Linear Smoothing of Noisy Spatial Temporal Series | Science Publications

Journal of Mathematics and Statistics

Luca ramognali¹  Ian dryden¹  Luigi ippoliti¹  Valter d. Giacinto¹ 

关键词: Gaussian markov random field;    image analysis;    maximum likelihood estimation;    measurement error;    Kalman filter;    STARMA model;    STARG model;    state space model;   

DOI  :  10.3844/jmssp.2005.309.321

学科分类：社会科学、人文和艺术（综合）

来源: Science Publications

【 摘 要 】

The main objective of the study is the development of a linear filter to extract the signal from a spatio-temporal series affected by measurement error. We assume that the evolution of the unobservable signal can be modelled by a space time autoregressive process. In its vectorial form, the model admits a state space representation allowing the direct application of the Kalman filter machinery to predict the unobservable state vector on the basis of the sample information. Having introduced the model, referred to as a STARG+Noise model, the study discusses Maximum Likelihood (ML) parameter estimation assuming knowledge of the variance of the noise process. Consistent method of moments estimators of the autoregressive coefficients and noise variance are also derived, primarily to be used as inputs in the ML estimation procedure. Finally, we consider some simulation studies and an investigation involving sulphur dioxide level monitoring.

【 授权许可】

Unknown