Incomplete Phase Space Reconstruction Method Based on Subspace Adaptive Evolution Approximation

Table 1

Extended Kalman filtering neural network algorithm.

Extended Kalman filtering neural network
(1) Initialization	𝜽0=𝐸𝜽0=𝐖0,𝐛0^𝑇; 𝐏0=𝐸𝜽0−𝜽0𝜽0−𝜽0^𝑇
(2) Time update (forecast)	𝜽^−𝑘=𝜽𝑘−1; 𝐏^−𝑘=𝐏𝑘−1+𝐐𝑘−1
(3) Measurement update (correct)	𝐊𝑘=𝐏^−𝑘𝐇𝑘^𝑇𝐇𝑘𝐏^−𝑘𝐇𝑘^𝑇+𝐑𝑘^−1; 𝜽𝑘=𝜽^−𝑘+𝐊𝑘𝐘𝑒𝑘−ℎ𝜽^−𝑘,𝐗𝑘; 𝐏𝑘=𝐈−𝐊𝑘𝐇𝑘𝐏^−𝑘

𝐐_𝑘−1 and 𝐑_𝑘 are process noise covariance and measurement noise covariance, respectively, 𝐇_𝑘 is the Jacobian matrix of observable model, 𝜽⁻_𝑘 is the optimal predictive value for step 𝑘 according to step 𝑘−1, and 𝜽_𝑘 is the optimal filter estimate for step 𝑘.