A Fisher Information based Receding Horizon Control Method for Signal Strength Model Estimation

TL;DR

The paper tackles active localization in wireless sensor networks by jointly estimating unknown RSS path-loss parameters and sensor locations using a mobile agent and RSS measurements. It introduces a Fisher Information Matrix-based receding-horizon control framework that alternates parameter estimation via Maximum Likelihood Estimation with multi-step trajectory optimization to maximize information gain, implemented with DP or a pruning heuristic. A penalty term is proposed to balance information across parameters, addressing biased information capture. Simulations show that the RH approaches outperform simple baselines, with pruning delivering large computational savings while preserving estimation performance; extensions to NLoS scenarios and continuous exploration-exploitation trajectories are discussed for future work.

Abstract

This paper considers the problem of localizing a set of nodes in a wireless sensor network when both their positions and the parameters of the communication model are unknown. We assume that a single agent moves through the environment, taking measurements of the Received Signal Strength (RSS), and seek a controller that optimizes a performance metric based on the Fisher Information Matrix (FIM). We develop a receding horizon (RH) approach that alternates between estimating the parameter values (using a maximum likelihood estimator) and determining where to move so as to maximally inform the estimation problem. The receding horizon controller solves a multi-stage look ahead problem to determine the next control to be applied, executes the move, collects the next measurement, and then re-estimates the parameters before repeating the sequence. We consider both a Dynamic Programming (DP) approach to solving the optimal control problem at each step, and a simplified heuristic based on a pruning algorithm that significantly reduces the computational complexity. We also consider a modified cost function that seeks to balance the information acquired about each of the parameters to ensure the controller does not focus on a single value in its optimization. These approaches are compared against two baselines, one based on a purely random trajectory and one on a greedy control solution. The simulations indicate our RH schemes outperform the baselines, while the pruning algorithm produces significant reductions in computation time with little effect on overall performance.

Figures (8)

• Figure 1: Sketch of the problem setup. A single agent flies over an environment while communicating with a collection of sensor nodes distributed on the ground.
• Figure 2: Block diagram of the estimation and control framework for active motion planning.
• Figure 3: Illustration of FIM for the relative positions and parameter $\gamma$ for the $i$th sensor node. The light color in (a), (b) and (c) represents the high value of FIM, while the light area in (d) means the high value of MSE lower bound.
• Figure 4: Demonstration of all possible control actions. (a) The vectors reflect eight horizontal control inputs. (b) The vectors reflect three vertical control inputs.
• Figure 5: Sketch of the pruning algorithm with $N_u=3$ and $M_u=3$. At each stage there are only $N_uM_u$ actions to consider.