State estimation and control for systems with perspective outputs

Abstract

In this paper we consider the problem of estimating the state of a system with perspective outputs. We formulate the problem in a deterministic setting by searching for the value of the state that is "most compatible" with the dynamics, in the sense that it requires the least amount of noise to explain the measured output. We show that, under appropriate observability assumptions, the optimal estimate converges globally to the true value of the state and can be used to design output-feedback controllers by using the estimated state to drive a state-feedback controller. We apply these results to the estimation of position and orientation of a controlled rigid body, using measurements from a charged-coupled-device camera attached to the body.

State Estimation of Continuous-Time Systems with Implicit Outputs from Discrete Noisy Time-Delayed Measurements

“…It was recently shown by Krener [16] that this type of estimators is globally convergent when the system is observable for every input. In [17], it was shown that for projective systems with multiple inputs, convergence can be obtained under less restrictive observability assumptions. In [18], we improve upon the results in [17] by incorporating quadratic state-constraints in the minimum-energy formulation.…”

A moments-based approach to estimation and data interpolation for a class of Wiener systems

“…In this context, the problem of reconstructing the 3D geometry of the scene can be formalized as a nonlinear filtering one: estimating Pkj from (Ukj, Vkj), potentially corrupted by measurement noise. In principle, this nonlinear filtering problem can be solved using the techniques proposed in [14], [8], [1], [6], [9]. However, proceeding in this fashion requires first obtaining a model of the Wiener system.…”

“…Obtaining the 3D geometry from these coordinates entails solving a chal lenging non-linear, non-convex optimization problem. On the other hand, filtering-type approaches require either the availability of a motion model for the target [14], [8], [6] or the solution to a non-linear optimization (bundle adjustment) problem [11]. As we show below, these difficulties can be circumvented by reformulating the problem as the estimation CThis constraint is similar to the hybrid decoupling constraint used in GPCA [22] of the internal signals in a Wiener system with an unknown linear component, and solved using the framework developed in this paper.…”

State Estimation for Systems with Implicit Outputs for the Integration of Vision and Inertial Sensors

“…It turns out that there exists a solution to (9)-(10) which is differentiable with respect to z and can be written as (8) for appropriately defined signalsx(t) and c(t). The signal x is then precisely the estimate for the state x of (1)-(3).…”

“…See also [4], [5] that address the observability problem of perspective linear systems. The system with implicitly defined outputs described in [6] and the state-affine systems with multiple perspective outputs considered in [7] (see also [8]- [10]) are also special cases of (1)- (3).…”