Assessment of an Anomaly Detector for Jet Engine Health Monitoring

Algorithm 1

Basic steps of the extended Kalman filter.

(1) 𝐰⁻_𝑘=𝐰_𝑘−1 and 𝐏⁻_𝐰,𝑘=𝐏_{𝐰,𝑘−1}+𝐐_𝑘

(2) acquire 𝐮_𝑘 and 𝐲_𝑘

(3) 𝐫_𝑘=𝐲_𝑘−𝒢(𝐮_𝑘,𝐰⁻_𝑘)

(4) compute Jacobian matrix, 𝐆_𝑘, as per(3)

(5) 𝐏_𝐲,𝑘=(𝐆_𝑘𝐏⁻_𝐰,𝑘𝐆^𝑇_𝑘+𝐑_𝐲)

(6) 𝐊_𝑘=𝐏⁻_𝐰,𝑘𝐆^𝑇_𝑘𝐏⁻¹_𝐲,𝑘

(7) 𝐰_𝑘=𝐰⁻_𝑘+𝐊_𝑘𝐫_𝑘 and 𝐏_𝐰,𝑘=(𝐼−𝐊_𝑘𝐆_𝑘)𝐏⁻_𝐰,𝑘