# US 2014/0192991 A1 · Method for self-calibration of a set of sensors, in particular microphones, and corresponding system > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2014/0192991 A1 - Document ID: US20140192991A1 - Status: Published application - Kind: A1 - Application number: 14/122,418 - Filed: 2012-05-24 - Published: 2014-07-10 - Earliest claimed: 2011-05-27 - Assignees: Fondazione Istituto Italiano Di Tecnologia - Inventors: Marco Crocco; Alessio Del Bue; Vittorio Murino - Web page: https://patentgrep.com/patent/US20140192991A1 ## CPC - H04R 29/005: {Microphone arrays} - H04R: LOUDSPEAKERS, MICROPHONES, GRAMOPHONE PICK-UPS OR LIKE ACOUSTIC ELECTROMECHANICAL TRANSDUCERS; ELECTRIC HEARING AIDS; PUBLIC ADDRESS SYSTEMS (producing sounds with frequency not determined by supply frequency G10K) ## Abstract A method for self-calibration of the position of a set of sensors of acoustic signals includes: providing a set of sources of acoustic events designed to generate acoustic waves; measuring times of flight of the acoustic events between each source of acoustic events and each microphone; and reconstructing the positions of the set of sensors and the positions of the sources of acoustic events through a maximum-likelihood estimation procedure executed on the basis of the measured times of flight. Times of emission of the acoustic events are acquired. Times of flight are obtained. Distances between the sources and the sensors are calculated. A matrix of estimated positions of the sensor microphones and a matrix of estimated positions of the sources of events are calculated. ## Claims ### Claim 1 A method for self-calibration of the position of a set of sensors of acoustic signals, arranged in a region of space, comprising: providing in said region of space a set of sources of acoustic events, in particular transducers able to generate acoustic waves; measuring times of flight of said acoustic events between each source of acoustic events and each sensor; and reconstructing the positions of the set of sensors and the positions of the sources of acoustic events through a maximum-likelihood estimation procedure executed on the basis of said measured times of flight, acquiring times of emission of said acoustic events; obtaining said times of flight as a function of the respective times of emission; calculating from said times of flight distances between said sources and said sensors and arranging said distances in a matrix of distances; and calculating a matrix of estimated positions of the sensors and a matrix of estimated positions of the sources of events via a maximum-likelihood procedure comprising performing a nonlinear least-squares optimization that minimizes a cost function between Euclidean distances of the positions of the sensors and of the sources and said calculated distances. ### Claim 2 (depends on 1) The method according to claim 1, further comprising: processing a set of equations associated to said maximum-likelihood procedure for calculating a reduced matrix of the measured distances as a bilinear form that is a function of a reduced matrix of positions of the sensors and of a reduced matrix of positions of the events; executing a procedure of singular-value decomposition of said reduced matrix of the measured distances in order to reduce the number of the unknowns in said maximum-likelihood procedure, in particular from three times the sum of the number of sensors and of the number of acoustic sources to nine. ### Claim 3 (depends on 2) The method according to claim 2, further comprising defining a mixing matrix that enables the reduced matrix of positions of the sensors and the reduced matrix of positions of the events to be expressed as a function of matrices performing said decomposition and calculating the values of said mixing matrix by minimizing a respective nonlinear least-squares cost function. ### Claim 4 (depends on 1) The method according to claim 1, further comprising acquiring said times of emission using sources synchronized with the sensors. ### Claim 5 (depends on 1) The method according to claim 1, wherein said operation of obtaining said times of flight as a function of the respective times of emission comprises measuring times of arrival and obtaining the times of flight as difference between the times of arrival and the times of emission. ### Claim 6 (depends on 1) The method according to claim 1, further comprising setting a sensor in a position where a source is located and applying a closed-form-solution procedure to said nonlinear least-squares optimization, in particular obtaining the values of said matrix of estimated positions of the sensors and said matrix of estimated positions of the sources from an right triangular matrix obtained from said mixing matrix via QR decomposition. ### Claim 7 (depends on 6) The method according to claim 6, further comprising using the estimation of position obtained via said solution, in particular said closed-form solution, as initial estimate for a gradient-descent self-calibration procedure. ### Claim 8 (depends on 1) The method according to claim 1, further comprising setting one of said sensors so that it may be reached by events emitted by each source of events and one of said sources of events so that it can reach all the sensors of said set of sensors. ### Claim 9 (depends on 8) The method according to claim 8, further comprising recovering missing data in the reduced matrix of the distances by: calculating matrices designed to reduce the unknowns in bilinear form on the basis of matrices of said singular-value decomposition; introducing variables instead of the missing data in the reduced matrix; and iteratively solving the optimization of a cost function of said variables and of said matrices designed to reduce the unknowns in bilinear form. ### Claim 10 (depends on 1) The method according to claim 1, further comprising providing in said region of space a set of sources of acoustic events, locating a single transducer in different spatial locations at successive instants of time. ### Claim 11 (depends on 1) A system for self-calibration of the position of a set of sensors of acoustic signals, arranged in a region of space, comprising, arranged in said region of space, a set of sources of acoustic events (EW) designed to generate acoustic waves or a single transducer that is set in different spatial locations at successive instants of time, configured for implementing the self-calibration method according to claim 1. ### Claim 12 (depends on 1) A computer-program product that can be directly loaded into the memory of a computer and comprises portions of software code for performing the method according to claim 1 when the product is run on a computer. ### Claim 13 (depends on 1) The system of claim 1 wherein the sensors comprise microphones.