Sensor Selection and State Estimation for Unobservable and Non-Linear System Models

Abstract

To comply with the increasing complexity of new mechatronic systems and stricter safety regulations, advanced estimation algorithms are currently undergoing a transformation towards higher model complexity. However, more complex models often face issues regarding the observability and computational effort needed. Moreover, sensor selection is often still conducted pragmatically based on experience and convenience, whereas a more cost-effective approach would be to evaluate the sensor performance based on its effective estimation performance. In this work, a novel estimation and sensor selection approach is presented that is able to stabilise the estimator Riccati equation for unobservable and non-linear system models. This is possible when estimators only target some specific quantities of interest that do not necessarily depend on all system states. An Extended Kalman Filter-based estimation framework is proposed where the Riccati equation is projected onto an observable subspace based on a Singular Value Decomposition (SVD) of the Kalman observability matrix. Furthermore, a sensor selection methodology is proposed, which ranks the possible sensors according to their estimation performance, as evaluated by the error covariance of the quantities of interest. This allows evaluating the performance of a sensor set without the need for costly test campaigns. Finally, the proposed methods are evaluated on a numerical example, as well as an automotive experimental validation case.

A Reinforcement Learning Approach to Sensing Design in Resource-Constrained Wireless Networked Control Systems

“…Sensors are usually fixed, so that the latency-accuracy tradeoff is not addressed, and local computation need not relate to communication latency. Similar considerations also apply to literature in sensor selection and resource allocation [24], [25], [26], [27], which considers sensing design in the presence of budget constraints, with little attention to impact of delays (or even dynamics) on performance. Also in recent work on co-design of sensing, estimation, and control [28], [29], there is still no unifying framework that ties adaptive local processing and sensing design with variable computation and communication delays.…”

To Compute or Not to Compute? Adaptive Smart Sensing in Resource-Constrained Edge Computing

“…where x k ∈ R n collects the variables (state) of the system, A k ∈ R n×n is the state matrix, and white noise w k ∼ N (0, W k ) captures model uncertainty. Such class of models is widely used in control applications, by virtue of their simplicity but also powerful expressiveness [28], [66]- [69]. For example, a standard approach in control of systems modeled through nonlinear differential equations is to approximate the original model as a parameter-or time-varying linear system, for which efficient control techniques are known [28], [70], [71].…”

Autonomous State Estimation and Observability Analysis for the Taiji Formation Using High-Precision Optical Sensors

“…Subsequently, we employ the fourth-order Runge-Kutta method to solve differential Equation ( 5) and simulate the true state of the SC from the initial time. For this simulation, we use a discrete step length of 1/3 s. The true measurement values for case 1 and case 2 at each time instant k are computed using Equations ( 17) and (18), respectively. It is assumed that the measurement information has been preprocessed, including time synchronization.…”

“…In these papers, they also show that, when using the measurements from the Sun sensor and the spectrometer sensor, the estimation accuracy of the absolute state of the SC can also be improved. Thus, like the study [18] that proposes a sensor selection algorithm to assess and compare the effects of different sensors on the accuracy of state estimation, for the Taiji mission, choosing the right sensors to model observation schemes for estimating the state of the SCs is an important study for the mission design.…”