The Extended Kalman Filter(EKF)를 이용한 비행체 궤적 추적

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연세대학교 학부대학원 공통과목인 로봇제어공학 프로젝트 입니다.

EKF를 이용하여 비행체의 궤적을 추적하였습니다.

목차

Ⅰ. Introduce
Ⅱ. Overview
Ⅲ. Theory
Ⅳ. Flow Chart
Ⅴ. Code Analysis
Ⅵ. Result

본문내용

Ⅲ. Theory
Extended Kalman Filter
In estimation theory, the extended Kalman filter (EKF) is the nonlinear version of the Kalman filter which linearizes about the current mean and covariance. The EKF has been considered the de facto standard in the theory of nonlinear state estimation, navigation systems and GPS.

Formulation
In the extended Kalman filter, the state transition and observation models need not be linear functions of the state but may instead be differentiable functions.

Where wk and vk are the process and observation noises which are both assumed to be zero mean multivariate Gaussian noises with covariance Qk and Rk respectively.

The function f can be used to compute the predicted state from the previous estimate and similarly the function h can be used to compute the predicted measurement from the predicted state. However, f and h cannot be applied to the covariance directly. Instead a matrix of partial derivatives (the Jacobian) is computed.

At each timestep the Jacobian is evaluated with current predicted states. These matrices can be used in the Kalman filter equations. This process essentially linearizes the non-linear function around the current estimate.

Predict and Update Equations
① Predict
Predicted state

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