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Author: Admin | 2025-04-28
The state transition matrix, Bk is the noise transition matrix, and Wk is the state noise whose covariance is Qk. where Zk is the observation vector, Hk is the observation transition matrix, and Vk is the observation noise whose covariance is Rk.There are N sample data in the system. The smoothing algorithm has two steps. Step 1: calculating (3) from k = 0 to k = N to obtain αk. Step 2: calculating (4) from k = N to k = 0 to acquire βk under the known αk from (3). X k + 1 α k = F k − K k H k K k − H k ( H k P k − 1 H k T + R k ) − 1 / 2 ( H k P k − 1 H k T + R k ) − 1 / 2 X k Z k , X 0 = 0 (3) Y k − 1 β k = F k T − H k T K k T H k T ( H k P k − 1 H k T + R k ) − 1 / 2 − K k T ( H k P k − 1 H k T + R k ) − 1 / 2 Y k α k , Y N = 0 (4) where Kk is the gain, which can be given as (5), and Pk is the mean square of the system, which is updated as (6). K k = F k P k − 1 H k T ( H k P k − 1 H k T + R k ) − 1 (5) P k = H k P k − 1 H k T − K k ( H k P k − 1 H k T + R k ) K k T + B k Q k B k T (6) Therefore, the estimated output is expressed as Z ^ k = Z k − R k β k (7) In CUMT, the authors of this paper proposed the global optimization model (GOM) for shearer trajectory through borrowing the simultaneous localization and mapping (SLAM) technology. The SLAM frame is divided into front-end and back-end procedures [34,35]. The front-end process acquires the environment information using a camera or lidar to realize the map construction. The back-end step is to realize the
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