An original approximate method for estimating the invariant probability distribution of a large class of multi-dimensional nonlinear stochastic oscillators

This paper proposes an original method for obtaining analytical approximations of the invariant probability density function of multi-dimensional Hamiltonian dissipative dynamic systems under Gaussian white noise excitations, with linear non-conservative parts and nonlinear conservative parts. The method is based on an exact result and a heuristic argument. Its pertinence is attested by numerical tests.     

Global complete observability and output-to-state stability imply the existence of a globally convergent observer

We consider systems which are globally completely observable and output-to-state stable. The former property guarantees the existence of coordinates such that the dynamics can be expressed in observability form. The latter property guarantees the existence of a state norm observer and therefore the possibility of bounding any continuous state functions. Both properties allow to conceptually build an observer from an approximation of an exponentially attractive invariant manifold in the space of the system state and an output driven dynamic extension. The proposed observer provides convergence to zero of the estimation error within the domain of definition of the solutions. The work of A. Astolfi is partly supported by the Leverhulme Trust.     

Development of a Sensor Fusion Strategy for Robotic Application Based on Geometric Optimization

Fusion of multi-sensor information is an important technology, which is growing exponentially due to its tremendous application potential in many areas. Effective fusion of data from sensors is very critical in increasing an intelligent system's capability to accomplish complex tasks. Appropriate fusion technologies are needed to be developed specially when a system requires redundant sensors to be used. More the redundancy in sensors, more is the computational complexity for controlling the system and more is its intelligence level. This research presents a strategy developed for multiple sensor fusion, based on geometric optimization. Each sensor's uncertainty has been modeled using classical Lagrangian optimization techniques. However, the uniqueness and effectiveness of the present technique lies on the fact that starting from the optimized value as initial estimate the accuracy of the sensory information has further been improved up to any pre defined bounded range, by developing two architectures – FFA (fission–fusion architecture) and FDD (fusion in differential domain). Sufficient evidences and analyses have been provided in the paper to show its effectiveness in various applications.     

Ergodicity of filtering process by vanishing discount approach

A new approach to study ergodicity of filtering processes is presented. It is based on the vanishing discount approach to discounted functional of filtering process. We show that limit superior of the Cesaro averages of the functionals is the same for all initial conditions from which the uniqueness of invariant measures of filtering processes follows. The approach is based on certain assumption for which we provide a sufficient condition using concavity arguments. In addition we show the existence of solutions to the Poisson equation corresponding to filtering process with concave functional. The assumptions are then extended to the controlled case and using similar concave arguments we obtain the existence of solutions to the Bellman equation corresponding to partially observed average cost per unit time problem.     

Self-calibration based on invariant view recognition: Dynamic approach to navigation

We extend a dynamic approach of behavior generation to the representation of spatial information. Two levels of dynamics integrate dead-reckoning, dominant far from home bases, and piloting, dominant near home bases. When the view-based piloting system recognizes a home base, visual place information recalibrates the dead-reckoning system, inverting the hierarchical ordering of the two dynamic levels by time scale inversion. Reference views taken at discrete home bases are recognized invariantly under rotation of views. This process yields compass information. Continuous translational information is obtained as a neural place representation built from view correlations with a scattered set of local views. This self-calibrating cognitive map couples into a dynamics of heading direction integrating the behaviors of obstacle avoidance and target acquisition. Targets can be designated in terms of the cognitive map. We demonstrate the dynamical model in simulation.     

A remark on bilinear systems and moduli spaces of instantons

Explicit equations are given for the moduli space of framed instantons as a quasi-affine variety, based on the representation theory of noncommutative power series, or equivalently, the minimal realization theory of bilinear systems.     

基于椭球拟合的三轴磁传感器误差补偿方法

考虑现有多轴磁传感器的标定补偿方法普遍存在计算量较大、操作时间长、场地要求面积大、标定设备要求高等问题,提出了基于椭球拟合的三轴磁传感器误差标定补偿方法。在分析传感器误差产生机理的基础上,建立了磁传感器误差模型,推导了误差系数的解算公式,并利用椭球拟合的方法对三轴磁传感器进行了测试标定与误差补偿。实验结果表明,该方法能够正确、有效地标定补偿三轴磁传感器不正交误差、灵敏度误差和零偏误差,具有修正过程简捷、省时、精度高特点不依赖于精密仪器提供准确的方向基准、水平基准等,能够广泛应用于多轴矢量传感器的误差标定和有效补偿。