Tham khảo tài liệu 'dynamic vision for perception and control of motion - ernst d. dickmanns part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Recursive Estimation Techniques for Dynamic Vision 195 P E x k - x k x k - x k T 1 r . . E x - x -K C ỗx . x - x -K C Sx r . The output error covariance with Sy CSx v and Equation is E Sy 8yT E CSx v CSx v T C P -CT R. Finding that matrix K that minimizes P under the given side constraints yields K P C C P C R 1. With this result Equation reduces to the well-known form for updating the error covariance matrix P k P k - K k C k P k . Complete Recursion Loop in Kalman Filtering These results are summarized in the following table as algorithmic steps for the basic version of the extended Kalman filter for real-time vision 4-D approach 1. Find a good guess for the n initial state components x 0 to start with initial hypothesis k 0 x0 x 0 . 2. Find an estimate for the probability distribution of this initial state in terms of the first and second moments of a Gaussian distribution mean value x0 and the nn error covariance matrix P0 . The diagonal terms are the components Ơ2 of the variance. 3. Find an estimate for the covariance matrices Q E vTv of system noise v and R E wTw of measurement noise w. - Entry point for recursively running loop 4. Increment time index k k 1 5. Compute expected values for state variables at time k 1 state prediction x k x k A k -1 x . B k -1 uk _1. 6. Predict expected error covariance matrix P k components state prediction and noise corruption P k A k -1 P k -1 AT k -1 Q k -1 . 7. Compute the expected measurement values y k h x k pm and the total Jacobian matrix C ổy ổx N as first-order approximations around this point. 8. Compute the gain matrix for prediction error feedback K P CT. C P CT R 1. 9. Update the state variables innovation to the best estimates including the last measurement values x k x k K k y k - y k . 10. Update the error covariance matrix innovation of statistical properties P k P k - K k C k P k . Go back to step 4 for next loop. Steps for monitoring convergence and progress in the
