LKRX detector-based hyperspectral real-time anomaly detection algorithm was proposed. Using local causal sliding array window, the causality of detection system is remained. According to Kalman filter, by using Hermitian lemma and Woodbury’s identity, the kernel covariance matrix and its inverse in KRX algorithm are updated recursively. This thereby leads to low computational complexity. Experimental results demonstrated that real-time KRX detector consumes less time in comparison with KRX detector by keeping the same detection performance, which detects more anomalies.