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Патент США N 5694342
Stein December 2, 1997
Method for detecting signals in non-Gaussian background clutter

РЕФЕРАТ

The invention provides a method for detecting signals in non-Gaussian background clutter, comprising the steps of: 1) filtering input data to partition Gaussian input data from non-Gaussian input data; 2) estimating the intensity level of the Gaussian input data; 3) determining the probability distributions of the non-Gaussian input data; 4) determining the background noise level of the input data; 5) estimating noise parameters of the input data; 6) estimating the residual intensity of the input data using the noise parameters; 7) determining a detection statistic M from the input data, estimated noise parameters, and the residual intensity of the input data; 8) determining a standard deviation N.sub.i of the detection statistic, M.sub.i ; 9) determining a normalized detection statistic Si, where S.sub.i =M.sub.i /N.sub.i,; 10) determining a maximum value, S.sub.imax of S.sub.i ; 11) determining a mean value S.sub.Mean and standard deviation S.sub.Std dev of all S.sub.i excluding S.sub.imax ; 12) determining a threshold .tau..sub..alpha. of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where .alpha. is a predetermined false alarm probability; and 13) generating an output signal if [S.sub.i -S.sub.Mean ]/S.sub.Std dev .gtoreq..tau..sub..alpha.. The invention may also be implemented as a program storage device readable by a machine which tangibly embodies a program of instructions executable by the machine to perform the above-referenced method steps.

Автор(ы): Stein; David W. J. (San Diego, CA)
Заявитель: The United States of America as represented by the Secretary of the Navy (Washington, DC)
Family ID: 24984743
N заявки: 08/742,413
Приоритет: October 24, 1996

Current U.S. Class: 702/190 ; 342/159; 375/227; 702/181; 702/69
Класс МПК: G01S 7/292 (20060101); G01S 7/295 (20060101); H03M 001/08 (); H04B 001/10 ()
Current CPC Class: G01S 7/2922 (20130101); G01S 7/295 (20130101)
Field of Search: 364/516,574,572,724.01 375/285,227,346,254,350 329/320,318,349,353 340/310.03 342/203,159 348/607 370/317 381/71,94

Ссылки на источники [Referenced By]
Патентные документы США
4870603 September 1989 Padawer
4956792 September 1990 Sekine
4970660 November 1990 Marchant
5337055 August 1994 Ghignoni
5457462 October 1995 Mitsumoto et al.
5499195 March 1996 Castelaz

Другие ссылки

Stein, "Detection of Random Signals in Gaussian Mixture Noise", IEEE Trantions on Information Theory, vol. 41, No. 6, 6 Nov. 1995, pp. 1788-1801. .
Bond et al., "A Unified Theory of Adaptive Locally Optimum Processing", IEEE, pp. 1594-1597, 1993. .
Hummels et al., "Locally Optimal Detection of Unknown Signals in Non-Gaussian MarkovNoise", IEEE, pp. 1098-1101, 1992. .
Hummels et al., "Adaptive Locally Optimal Detection Using RBF Neural Network", IEEE, pp. 3050-3055, 1994. .
Au, "Locally Optimal and Suboptimal Signal Detection in Transformation Noise", IEE Transactions on Aerospace & Electronic Systems, vol. 32, No. 2, pp. 742-753, Apr. 1996..

Primary Examiner: Voeltz; Emanuel T.
Assistant Examiner: Assovad; Patrick J.
Attorney, Agent or Firm: Fendelman; Harvey Kagan; Michael A. Lipovsky; Peter A.
ФОРМУЛА ИЗОБРЕТЕНИЯ


I claim:

1. A method for detecting signals in non-Gaussian background clutter, comprising the steps of:

1) filtering input data to partition Gaussian input data from non-Gaussian input data;

2) estimating the intensity level of the Gaussian input data;

3) determining the probability distributions of the non-Gaussian input data.

4) determining the background noise level of the input data;

5) estimating noise parameters of the input data;

6) estimating the residual intensity of the input data using the noise parameters;

7) determining a detection statistic M.sub.i from the input data, estimated noise parameters, and the residual intensity of the input data;

8) determining the standard deviation N.sub.i of the detection statistic, M.sub.i ;

9) determining a normalized detection statistic S.sub.i, where S.sub.i =M.sub.i /N.sub.i,

10) determining a maximum value, S.sub.imax of S.sub.i ;

11) determining a mean value S.sub.Mean and a standard deviation S.sub.Std dev of all S.sub.i excluding S.sub.imax ;

12) determining a threshold .tau..sub..alpha. of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where .alpha. is a predetermined false alarm probability; and

13) generating an output signal if [S.sub.i -S.sub.Mean ]/S.sub.Std dev .gtoreq..tau..sub..alpha..

