convx定位凸规划案例.pptx

Convex Position Estimation in Wireless Sensor Networks杭小杰 Abstract A method for estimating unknown node positions in a sensor network based exclusively on connectivity-induced constraints is described. Additionally, a method for placing rectangular bounds around the possible positions for all unknown nodes in the network is given. Specific models are suggested and simulated for isotropic and directional communication, representative of broadcast-based and optical transmission respectively I. INTRODUCTION In a network of thousands of nodes, it is unlikely that the designer will determine the position of each node.GPS is too expensive. Positional information can be inferred from connection-imposed proximity constraints. In this model, only a few nodes have known positions and the remainder of the node positions are computed from knowledge about communication links. II. MATHEMATICAL FORMULATION A linear program (LP) is a problem of the form: Minimize Subject to: Ax b A generalization of the LP is the semidefinite program (SDP) of the form: Minimize Subject to: Ax b In two dimensions, each node has a position (x,y). For position estimation, a single vector with all the positions is formed: x =[x1 y1 ... xm ym... xm+1 ym+1 ... xn yn]T m:known position nodes n:all nodes III. CONVEX CONSTRAINT MODELS A. Connections as convex constraints Given the position of node A, what is the set of possible positions for node B B.Radial constraint – RF communication The RF transmitter of a wireless sensor node can be modeled as having a rotationally symmetric range as illustrated in Figure (a). In this symmetric model, a connection between nodes can be represented by a 2-norm constraint on the node positions.Sp