Optimal estimation policies of stochastic linear systems with time- varying parameters (Q1202460)

The author considers the linear discrete time model \(x_ n= u_ n^ T\alpha_ n+ w_ n\), \((n=1,2,\dots,n)\), where \(u_ n= [u_{1n} u_{2n}\cdots u_{mn}]^ T\), \(\alpha_ n= [\alpha_{1n}\alpha_{2n}\cdots\alpha_{mn}]^ T\), \(x_ n\) are scalar observations on the dependent variables; \(w_ n\) are white noise disturbances with common (known) variance; \(u_{in}\) \((i=1,\dots,n)\) are observed values of the control variables at time \(n\); \(\alpha_{in}\) are coloured noise disturbances defined by \(\alpha_ n= A_ n\alpha_{n- 1}+ v_ n\), where \(v_ n\) and \(\alpha_ 0\) are normal variables \(v_ n\sim N(0;\sigma_ v)\), \(\alpha_ 0\sim N(\bar\alpha_ 0,\sigma_ \alpha)\), \(A_ n\), \(\sigma_ n\), \(\bar\alpha_ 0\), \(\sigma_ \alpha\) are assumed known and the sequences \(w_ n\) and \(v_ n\) are assumed uncorrelated. The author uses control theoretic concepts to develop a methodology for designing optimal strategies for precise parameter estimation. Before the control policies are implemented, and estimation phase is introduced to determine the unknown model parameters.