應用卡爾曼濾波器在GPS接收器的追蹤技術

Abstract

訊號擷取在全球定位系統(GPS)接收器中的目的是為了追蹤估測偽隨機碼(Pseudo-Random Number, PRN)的延遲時間和都普勒頻率。追蹤方法利用延遲/提早的方法並且經由一個擁有迴路濾波器的閉迴路系統來實現。而迴路濾波器往往使用一個比例積分(Proportional-Integral, PI)濾波器。使用比例積分濾波器的參數需要依賴經驗來調整，追蹤效能隨著比例積分濾波器參數的選擇而變動。本篇論文把估測偽隨機的延遲時間和都普勒頻率的追蹤設定為觀察者設計的問題，如此擴張卡爾曼濾波器被用來實現這個觀察者。估測偽隨機的延遲時間的追蹤可用數位延遲鎖相迴路(digital delayed-locked loop, DDLL)來實現，並且設定為一個非線性觀察者問題，如此擴張卡爾曼濾波器可被用來估測延遲時間。都普勒頻率的追蹤可用數位鎖相迴路(digital phase-locked loop, DPLL)來實現，並且設定為一個線性觀察者問題，因此卡爾曼濾波器可當作是觀察者。此方法不但減輕設計濾波器參數的負擔並且是一個快速追蹤的演算法。使用電腦模擬來驗證本論文所題方法之優越性。

The goal of signal tracking in GPS receiver is to track the Pseudo-Random Number (PRN) code delay and the Doppler frequency. The tracking methods are performed using early-late method via a closed loop with a loop filter. The PI is commonly used to realize the loop filter; The PI parameters are empirically determined. The tracking performance varies with the choice of PI parameters. This thesis configures the tracking of PRN code delay and Doppler frequency as problems of observer design, such that the extended Kalman filter (EKF) and Kalman filter (KF) algorithm are applied realize the observers. The tracking of PRN code delay which is realized by a digital delay-locked loop is configured as a nonlinear observer problem such that the EKF can be used to estimate the delay, while the tracking of the Doppler frequency realized by a digital phase-locked loop, is configured as a linear observer problem, hence the KF can be used as the observer. This approach not only alleviates the burden of designing PI parameters but also obtain a fast tracking algorithm. Computer simulations are also performed to demonstrate the advantages of our proposed method.