We propose centralized and distributed fusion algorithms for estimation of nonlinear cost function (NCF) in multisensory mixed continuous-discrete stochastic systems. The NCF represents a nonlinear multivariate functional of state variables. For polynomial NCFs, we propose a closed-form estimation procedure based on recursive formulas for high-order moments for a multivariate normal distribution. In general case, the unscented transformation is used for calculation of nonlinear estimates of a cost functions. To fuse local state estimates, the mixed differential difference equations for error cross-covariance between local estimates are derived. The subsequent application of the proposed fusion estimators for a multisensory environment demonstrates their effectiveness.

This study focuses on fusion algorithms for the estimation of a non-linear function of the state vector in a multisensory continuous-time stochastic system. The non-linear function of the state (NFS) represents a non-linear multivariate function of state variables, which can indicate useful information of a target system for control. To estimate a NFS using multisensory information, they propose one centralised and three distributed estimation fusion algorithms. For multivariate polynomial functions, they derive a closed-form estimation procedure. In the general case, an unscented transformation is used for evaluation of the fusion estimate of an NFS. The subsequent application of the proposed fusion estimators to a linear stochastic system within a multisensor environment demonstrates their effectiveness.

To design highly efficient and robust detectors of a weak signal, an asymptotic approach to stable estimation exploiting redescending score functions is used. Two new indicators of robustness of detection, the detection error sensitivity and detection stability, are introduced. The optimal Neyman-Pearson rules maximizing detection efficiency under the guaranteed level of detection stability are written out. Under heavy-tailed noise distributions, the proposed asymptotically stable detectors based on redescending score functions, namely, the minimum error sensitivity and the radical ones, outperform conventional linear bounded Huber's and redescending Hampel's detectors both on small and large samples.

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