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Real-time numerical differentiation plays a crucial role in many digital control algorithms, such as PID control, which requires numerical differentiation to implement derivative action. This paper proposes an algorithm for estimating the numerical derivative of a signal from noisy sampled data measurements. The method uses adaptive input estimation with adaptive state estimation (AIE/ASE), and thus it requires only minimal prior information about the signal and noise statistics. Furthermore, since the estimates of the derivative at step k provided by AIE/ASE depend only on data available up to step k, AIE/ASE is thus implementable in real time. The accuracy of AIE/ASE is compared numerically to several conventional numerical differentiation methods. Finally, AIE/ASE is applied to simulated vehicle position data, generated in the CarSim simulator software.more » « lessFree, publicly-accessible full text available December 1, 2025
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Pulkit Verma, Shashank Rao (, Proceedings of the AAAI Conference on Artificial Intelligence)This paper develops a new approach for estimating an interpretable, relational model of a black-box autonomous agent that can plan and act. Our main contributions are a new paradigm for estimating such models using a rudimentary query interface with the agent and a hierarchical querying algorithm that generates an interrogation policy for estimating the agent's internal model in a user-interpretable vocabulary. Empirical evaluation of our approach shows that despite the intractable search space of possible agent models, our approach allows correct and scalable estimation of interpretable agent models for a wide class of black-box autonomous agents. Our results also show that this approach can use predicate classifiers to learn interpretable models of planning agents that represent states as images.more » « less
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