Estimator for determining updates to an estimated local state vector

A method for updating an estimated local state vector for a plurality of nodes that are part of a communication network by a centralized portion of an estimator, the method comprising:

• receiving, by the centralized portion of the estimator, a respective estimated local state vector, a respective estimated local measurement, a respective local residual, and a respective local measurement from each of the plurality of nodes that are part of the communication network;
• determining, by the centralized portion of the estimator, a total error covariance matrix for the communication network based on the respective estimated local state vector for each of the plurality of nodes that are part of the communication network;
• determining, by the centralized portion of the estimator, a respective local measurement sensitivity matrix representing an amount of change that local measurements for a particular node undergo based on a change in a respective local state vector for a particular node;
• determining, by the centralized portion of the estimator, a respective local measurement variance matrix that represents an uncertainty in the local measurements for the particular node;
• determining, by the centralized portion of the estimator, a respective local residual covariance matrix for each of the plurality of nodes that are part of the communication network based on the total error covariance matrix for the communication network and the respective local measurement variance matrix;
• determining, by the centralized portion of the estimator, a respective local gain matrix for the particular node based on the respective local residual covariance matrix for the particular node, the total error covariance matrix for the communication network, and the respective local measurement sensitivity matrix for the particular node;
• combining, by the centralized portion of the estimator, the respective local gain matrix with the local residual of the particular node to create a respective local update;
• predicting, by centralized portion of the estimator, an estimated collaborative measurement based on a collaborative measurement between a pair of collaborating nodes that are part of the communication network, wherein a collaborative residual is associated with the estimated collaborative measurement;
• determining, by the centralized portion of the estimator, a collaborative measurement sensitivity matrix representing an amount of change that the collaborative measurement undergoes based on a corresponding change in the respective local state vector for the particular node that the collaborative measurement is taken with respect to;
• determining, by the centralized portion of the estimator, a compound covariance matrix that characterizes an uncertainty in the collaborative measurement when an impact of one or more states of a collaborative node of the pair of collaborating nodes are modeled as random noise;
• determining, by the centralized portion of the estimator, a collaborative error covariance matrix of the collaborative residual based on at least the collaborative measurement sensitivity matrix and the compound covariance matrix;
• determining, by the centralized portion of the estimator, a collaborative gain matrix based on the collaborative error covariance matrix of the collaborative residual and the collaborative measurement sensitivity matrix;
• and
• combining, by the centralized portion of the estimator, the collaborative gain matrix with the collaborative residual to create the collaborative update.