In this section, we present the GFCL algorithm for soft user position inference. The algorithm can be divided into three main steps:
Step 1: Soft User Position Inference
The first step is to infer the most probable soft user position for each user in the network. This is done by estimating the mean and covariance matrix of the soft positions based on the received signals. The estimated mean and covariance matrix are then used to compute the probability distribution of the soft positions.
Step 2: Select the Soft Relative Position
In the second step, we select the soft relative position with the least cost for each user in the network. This is done by minimizing the cost function that measures the distance between the estimated mean and covariance matrix of the soft positions and the desired mean and covariance matrix.
Step 3: Fuse Soft Positions
In the final step, we fuse all the selected soft positions to obtain the final user localization. This is done by computing the weighted average of the soft positions based on their respective costs. The weights are determined based on the consistency indicator, which measures the similarity between two soft positions. If the consistency indicator indicates that two soft positions are similar, they are fused together.
Summary: GFCL Algorithm for Soft User Position Inference
In this article, we proposed a novel algorithm called GFCL (Generalized Feedback-based Cooperative Localization) for soft user position inference in wireless sensor networks. The algorithm can accurately localize users in a distributed manner by exchanging messages and using belief propagation techniques. Unlike traditional methods that directly use a noisy measurement model, our algorithm calculates position-related parameters and uses a consistency strategy to determine whether each soft position contributes constructively or destructively to the final user localization. The proposed algorithm can converge to the true solution in high SNR regimes, demonstrating its effectiveness in accurately localizing users.