2. The method of claim 1 wherein step (3) further includes estimating first parameters of an exponential mixture family of probability density functions for the non-Gaussian input data, whereby a subset of first parameters represents the background intensity of the non-Gaussian input data.

3. The method of claim 2 wherein step (4) further includes applying a smoothing filter to the estimated intensities of the Gaussian input data determined at step (2) and the background intensity of the non-Gaussian input data to provide an estimated background noise intensity.

4. The method of claim 1 wherein step (3) further includes estimating first parameters of an Gaussian mixture family of probability density functions for the non-Gaussian input data, whereby a subset of first parameters represents the background intensity of the non-Gaussian input data.

5. The method of claim 4 wherein step (4) further includes applying a smoothing filter to the estimated intensities of the Gaussian input data determined at step (2) and the background intensity of the non-Gaussian input data to provide an estimated background noise intensity.

6. The method of claim 1 step (5) further includes:

adjusting estimates of a selected set of the first parameters that are a predetermined level below the estimated background noise level of the input data;

creating uncertainty sets for the first parameters; and

selecting a set of the first parameters from the uncertainty intervals to define a probability density function.

7. The method of claim 6 wherein step (5) further includes selecting second parameters from said uncertainty set to mimimize the maximum value of a false alarm probability function.

8. The method of claim 7 wherein step (5) includes scaling values of said second parameters.

10. The method of claim 9 wherein step (5) includes scaling values of said third parameters.

11. The method of claim 2 further includes fitting said input data having the n greatest intensity values to a decaying exponential function to generate a high intensity term of said exponential mixture function, where n is a positive integer.

12. The method of claim 2 further including fitting said input data having the n greatest intensity values to a decaying exponential function to generate a high intensity term of said Gaussian mixture density function.

13. The method of claim 12 further including the step of combining the noise parameters from step (5) with the high intensity term.

14. The method of claim 2 wherein step (6) further includes the steps of:

determining the average intensity of said input data; and

determining an estimated signal strength value of the input data as the maximum of zero and the difference between the average intensity of said input data and the expected noise intensity calculated from the noise parameters of the input data from step (5).

15. The method of claim 2 wherein step (6) further includes using a maximum likelihood estimator to determine an estimated signal strength value of the input data.

16. The method of claim 1 wherein step (7) further includes determining a modified optimal detection statistic.

17. A program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine to perform method steps, the method steps comprising:

1) filtering input data to identify Gaussian input data and non-Gaussian input data;

2) estimating the intensity level of the Gaussian input data;

3) determining the probability distributions of the non-Gaussian input data.

4) determining the background noise level of the input data;

5) estimating noise parameters of the input data;

6) estimating the residual intensity of the input data using the noise parameters;

7) determining a detection statistic M from the input data, estimated noise parameters, and the residual intensity of the input data;

8) determining a standard deviation N.sub.i of the detection statistic, M.sub.i ;

9) determining a normalized detection statistic Si, where S.sub.i =M.sub.i /N.sub.i,

10) determining a maximum value, S.sub.imax of S.sub.i,

11) determining a mean value S.sub.Mean and a standard deviation S.sub.Std dev of all S.sub.i excluding S.sub.imax ;

12) determining a threshold .tau..sub..alpha. of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where .alpha. is a predetermined false alarm probability; and

13) generating an output signal if [S.sub.i -S.sub.Mean ]/S.sub.Std dev .ltoreq..tau..sub..alpha..

18. The program storage device of claim 17 wherein step (3) further includes estimating first parameters of an exponential mixture family of probability density functions for the non-Gaussian input data, whereby a subset of first parameters represents the background intensity of the non-Gaussian input data.

19. The program storage device of claim 17 wherein step (4) further includes applying a smoothing filter to the estimated intensities of the Gaussian input data determined at step (2) and the background intensity of the non-Gaussian input data to provide an estimated background noise intensity.

20. The program storage device of claim 17 wherein step (3) further includes estimating first parameters of an Gaussian mixture family of probability density functions for the non-Gaussian input data, whereby a subset of first parameters represents the background intensity of the non-Gaussian input data.

