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In the last decades, the increasing complexity of the fusion of proprioceptive and exteroceptive sensors with Global Navigation Satellite System (GNSS) has motivated the exploration of Artificial Intelligence related strategies for the implementation of the navigation filters. In order to meet the strict requirements of accuracy and precision for Intelligent Transportation Systems (ITS) and Robotics, Bayesian inference algorithms are at the basis of current Positioning, Navigation, and Timing (PNT). Some scientific and technical contributions resort to Sequential Importance Resampling (SIR) Particle Filters (PF) to overcome the theoretical weaknesses of the more popular and efficient Kalman Filters (KFs) when the application relies on non-linear measurements models and non-Gaussian measurements errors. However, due to its higher computational burden, SIR PF is generally discarded. This paper presents a methodology named Multiple Weighting (MW) that reduces the computational burden of PF by considering the mutual information provided by the input measurements about the unknown state. An assessment of the proposed scheme is shown through an application to standalone GNSS estimation as a baseline of more complex multi-sensors, integrated solutions. By relying on the a-priori knowledge of the relationship between states and measurements, a change in the conventional PF routine allows performing a more efficient sampling of the posterior distribution. Results show that the proposed strategy can achieve any desired accuracy with a considerable reduction in the number of particles. Given a fixed and reasonable available computational effort, the proposed scheme allows for an accuracy improvement of the state estimate in the range of 20-40%.

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We develop a parameter estimation method based on approximate Bayesian computation (ABC) for a stochastic cell invasion model using fluorescent cell cycle labelling with proliferation, migration and crowding effects. Previously, inference has been performed on a deterministic version of the model fitted to cell density data, and not all parameters were identifiable. Considering the stochastic model allows us to harness more features of experimental data, including cell trajectories and cell count data, which we show overcomes the parameter identifiability problem. We demonstrate that, while difficult to collect, cell trajectory data can provide more information about the parameters of the cell invasion model. To handle the intractability of the likelihood function of the stochastic model, we use an efficient ABC algorithm based on sequential Monte Carlo. Rcpp and MATLAB implementations of the simulation model and ABC algorithm used in this study are available at https://github.com/michaelcarr-stats/FUCCI.

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Since the submarine has become the major threat to maritime security, there is an urgent need to find a more efficient method of anti-submarine warfare (ASW). The digital twin theory is one of the most outstanding information technologies, and has been quite popular in recent years. The most influential change produced by digital twin is the ability to enable real-time dynamic interactions between the simulation world and the real world. Digital twin can be regarded as a paradigm by means of which selected online measurements are dynamically assimilated into the simulation world, with the running simulation model guiding the real world adaptively in reverse. By combining digital twin theory and random finite sets (RFSs) closely, a new framework of sensor control in ASW is proposed. Two key algorithms are proposed for supporting the digital twin-based framework. First, the RFS-based data-assimilation algorithm is proposed for online assimilating the sequence of real-time measurements with detection uncertainty, data association uncertainty, noise, and clutters. Second, the computation of the reward function by using the results of the proposed data-assimilation algorithm is introduced to find the optimal control action. The results of three groups of experiments successfully verify the feasibility and effectiveness of the proposed approach.

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We observe an undirected graph G without multiple edges and self-loops, which is to represent a protein-protein interaction (PPI) network. We assume that G evolved under the duplication-mutation with complementarity (DMC) model from a seed graph, G0, and we also observe the binary forest Γ that represents the duplication history of G. A posterior density for the DMC model parameters is established, and we outline a sampling strategy by which one can perform Bayesian inference; that sampling strategy employs a particle marginal Metropolis-Hastings (PMMH) algorithm. We test our methodology on numerical examples to demonstrate a high accuracy and precision in the inference of the DMC model's mutation and homodimerization parameters.

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We address the problem of estimating the unknown parameters of a model of tracer kinetics from sequences of positron emission tomography (PET) scan data using a statistical sequential algorithm for the inference of magnitudes of dynamic parameters. The method, based on Bayesian statistical inference, is a modification of a recently proposed particle filtering and sequential Monte Carlo algorithm, where instead of preassigning the accuracy in the propagation of each particle, we fix the time step and account for the numerical errors in the innovation term. We apply the algorithm to PET images of [1-¹¹C]-acetate-derived tracer accumulation, estimating the transport rates in a three-compartment model of astrocytic uptake and metabolism of the tracer for a cohort of 18 volunteers from 3 groups, corresponding to healthy control individuals, cirrhotic liver and hepatic encephalopathy patients. The distribution of the parameters for the individuals and for the groups presented within the Bayesian framework support the hypothesis that the parameters for the hepatic encephalopathy group follow a significantly different distribution than the other two groups. The biological implications of the findings are also discussed.

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