Multi-stage maximum likelihood target estimator

• US 7,266,042 B1
• Filed: 03/31/2006
• Issued: 09/04/2007
• Est. Priority Date: 03/31/2006
• Status: Expired due to Fees

• Current Assignee: Government of the United States of America
• Original Assignee: the united states of america as represented by the secretary of the navy
• Inventors: McPhillips, Kenneth J., Gent, Kurt
• Primary Examiner(s): PIHULIC, DANIEL T
• Application Number:
  US11/398,732
• Time in Patent Office: 522 Days
• Field of Search: 367/118, 342/195
• US Class Current: 367/118
• CPC Class Codes: G01S 13/726 Multiple target tracking
• CPC Class Codes: G01S 15/66 Sonar tracking systems

Abstract

A multi-stage maximum likelihood target estimator for use with radar and sonar systems is provided. The estimator is a software implemented algorithm having four computational stages. The first stage provides angle smoothing for data endpoints thereby reducing angle errors associated with tie-down times. The second stage performs a coarse grid search to obtain the initial approximate target state to be used as a starting point for stages 3 and 4. The third stage is an endpoint Gauss-Newton type maximum likelihood target estimate which determines target range along two time lines. The final refinement of the target state is obtained by the fourth stage which is a Cartesian coordinate maximum likelihood target estimate. The four-stage processing allows the use of target historic data while reducing processing time and computation power requirement.

Claims

1. A multi-stage target estimation method for underwater and airborne targets, said method comprising the steps of:

receiving data inputs from a target tracker;

smoothing angle measurements at the endpoints of the data inputs;

searching a coarse grid in endpoint coordinates to produce an initial target state estimate at two time lines, the time line 1 and the time line 2;

performing a Gauss-Newton maximum endpoint coordinate likelihood estimate at the two time lines;

calculating a Cartesian coordinate maximum likelihood estimate subsequent to said step of performing a Gauss-Newton maximum endpoint coordinate likelihood estimate; and

outputting a target state to a display computer.

2. A multi-stage target estimation method as in claim 1 wherein said step of coarse grid searching comprises the steps of:

selecting three frequency measurements from a target sensor and assigning, as a base frequency, a most recent frequency measurement;

setting a minimum and maximum range at the time line 1 with respect to a sensor associated with the time line 1;

setting a minimum and maximum range at the time line 2 with respect to a sensor associated with the time line 2;

computing three values of range at time line 1 with respect to the sensor associated with the time line 1;

computing three values of range at time line 2 with respect to the sensor associated with the time line 2;

processing frequency data by computing five base frequency estimates;

computing an endpoint coordinate performance index for each combination of the computed values of range and the computed base frequency estimates; and

selecting the initial target state estimate of the computed values of range and the computed base frequency estimate associated with a smallest performance index.

3. A multi-stage target estimation method as in claim 2 wherein said step of performing a Gauss-Newton endpoint coordinate maximum likelihood estimation comprises the steps of:

initializing values for the range at the time line 1 with respect to the sensor associated with the time line 1 using the estimates from said step of course grid searching;

initializing values for the range at the time line 2 with respect to the sensor associated with the time line 2 using the estimates from said step of course grid searching;

initializing the base frequency state using the computed base frequency estimate from said step of course grid searching; and

performing Gauss-Newton iterations until an endpoint coordinate maximum likelihood is estimated.

4. A multi-stage target estimation method as in claim 3 wherein said step of performing Gauss-type iterations comprises the steps of:

computing endpoint parameters at the time of measurement of the time lines 1 and 2;

computing a matrix of partial derivatives;

performing a Householder transformation on the matrix;

extracting an upper matrix from the Householder transformed matrix;

setting a Y vector to a last column of the Householder transformed matrix;

computing a gain vector; and

updating the states in which the states represent the endpoint coordinate maximum likelihood estimates at the two time lines.

5. A multi-stage target estimation method as in claim 4 wherein said step of calculating a Cartesian coordinate maximum likelihood estimate comprises the steps of:

initializing values for an x-coordinate of target position from the Gauss-Newton endpoint coordinate maximum likelihood estimate;

initializing values for a y-coordinate of target position from the Gauss-Newton endpoint coordinate maximum likelihood estimate;

initializing values for an x-coordinate of target velocity from the Gauss-Newton endpoint coordinate maximum likelihood estimate;

initializing values for a y-coordinate of target velocity from the Gauss-Newton endpoint coordinate maximum likelihood estimate; and

performing Gauss-Newton iterations until the Cartesian coordinate maximum likelihood is estimated.

6. A multi-stage target estimation method as in claim 5 wherein said step of performing Gauss-type iterations for Cartesian coordinate maximum likelihood comprises the steps of:

computing Cartesian endpoint parameters at the time of measurement of the time lines 1 and 2;

computing an assigned matrix of partial derivatives;

performing a Householder transformation on the assigned matrix;

extracting an upper matrix from the assigned Householder transformed matrix;

setting an assigned Y vector to a last column of the assigned Householder transformed matrix;

computing an assigned gain vector; and

updating the states in which the states represent the Cartesian coordinate maximum likelihood estimates at the two time lines at current time.

7. A multi-stage target estimation method as in claim 6 wherein said step of outputting a target state to a display computer comprises the steps of:

computing a Cartesian coordinate covariance matrix;

extrapolating the covariance matrix to current time;

computing target range;

computing target bearing;

computing target course;

computing target speed;

computing base frequency standard deviations;

computing major and minor localization ellipse axis length and orientation of major axis from North; and

outputting as the target state.

8. A multi-stage target estimation method as in claim 7 wherein said step of coarse grid searching further comprises constraining a target to lie on azimuthal bearing lines.

9. A multi-stage target estimation method as in claim 7 wherein said step of coarse grid searching further comprises constraining a target to lie on conical angle hyperbolas.

10. A multi-stage target estimation method as in claim 7 wherein said step of coarse grid searching further comprises constraining a target to lie on conical angle hyperbolic asymptotes.