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Even if path planning can be solved using standard techniques from dynamic programming and control, the problem can also be approached using probabilistic inference. The algorithms that emerge using the latter framework bear some appealing characteristics that qualify the probabilistic approach as a powerful alternative to the more traditional control formulations. The idea of using estimation on stochastic models to solve control problems is not new and the inference approach considered here falls under the rubric of Active Inference (AI) and Control as Inference (CAI). In this work, we look at the specific recursions that arise from various cost functions that, although they may appear similar in scope, bear noticeable differences, at least when applied to typical path planning problems. We start by posing the path planning problem on a probabilistic factor graph, and show how the various algorithms translate into specific message composition rules. We then show how this unified approach, presented both in probability space and in log space, provides a very general framework that includes the Sum-product, the Max-product, Dynamic programming and mixed Reward/Entropy criteria-based algorithms. The framework also expands algorithmic design options for smoother or sharper policy distributions, including generalized Sum/Max-product algorithm, a Smooth Dynamic programming algorithm and modified versions of the Reward/Entropy recursions. We provide a comprehensive table of recursions and a comparison through simulations, first on a synthetic small grid with a single goal with obstacles, and then on a grid extrapolated from a real-world scene with multiple goals and a semantic map.

In this paper, we consider the problem of state of charge estimation for rechargeable batteries. Coulomb counting is one of the traditional approaches to state of charge estimation and it is considered reliable as long as the battery capacity and initial state of charge are known. However, the Coulomb counting method is susceptible to errors from several sources and the extent of these errors are not studied in the literature. In this paper, we formally derive and quantify the state of charge estimation error during Coulomb counting due to the following four types of error sources: (i) current measurement error; (ii) current integration approximation error; (iii) battery capacity uncertainty; and (iv) the timing oscillator error/drift. It is shown that the resulting state of charge error can either be of the time-cumulative or of state-of-charge-proportional type. Time-cumulative errors increase with time and has the potential to completely invalidate the state of charge estimation in the long run. State-of-charge-proportional errors increase with the accumulated state of charge and reach its worst value within one charge/discharge cycle. Simulation analyses are presented to demonstrate the extent of these errors under several realistic scenarios and the paper discusses approaches to reduce the time-cumulative and state of charge-proportional errors.

Real-time identification of electrical equivalent circuit models is a critical requirement in many practical systems, such as batteries and electric motors. Significant work has been done in the past developing different types of algorithms for system identification using reduced equivalent circuit models. However, little work was done in analyzing the theoretical performance bounds of these approaches. Proper understanding of theoretical bounds will help in designing a system that is economical in cost and robust in performance. In this paper, we analyze the performance of a linear recursive least squares approach to equivalent circuit model identification and show that the least squares approach is both unbiased and efficient when the signal-to-noise ratio is high enough. However, we show that, when the signal-to-noise ratio is low - resembling the case in many practical applications - the least squares estimator becomes significantly biased. Consequently, we develop a parameter estimation approach based on total least squares method and show it to be asymptotically unbiased and efficient at practically low signal-to-noise ratio regions. Further, we develop a recursive implementation of the total least square algorithm and find it to be slow to converge; for this, we employ a Kalman filter to improve the convergence speed of the total least squares method. The resulting total Kalman filter is shown to be both unbiased and efficient in equivalent circuit model parameter identification. The performance of this filter is analyzed using real-world current profile under fluctuating signal-to-noise ratios. Finally, the applicability of the algorithms and analysis in this paper in identifying higher order electrical equivalent circuit models is explained.

The COVID-19 pandemic has, worldwide and up to December 2020, caused over 1.7 million deaths, and put the world's most advanced healthcare systems under heavy stress. In many countries, drastic restrictive measures adopted by political authorities, such as national lockdowns, have not prevented the outbreak of new pandemic's waves. In this article, we propose an integrated detection-estimation-forecasting framework that, using publicly available data, is designed to: (i) learn relevant features of the pandemic (e.g., the infection rate); (ii) detect as quickly as possible the onset (or the termination) of an exponential growth of the contagion; and (iii) reliably forecast the pandemic evolution. The proposed solution is validated by analyzing the COVID-19 second and third waves in the USA., Comment: Accepted to be published in IEEE Communications Magazine, feature topic "Networking Technologies to Combat the COVID-19 Pandemic"

During the course of an epidemic, one of the most challenging tasks for authorities is to decide what kind of restrictive measures to introduce and when these should be enforced. In order to take informed decisions in a fully rational manner, the onset of a critical regime, characterized by an exponential growth of the contagion, must be identified as quickly as possible. Providing rigorous quantitative tools to detect such an onset represents an important contribution from the scientific community to proactively support the political decision makers. In this paper, leveraging the quickest detection theory, we propose a mathematical model of the COVID-19 pandemic evolution and develop decision tools to rapidly detect the passage from a controlled regime to a critical one. A new sequential test -- referred to as MAST (mean-agnostic sequential test) -- is presented, and demonstrated on publicly available COVID-19 infection data from different countries. Then, the performance of MAST is investigated for the second pandemic wave, showing an effective trade-off between average decision delay $\Delta$ and risk $R$, where $R$ is inversely proportional to the time required to declare the need to take unnecessary restrictive measures. Ideally, the decision mechanism should react as quick as possible for a given level of risk. We find that all the countries share the same behaviour in terms of quickest detection, specifically the risk scales exponentially with the delay, $R \sim \exp{(-\omega \Delta)}$, where $\omega$ depends on the specific nation. For a reasonably small risk level, say, one possibility in ten thousand (i.e., unmotivated implementation of countermeasures every 27 years, on the average), the proposed algorithm detects the onset of the critical regime with delay between a few days to three weeks, much earlier than when the exponential growth becomes evident.

This paper develops an easily-implementable version of Page's CUSUM quickest-detection test, designed to work in certain composite hypothesis scenarios with time-varying data statistics. The decision statistic can be cast in a recursive form and is particularly suited for on-line analysis. By back-testing our approach on publicly-available COVID-19 data we find reliable early warning of infection flare-ups, in fact sufficiently early that the tool may be of use to decision-makers on the timing of restrictive measures that may in the future need to be taken., Comment: Accepted to be published in IEEE Signal Processing Letters

Probability models have been proposed in the literature to account for "intelligent" behavior in many contexts. In this paper, probability propagation is applied to model agent's motion in potentially complex scenarios that include goals and obstacles. The backward flow provides precious background information to the agent's behavior, viz., inferences coming from the future determine the agent's actions. Probability tensors are layered in time in both directions in a manner similar to convolutional neural networks. The discussion is carried out with reference to a set of simulated grids where, despite the apparent task complexity, a solution, if feasible, is always found. The original model proposed by Attias has been extended to include non-absorbing obstacles, multiple goals and multiple agents. The emerging behaviors are very realistic and demonstrate great potentials of the application of this framework to real environments., Comment: Submitted for journal publication