# US 2018/0026607 A1 · Method for the non-linear estimation of a mixture of signals > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 2018/0026607 A1 - Document ID: US20180026607A1 - Status: Published application - Kind: A1 - Application number: 15/539,386 - Filed: 2015-12-23 - Published: 2018-01-25 - Earliest claimed: 2014-12-23 - Assignees: Thales - Applicants: Thales - Inventors: Anne LE MEUR; Jean-Yves DELABBAYE - Web page: https://patentgrep.com/patent/US20180026607A1 ## CPC - G06F 17/18: for evaluating statistical data {, e.g. average values, frequency distributions, probability functions, regression analysis (forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04)} - G06F 17/141: {Discrete Fourier transforms} - G06F 17/16: Matrix or vector computation {, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization (matrix transposition G06F7/78)} - G06F 18/21345: {enforcing sparsity or involving a domain transformation} - G06F 18/2321: using statistics or function optimisation, e.g. modelling of probability density functions - H03H 17/0202: {Two or more dimensional filters; Filters for complex signals (multidimensional convolutions G06F17/153)} - H03H 17/0213: {Frequency domain filters using Fourier transforms} - G01S 3/74: Multi-channel systems specially adapted for direction-finding, i.e. having a single antenna system capable of giving simultaneous indications of the directions of different signals (systems in which the directions of different signals are determined sequentially and displayed simultaneously G01S3/04, G01S3/14) - G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N) - H03H: IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS (waveguides, resonators, lines or other devices of the waveguide type H01P) - G01S: RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES ## Abstract This method for the non-linear estimation of no more than two mixed signals from separate sources, the time/frequency representation of which shows an unknown non-zero proportion of zero components, using an array made up of P>2 antennas, when the directional vectors U and V of the sources emitting these signals are additionally known or estimated, includes the following steps: a) Calculating the successive discrete Fourier transforms of the signal received by the antennas and sampled to obtain a time-frequency P-vector grid of the signal; each element of the grid being referred to as a box and containing a complex vector X forming a measurement; b) For each box, calculating the conditional expectation estimator of the signal, or of the signals, from the measurement X and an a priori probability density for the signals that is a Gaussian mixture. ## Claims ### Claim 1 A method for the non-linear estimation of no more than two mixed signals from separate sources, the time/frequency representation of which shows an unknown non-zero proportion of zero components, using an array made up of P>2 antennas, when the directional vectors U and V of the sources emitting these signals are additionally known or estimated, comprising the following steps: a) calculating the successive discrete Fourier transforms of the signal received by the antennas and sampled to obtain a time-frequency P-vector grid of the signal; each element of the grid being referred to as a box and containing a complex vector X forming a measurement; and b) for each box, calculating the conditional expectation estimator of the signal, or of the signals, from the measurement X and an a priori probability density (p(s)) for the signals that is a Gaussian mixture. ### Claim 2 (depends on 1) The method according to claim 1, characterized in that it includes a step for estimating parameters (qj,σ12,σ22) necessary to establish the conditional expectation using the method of moments operating on the boxes of a divided window in the time/frequency grid. ### Claim 3 (depends on 1) The method according to claim 1, characterized in that the calculation of the conditional expectation estimator is approximated by a Conditional Expectation with 4 Linear Filters obtained by a four-hypothesis decision processing pertaining to four Hermitian forms of the measurement X, followed by linear filtering commanded by the result of the decision. ### Claim 4 (depends on 3) The method according to claim 3, characterized in that the calculation of the Conditional Expectation estimator with 4 Linear Filters is approximated by a Conditional Expectation with Independent Decisions obtained by a two-hypothesis decision processing pertaining to U*X and V*X, followed by linear filtering commanded by the result of the decision. ### Claim 5 (depends on 4) The method according to claim 4, characterized in that, as a function of the result of the decision, the linear filtering processing yielding the Conditional Expectation estimator with Independent Decisions, is either: the estimator of the dual-source maximum likelihood for each source; the single-source maximum likelihood estimator for the first source, 0 for the second source; 0 for the first source, the single-source maximum likelihood estimator for the second source; 0 for each source. ### Claim 6 (depends on 5) The method according to claim 5, characterized in that the calculation of the Conditional Expectation estimator with Independent Decisions is approximated by a Thresholded Maximum Likelihood obtained by estimating the signal(s) using the maximum likelihood method followed by the comparison of each estimate to a threshold. ### Claim 7 (depends on 4) The method according to claim 4, characterized in that the or each decision threshold is chosen to respect a so-called false alarm likelihood consisting of declaring the signal to be non-zero when it is zero. ### Claim 8 (depends on 4) The method according to claim 4, characterized in that it includes: a first estimate of the signals done using the Conditional Expectation with Independent Decisions or Thresholded Maximum Likelihood method, an estimate of parameters (qj,σ12,σ22) done from the components of the signal obtained in the previous step, and a second estimate of the signals done using the Conditional Expectation method or the Conditional Expectation with 4 Linear Filters method, informed of the values of the parameters (qj,σ12,σ22) obtained in the previous step. ### Claim 9 (depends on 5) The method according to claim 5, characterized in that it includes: a first estimate of the signals done using the Conditional Expectation with Independent Decisions or Thresholded Maximum Likelihood method, an estimate of parameters (qj,σ12,σ22) done from the components of the signal obtained in the previous step, and a second estimate of the signals done using the Conditional Expectation method or the Conditional Expectation with 4 Linear Filters method, informed of the values of the parameters (qj,σ12,σ22) obtained in the previous step. ### Claim 10 (depends on 6) The method according to claim 6, characterized in that it includes: a first estimate of the signals done using the Conditional Expectation with Independent Decisions or Thresholded Maximum Likelihood method, an estimate of parameters (qj,σ12,σ22) done from the components of the signal obtained in the previous step, and a second estimate of the signals done using the Conditional Expectation method or the Conditional Expectation with 4 Linear Filters method, informed of the values of the parameters (qj,σ12,σ22) obtained in the previous step. ### Claim 11 (depends on 4) The method according to claim 4, characterized in that it includes: a first estimate of the signals done using the Conditional Expectation with Independent Decisions or Thresholded Maximum Likelihood method, an estimate of parameters (qj,σ12,σ22) done from the components of the signal obtained in the previous step, and a second estimate of the signals done using the Conditional Expectation method or the Conditional Expectation with 4 Linear Filters method, informed of the values of the parameters (qj,σ12,σ22) obtained in the previous step. ### Claim 12 (depends on 5) The method according to claim 5, characterized in that it includes: a first estimate of the signals done using the Conditional Expectation with Independent Decisions or Thresholded Maximum Likelihood method, an estimate of parameters (qj,σ12,σ22) done from the components of the signal obtained in the previous step, and a second estimate of the signals done using the Conditional Expectation method or the Conditional Expectation with 4 Linear Filters method, informed of the values of the parameters (qj,σ12,σ22) obtained in the previous step. ### Claim 13 (depends on 6) The method according to claim 6, characterized in that it includes: a first estimate of the signals done using the Conditional Expectation with Independent Decisions or Thresholded Maximum Likelihood method, an estimate of parameters (qj,σ12,σ22) done from the components of the signal obtained in the previous step, and a second estimate of the signals done using the Conditional Expectation method or the Conditional Expectation with 4 Linear Filters method, informed of the values of the parameters (qj,σ12,σ22) obtained in the previous step.