Method and system calibration receivers and location of objects for simultaneous multilateration

摘要

A multilateration process at least one of a plurality of objects P, using: a plurality of N sensors located at known positions S1, ..., SN; a processing unit; a transmission device in each of the objects in a unknown positions ** ** Formula, wherein each of the transmission devices is configured to transmit a respective signal; the method comprising the steps of: transmitting, the transmission device of each of the objects, signals in a time of transmission unknown; receive, each sensor i, the signals transmitted from each of the objects P, j, and measure the times of reception uncalibrated ** ** Formula respective; combining receive times measured uncalibrated signals received in an ordered series of chronologically message set, wherein each of the sets of messages comprises reception times of a single transmitted signal; collect all sets of valid messages that take place within a predetermined time interval ΔTk, wherein the index k Ε {1, ..., NΔT} indicates a time step k, and wherein a set of valid messages containing at least N times of reception uncalibrated measured; provide a measurement equation for P and N objects Formula ** ** sensors that, for any time step k, describes a relationship between a set of messages and k, and where k is dependent on: c, which is the propagation speed of the signals transmitted in the medium under consideration; a position vector of xk object in a time step k, comprising the Formula ** ** positions of each of the objects P in the time step k, where j Ε {1, ..., P }; a position vector of sensor S comprising positions If each of the N sensors, where i Ε {1, ..., N}; where || . || is conventional Euclidean norm; the displacement vector time ok, wherein ** ** Formula general noise vector vk comprising general noise in the time step k, where i Ε {1, ..., N} yj Ε {1 P}; wherein the numbers N and P sensors objects meet the following condition: N · P = N + P · (D + 1); and wherein D is the dimension considered; and processing at least one of message sets obtained chronologically through performing, by said processing unit, an estimation process, in which during the estimation process a displacement vector time ok is estimated, wherein ok 35 comprising time offsets ** ** Formula measurements of each of the N sensors on the time step kei Ε {1, ..., N}; and wherein a vector bk transmission time is estimated, wherein bk comprises the transmission times of each of the objects P in the time step k, where j E {1, ..., P }; calculating positions of the object ** ** Formula and time displacement vector ** ** Formula and outputting the position of said at least one of a plurality of objects.