Square-root algorithms for parallel processing in optimal estimation,

We give explicit algorithms in square-root form that allow measurements for the standard state estimation problem to be processed in a highly parallel fashion with little communication between processors. After this preliminary processing, blocks of measurements may be incorporated into state estimates with essentially the same computation as usually accompanies the incorporation of a single measurement. This formulation also leads to square-root doubling formulae for calculating the steady-state error-covariance matrix of constant models, and an extension of the class of problems for which Chandrasekhar-type algorithms offer computational reductions to include piecewise constant systems with arbitrary initial conditions.