Optimal Active Sensing with Process and Measurement Noise

Abstract

The goal of this paper is to increase the estimation performance of an Extended Kalman Filter for a nonlinear differentially flat system by planning trajectories able to maximize the amount of information gathered by onboard sensors in presence of both process and measurement noises. In a previous work, we presented an online gradient descent method for planning optimal trajectories along which the smallest eigenvalue of the Observability Gramian (OG) is maximized. As the smallest eigenvalue of the OG is inversely proportional to the maximum estimation uncertainty, its maximization reduces the maximum estimation uncertainty of any estimation algorithm employed during motion. However, the OG does not consider the process noise that, instead, in several applications is far from being negligible. For this reason, this paper proposes a novel solution able to cope with non-negligible process noise: this is achieved by minimizing the largest eigenvalue of the a posteriori covariance matrix obtained by solving the Continuous Riccati Equation as a measure of the total available information. This minimization is expected to maximize the information gathered by the outputs while, at the same time, limiting as much as possible the negative effects of the process noise. We apply our method to a unicycle robot. The comparison between the novel method and the one of our previous work (which did not consider process noise) shows significant improvements in the obtained estimation accuracy.

Online Optimal Perception-Aware Trajectory Generation

“…Moreover, we are also interested in including the actuation/process noise in our optimization problem, which can be quite relevant when dealing with uncertain robotics systems such as UAVs (for which the aerodynamics can be hardly modeled accurately). In [31], we have already proposed a possible solution consisting in minimizing the largest eigenvalue of the covariance matrix directly, as the solution of the Riccati differential equation.…”

Trajectory Optimization for Target Localization With Bearing-Only Measurement

“…This will minimise the cost functionJ since σ = 0. Therefore, the candidate optimal heading satisfies condition (35). Simplifying Eq.…”

“…Using the same objective function, exhaustive search was utilised in [32] to find optimal sensor heading commands with motion constraints. On the basis of the nonlinear observability analysis tool, i.e., Observability Gramian (OG) [33], the authors in [34], [35] provided online gradient descent path planning strategies to actively maximise the smallest eigenvalue of the OG. A cautious greedy active sensing strategy was proposed in [36], [37] for localising a stationary target with bearing-only measurement in minimum time.…”

Optimization-Based Control for Bearing-Only Target Search With a Mobile Vehicle

“…To estimate unknown target positions, various sensor measurements have been utilized, such as bearing angles [10], [11], ranges [12], and time difference of arrivals [13], [14]. However, most of existing works only consider either controlling a mobile vehicle to a known target position as fast as possible [6]- [9] or maximizing the estimation performance of sensor measurements [10]- [17]. In this work, they are called the control objective and the estimation objective, respectively, and are both essential for the target search problem.…”