7B-4-11 
Table 1 The extended Kalman filter for DGPS/DR system 
Prediction equation 
X(k + l/k) = ®(k + l)X(k/k) 
P(k + Uk) = + l)P(k / k)<t> T (k +1) + T{k)Q{k)V T (k) 
Gain equation 
K(k +1) = P(k + 1 / k)H T (k)[H(k)P(k + /k)H T (k) + R(k)]- 
Update equation 
P{k + 1 /k + 1) = [7 - K{k + 1 )H(k)]P(k + 1 Ik) 
X{k +1 / k +1) = X(k +1 / k) + K{k)[p m - H(k)X(k +1 / k)] 
where 
X(k + 1/ k) = projected state vector 
O(k) = the state transition matrix 
P(k+l/k) = projected covariance matrix 
K(k) = the gain matrix 
X(k + 1/ k + \) = updated state vector 
P(k+l/k+l) = updated covariance matrix