Robust Identification of Nonlinear Systems With Missing Observations: The Case of State-Space Model Structure

2019 ◽  
Vol 15 (5) ◽  
pp. 2763-2774 ◽  
Author(s):  
Xianqiang Yang ◽  
Xin Liu ◽  
Shen Yin
2010 ◽  
Vol 67 (9) ◽  
pp. 1939-1947 ◽  
Author(s):  
Mark R. Payne

Abstract Payne, M. R. 2010. Mind the gaps: a state-space model for analysing the dynamics of North Sea herring spawning components. – ICES Journal of Marine Science, 67: 1939–1947. The North Sea autumn-spawning herring (Clupea harengus) stock consists of a set of different spawning components. The dynamics of the entire stock have been well characterized, but although time-series of larval abundance indices are available for the individual components, study of the dynamics at the component level has historically been hampered by missing observations and high sampling noise. A simple state-space statistical model is developed that is robust to these problems, gives a good fit to the data, and proves capable of both handling and predicting missing observations well. Furthermore, the sum of the fitted abundance indices across all components proves an excellent proxy for the biomass of the total stock, even though the model utilizes information at the individual-component level. The Orkney–Shetland component appears to have recovered faster from historic depletion events than the other components, whereas the Downs component has been the slowest. These differences give rise to changes in stock composition, which are shown to vary widely within a relatively short time. The modelling framework provides a valuable tool for studying and monitoring the dynamics of the individual components of the North Sea herring stock.


Author(s):  
Minh Q. Phan ◽  
Francesco Vicario ◽  
Richard W. Longman ◽  
Raimondo Betti

This paper describes an algorithm that identifies a state-space model and an associated steady-state Kalman filter gain from noise-corrupted input–output data. The model structure involves two Kalman filters where a second Kalman filter accounts for the error in the estimated residual of the first Kalman filter. Both Kalman filter gains and the system state-space model are identified simultaneously. Knowledge of the noise covariances is not required.


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