This paper is the second in a series of three in which performance bounds are derived for causal state estimation and regulation problems employing mean square criteria. The systems considered are partially-observed finite dimensional continuous-time stochastic processes driven by additive white Gaussian noise. The particular systems to which the bounds apply are those which, when modeled by Ito differential equations, contain drift (.dt) coefficients which are, to within a uniformly Lipschitz residual, jointly linea in the system state and externally applied control.nThe bounds derived in the complete series of papers include both upper and lower bounds for causal state estimation and for a quadratic regulator problem. The upper bounds pertain to the performance of some simple, almost-linear designs reminiscent of the designs which are optimal in the linear case. The lower bounds pertain to the optimum performance attainable within a broad class of admissible control laws.nThe present paper treats the lower bound for estimation. The estimation performance bounds are independent of the control law, giving a particularly simple form to the control performance bounds which are developed in the third and final paper. All the bounds converge with vanishing nonlinearity (vanishing Lipschitz constants) to the known optimum performance for the limiting linear system. Consequently, the bounds are asymptotically tight and the simple designs studied are asymptotically optimal with vanishing nonlinearity.
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