اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDeterministic filtering and max-plus methods for robust state estimation in multi-sensor settings
65
0
0.0
(
0
)
تأليف
Srinivas Sridharan
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
A robust (deterministic) filtering approach to the problem of optimal sensor selection is considered herein. For a given system with several sensors, at each time step the output of one of the sensors must be chosen in order to obtain the best state estimate. We reformulate this problem in an optimal control framework which can then be solved using dynamic programming. In order to tackle the numerical computation of the solution in an efficient manner, we exploit the preservation of the min-plus structure of the optimal cost function when acted upon by the dynamic programming operator. This technique yields a grid free numerical approach to the problem. Simulations on an example problem serve to highlight the efficacy of this generalizable approach to robust multi-sensor state estimation.
قيم البحث
اقرأ أيضاً
In this article we introduce the use of recently developed min/max-plus techniques in order to solve the optimal attitude estimation problem in filtering for nonlinear systems on the special orthogonal (SO(3)) group. This work helps obtain computatio
nally efficient methods for the synthesis of deterministic filters for nonlinear systems -- i.e. optimal filters which estimate the state using a related optimal control problem. The technique indicated herein is validated using a set of optimal attitude estimation example problems on SO(3).
This article approaches deterministic filtering via an application of the min-plus linearity of the corresponding dynamic programming operator. This filter design method yields a set-valued state estimator for discrete-time nonlinear systems (nonline
ar dynamics and output functions). The energy bounds in the process and the measurement disturbances are modeled using a sum quadratic constraint. The filtering problem is recast into an optimal control problem in the form of a Hamilton-Jacobi-Bellman (HJB) equation, the solution to which is obtained by employing the min-plus linearity property of the dynamic programming operator. This approach enables the solution to the HJB equation and the design of the filter without recourse to linearization of the system dynamics/ output equation.
We consider deterministic Markov decision processes (MDPs) and apply max-plus algebra tools to approximate the value iteration algorithm by a smaller-dimensional iteration based on a representation on dictionaries of value functions. The setup natura
lly leads to novel theoretical results which are simply formulated due to the max-plus algebra structure. For example, when considering a fixed (non adaptive) finite basis, the computational complexity of approximating the optimal value function is not directly related to the number of states, but to notions of covering numbers of the state space. In order to break the curse of dimensionality in factored state-spaces, we consider adaptive basis that can adapt to particular problems leading to an algorithm similar to matching pursuit from signal processing. They currently come with no theoretical guarantees but work empirically well on simple deterministic MDPs derived from low-dimensional continuous control problems. We focus primarily on deterministic MDPs but note that the framework can be applied to all MDPs by considering measure-based formulations.
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 suffe
rs 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.
The design of deterministic filters can be cast as a problem of minimizing an associated cost function for an optimal control problem. Employing the min-plus linearity property of the dynamic programming operator (associated with the control problem)
results in a computationally feasible approach (while avoiding linearization of the system dynamics/output). This article describes the salient features of this approach and a specific form of pruning/projection, based on clustering, which serves to facilitate the numerical efficiency of these methods.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
