A linear estimation problem of decentralized processing of measurements is considered, which involves the estimate of the state vector of a dynamic system by fusion of the estimates generated in local filters using the data from distributed (separate) sensors. The conditions are discussed that ensure the coincidence of the estimates and calculated covariance matrices of estimation errors generated in this way with the results obtained in the optimal centralized Kalman filter. The features of these conditions for recursive and nonrecursive schemes are analyzed. The comparison of two schemes is illustrated using an example of random walk estimation.

In the framework of the Bayesian approach, a suboptimal recursive algorithm for the nonlinear filtering problem of Markov process is proposed. The specificity of this problem is due to the nonlinearity of measurements with a linear nature of the shaping filter for the Markov process being estimated. This algorithm is compared in terms of accuracy, consistency and computational complexity with the algorithm that is close to the optimal one. An illustrative example is given.

Two schemes of suboptimal estimation algorithms synthesized using the Bayesian approach and based on the linearization of functions describing the behavior of the estimated state vector and measurement model are compared for one class of nonlinear estimation problems. One of them is traditional, in which the estimate is found recursively with respect to measurements, and the other one, nonrecursive, involves the simultaneous use of the full set of all available measurements. The advantages and disadvantages of the analyzed algorithms are discussed and illustrated by an example.

Acute Myeloid Leukemia (AML) is a fatal hematological cancer. The genetic abnormalities underlying AML are extremely heterogeneous among patients, making prognosis and treatment selection very difficult. While clinical proteomics data has the potential to improve prognosis accuracy, thus far, the quantitative means to do so have yet to be developed. Here we report the results and insights gained from the DREAM 9 Acute Myeloid Prediction Outcome Prediction Challenge (AML-OPC), a crowdsourcing effort designed to promote the development of quantitative methods for AML prognosis prediction. We identify the most accurate and robust models in predicting patient response to therapy, remission duration, and overall survival. We further investigate patient response to therapy, a clinically actionable prediction, and find that patients that are classified as resistant to therapy are harder to predict than responsive patients across the 31 models submitted to the challenge. The top two performing models, which held a high sensitivity to these patients, substantially utilized the proteomics data to make predictions. Using these models, we also identify which signaling proteins were useful in predicting patient therapeutic response.

Similarities and differences between the algorithms based on the Bayesian approach, commonly used for solution of nonlinear navigation estimation problems, and the algorithms based on neural networks (NN) are analyzed. The possibilities of using NN for solution of nonlinear navigation problems are discussed.