循環式狀態觀察器應用於非線性高階車輛模型之研究

Abstract

為了解決擴增卡曼濾波器應用於高階非線性觀察器時，需以人工推導大量偏微分方程式的問題，許齡元博士提出了一種新穎的觀察器建構方式，循環式狀態觀察器[1]，只要在符合觀察性充足的條件下，可以切割觀察器模型的方式來降低偏微分方程式的數量，藉此來降低工程師在推導方程式所需要的時間。

降低方程式數量所帶來的影響不單單只是用於降低工程師的負擔，其會直接影響到此系統的估測精確度與系統的估測花費時間，本論文會將循環式狀態觀察器應用在一個具有20個系統階數的高階非線性車輛系統，並將其建構在單晶片數位信號處理器上進行real-time環境下的模擬，透過模擬結果可以得到循環式狀態觀察器對精確度與花費時間的影響程度。

在現實中，人們往往無法找車體的重心位置並將感測器裝置在重心上，而我們發現裝置於車體非重心位置的感測器會因車體的旋轉量測到與重心位置不同的線速度與線加速度，因此本論文同時探討此量測差異對觀察器估測的影響。

依據模擬結果可得到循環式狀態觀察器運用在此高階非線性車輛模型時可減少10.787%的估測時間。經本論文模擬，由於車體旋轉造成的量測差異相對於車體本身的線速度、線加速度小很多，就算不知道感測器與重心的相對位置關係，亦不會對觀察器估測結果造成太大的影響。

In order to reduce the time consumption caused by partial differential equations derived by human when applying Extended Kalman Filter (EKF) to high order nonlinear observers, Dr. Ling-Yuan Hsu brings up a novel observer construction method, 「Switching Observer」. If the system is observable, we could reduce partial differential equations by separating the system into two sub-systems. Reducing equations is not only release the loading of engineers but also influence estimated time and estimated precision of the computation system. This thesis will build a switching observer system with a twenty states high order vehicle model on a single digital processor (DSP) to do real-time simulations.

In the reality, it’s difficult for people to find the center of gravity (C.G) on vehicle and set the sensors on it. We find that the velocity and acceleration measurements of sensors on C.G position are different from non-C.G position because of the vehicle spin. How it influence the observer will also be discussed in this thesis.

The results indicate that the switching observer could save 10.787% of computation time than conventional observer when applying on a high order vehicle model. In this case, the velocity and acceleration measurements caused by spin are much smaller than original velocity and acceleration. Therefore, it will not strongly impact the result of observer.