of the UH. At the same time, a same conclusion on the estimation accuracy of these filters was also come by analyzing simulation results of the EKF and the SPKF.In practical applications, because statistic characters of noise embedded in the dynamic model may be partially known, approximate, or totally unknown, adaptive Kalman filters(AKF) should be adopted to estimate the state of the UH. However, applications of AKFs are restricted due to their unproved convergence. To escape from this limitation, we proposed the concept of the weak convergence in AKFs based on the idea that the covariance matrix of state estimation error should own a superior bound. Thereby, a series of practical judgment rules on the weak convergence of AKFs were given. Some of the rules can be used both for judging the weak convergence of an AKF and for designing a weak convergent adaptive Kalman filter(WC-AKF). Naturally, a WC-AKF based on such weak convergence rules was proposed and implemented for estimating the state of the UH. The simulation results showed the WC-AKF could successfully estimate the state of the UH.Observing the SPKF and the WC-AKF, we can find some free parameters exist in them, which influence the estimation accuracy. Obviously, the estimation accuracy of the SPKF and the WC-AKF can be improved by properly selecting these parameters which leads to parameter optimization. One critical issue in parameter optimization is how to select the cost function. We proposed two kinds of cost functions, and proved that they were both optimal. Adopting these cost functions in the SPKF and the WC-AKF, the optimized SPKF(OSPKF) and the optimized WC-AKF(OWC-AKF) were respectively designed. The OSPKF can be used to deal with systems whose noise characters are known, and the OWC-AKF can be used to deal with systems whose noise characters are unknown. Since weights in them are updated according to the optimal cost function, the more accurate estimation may be obtained. At last, we applied these filters to estimate the state of the UH by simulations. The simulation results showed the OSPKF and the OWC-AKF could successfully estimate the state of the UH.