Parallel direct method of optimal adaptive estimation for discrete linear systems (Q1281070)

The authors study a discrete-time system of autoregressive type. Its state evolution is described by the equation \[ x(k+1)=Ax(k)+bu(k) ,\qquad x(0)=x_0 , \] where \(x(.)\) is the state vector, \(u(k)\) is the (scalar) input, \(A\) is a companion matrix. The observation (or output) \(y(k)\) is equal to the first element of the vector \(x(k)\). The unknown parameters are \(A\) and \(b\). Estimation of the state \(x(k)\) is also necessary. An algorithm is proposed for their estimation. In the main part of the paper the authors study parallel implementations of that algorithm. The parallel architecture considered is SIMD (Single Instruction-Multiple Data). Separate analyses are provided for the case of ``large'' and ``small'' problems. Results of numerical experiments are reported.