A process plant can have multiple modes of operation due to varying demand, availability of resources or the fundamental design of a process. Each of these modes is considered as normal operation. Anomalies in the process are characterised as deviations away from normal operation. Such anomalies can be indicative of developing faults which, if left unresolved, can lead to failures and unplanned downtime. The Field Kalman Filter (FKF) is a model-based approach, which is adopted in this paper for monitoring a multimode process. Previously, the FKF has been applied in process monitoring to differentiate normal operation from known faulty modes of operation. This paper extends the FKF so that it may detect occurrences of anomalies and differentiate them from the various normal modes of operation. A method is proposed for offline training an FKF monitoring model and on-line monitoring. The off-line part comprises training an FKF model based on Multivariate Autoregressive State-Space (MARSS) models fitted to historical process data. A monitoring indicator is also introduced. On-line monitoring, on the basis of the FKF for anomaly detection and mode identification, is demonstrated using a simulated multimode process. The performance of the proposed method is also demonstrated using data obtained from a pilot scale multiphase flow facility. The results show that the method can be applied successfully for anomaly detection and mode identification.