Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMAP moving horizon estimation for threshold measurements with application to field monitoring
81
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The paper deals with state estimation of a spatially distributed system given noisy measurements from pointwise-in-time-and-space threshold sensors spread over the spatial domain of interest. A Maximum A posteriori Probability (MAP) approach is undertaken and a Moving Horizon (MH) approximation of the MAP cost-function is adopted. It is proved that, under system linearity and log-concavity of the noise probability density functions, the proposed MH-MAP state estimator amounts to the solution, at each sampling interval, of a convex optimization problem. Moreover, a suitable centralized solution for large-scale systems is proposed with a substantial decrease of the computational complexity. The latter algorithm is shown to be feasible for the state estimation of spatially-dependent dynamic fields described by Partial Differential Equations (PDE) via the use of the Finite Element (FE) spatial discretization method. A simulation case-study concerning estimation of a diffusion field is presented in order to demonstrate the effectiveness of the proposed approach. Quite remarkably, the numerical tests exhibit a noise-assisted behavior of the proposed approach in that the estimation accuracy results optimal in the presence of measurement noise with non-null variance.
rate research
Read More
Estimating and reacting to external disturbances is of fundamental importance for robust control of quadrotors. Existing estimators typically require significant tuning or training with a large amount of data, including the ground truth, to achieve satisfactory performance. This paper proposes a data-efficient differentiable moving horizon estimation (DMHE) algorithm that can automatically tune the MHE parameters online and also adapt to different scenarios. We achieve this by deriving the analytical gradient of the estimated trajectory from MHE with respect to the tuning parameters, enabling end-to-end learning for auto-tuning. Most interestingly, we show that the gradient can be calculated efficiently from a Kalman filter in a recursive form. Moreover, we develop a model-based policy gradient algorithm to learn the parameters directly from the trajectory tracking errors without the need for the ground truth. The proposed DMHE can be further embedded as a layer with other neural networks for joint optimization. Finally, we demonstrate the effectiveness of the proposed method via both simulation and experiments on quadrotors, where challenging scenarios such as sudden payload change and flying in downwash are examined.
This work studies how to estimate the mean-field density of large-scale systems in a distributed manner. Such problems are motivated by the recent swarm control technique that uses mean-field approximations to represent the collective effect of the swarm, wherein the mean-field density (and its gradient) is usually used in feedback control design. In the first part, we formulate the density estimation problem as a filtering problem of the associated mean-field partial differential equation (PDE), for which we employ kernel density estimation (KDE) to construct noisy observations and use filtering theory of PDE systems to design an optimal (centralized) density filter. It turns out that the covariance operator of observation noise depends on the unknown density. Hence, we use approximations for the covariance operator to obtain a suboptimal density filter, and prove that both the density estimates and their gradient are convergent and remain close to the optimal one using the notion of input-to-state stability (ISS). In the second part, we continue to study how to decentralize the density filter such that each agent can estimate the mean-field density based on only its own position and local information exchange with neighbors. We prove that the local density filter is also convergent and remains close to the centralized one in the sense of ISS. Simulation results suggest that the (centralized) suboptimal density filter is able to generate convergent density estimates, and the local density filter is able to converge and remain close to the centralized filter.
In autonomous applications for mobility and transport, a high-rate and highly accurate vehicle states estimation is achieved by fusing measurements of global navigation satellite systems and inertial sensors. Since this kind of state estimation suffers from poor parameterization, environment disturbances, or even software and hardware failures, this paper introduces a novel scheme of multi-sensor navigation system involving extended H$_infty$ filter for robustness enhancement of the navigation solution and zonotope for protection level generation in combination with vehicle dynamic-model-aided fault detection of the inertial sensor for reliable integrity monitoring. The innovative scheme, applying extended H$_infty$ filter and zonotope, is shown as part of a tightly-coupled navigation system. Further, the consideration of redundant information, e.g., vehicle dynamic model, for fault detection purpose has long been investigated and is systematically described and discussed using interval analysis theory in current publication. The robustness of the designed approach is validated with real-world data in post-processing: decimeter positioning accuracy is maintained, while the solution of conventional extended Kalman filter diverges from ground truth; the difference is also significant under inertial sensor faults. A real-time implementation of the designed approach is promising and aimed in the future work.
We study the problem of estimating the parameters (i.e., infection rate and recovery rate) governing the spread of epidemics in networks. Such parameters are typically estimated by measuring various characteristics (such as the number of infected and recovered individuals) of the infected populations over time. However, these measurements also incur certain costs, depending on the population being tested and the times at which the tests are administered. We thus formulate the epidemic parameter estimation problem as an optimization problem, where the goal is to either minimize the total cost spent on collecting measurements, or to optimize the parameter estimates while remaining within a measurement budget. We show that these problems are NP-hard to solve in general, and then propose approximation algorithms with performance guarantees. We validate our algorithms using numerical examples.
Optimization-based state estimation is useful for handling of constrained linear or nonlinear dynamical systems. It has an ideal form, known as full information estimation (FIE) which uses all past measurements to perform state estimation, and also a practical counterpart, known as moving-horizon estimation (MHE) which uses most recent measurements of a limited length to perform the estimation. Due to the theoretical ideal, conditions for robust stability of FIE are relatively easier to establish than those for MHE, and various sufficient conditions have been developed in literature. This work reveals a generic link from robust stability of FIE to that of MHE, showing that the former implies at least a weaker robust stability of MHE which implements a long enough horizon. The implication strengthens to strict robust stability of MHE if the system satisfies a mild Lipschitz continuity or equivalently a robust exponential stability condition. The revealed implications are then applied to derive new sufficient conditions for robust stability of MHE, which further reveal an intrinsic relation between the existence of a robustly stable FIE/MHE and the system being incrementally input/output-to-state stable.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