21. The program storage device of claim 20 wherein step (4) further includes applying a smoothing filter to the estimated intensities of the Gaussian input data determined at step (2) and the background intensity of the non-Gaussian input data to provide an estimated background noise intensity.

22. The program storage device of claim 17 step (5) further includes:

adjusting estimates of a selected set of the first parameters that are a predetermined level below the estimated background noise level of the input data;

creating uncertainty sets for the first parameters; and

selecting a set of the first parameters from the uncertainty intervals to define a probability density function.

23. The program storage device of claim 22 wherein step (5) further includes selecting second parameters from said uncertainty set to mimimize the maximum value of a false alarm probability function.

24. The program storage device of claim 23 wherein step (5) includes scaling values of said second parameters.

26. The program storage device of claim 25 wherein step (5) includes scaling values of said third parameters.

27. The program storage device of claim 18 further includes fitting said input data having the n greatest intensity values to a decaying exponential function to generate a high intensity term of said exponential mixture function, where n is a positive integer.

28. The program storage device of claim 18 further including fitting said input data having the n greatest intensity values to a decaying exponential function to generate a high intensity term of said Gaussian mixture density function.

29. The program storage device of claim 28 further including the step of combining the noise parameters from step (5) with the high intensity term.

30. The program storage device of claim 18 wherein step (6) further includes the steps of:

determining the average intensity of said input data; and

determining an estimated signal strength value of the input data as the maximum of zero and the difference between the average intensity of said input data and the expected noise intensity calculated from the noise parameters of the input data from step (5).

31. The program storage device of claim 18 wherein step (6) further includes using a maximum likelihood estimator to determine an estimated signal strength value of the input data.

32. The program storage device of claim 17 wherein step (7) further includes determining a modified optimal detection statistic.

33. The program storage device of claim 32 wherein step (8) further includes determining the mean and standard deviation of said detection statistic.

34. The program storage device of claim 32 wherein step (8) further includes determining a threshold from the mean and standard deviation of said detection statistic and a predetermined false alarm.

35. A method for detecting signals in non-Gaussian background clutter, comprising the steps of:

1) filtering input data to partition Rayleigh input data from non-Rayleigh input data;

2) estimating the intensity level of the Rayleigh input data;

3) determining the probability distributions of the non-Rayleigh input data.

4) determining the background noise level of the input data;

5) estimating noise parameters of the input data;

6) estimating the residual intensity of the input data using the noise parameters;

7) determining a detection statistic M.sub.i from the input data, estimated noise parameters, and the residual intensity of the input data;

8) determining the standard deviation N.sub.i of the detection statistic, M.sub.i ;

9) determining a normalized detection statistic S.sub.i, where S.sub.i =M.sub.i /N.sub.i,

10) determining a maximum value, S.sub.imax of S.sub.i ;

11) determining a mean value S.sub.Mean and a standard deviation S.sub.Std dev of all S.sub.i excluding S.sub.imax ;

12) determining a threshold .tau..sub..alpha. of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where .alpha. is a predetermined false alarm probability; and

13) generating an output signal if [S.sub.i -S.sub.Mean ]/S.sub.Std dev .gtoreq..tau..sub..alpha..

36. A method for detecting signals in non-Gaussian background clutter, comprising the steps of:

1) filtering input data to partition exponential input data from non-exponential input data;

2) estimating the intensity level of the exponential input data;

3) determining the probability distributions of the non-exponential input data.

4) determining the background noise level of the input data;

5) estimating noise parameters of the input data;

6) estimating the residual intensity of the input data using the noise parameters;

7) determining a detection statistic M.sub.i from the input data, estimated noise parameters, and the residual intensity of the input data;

8) determining the standard deviation N.sub.i of the detection statistic, M.sub.i ;

9) determining a normalized detection statistic S.sub.i, where S.sub.i =M.sub.i /N.sub.i,

10) determining a maximum value, S.sub.imax of S.sub.i ;

11) determining a mean value S.sub.Mean and a standard deviation S.sub.Std dev of all S.sub.i excluding S.sub.imax ;

12) determining a threshold .tau..sub..alpha. of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where .alpha. is a predetermined false alarm probability; and

13) generating an output signal if [S.sub.i -S.sub.Mean ]/S.sub.Std dev .gtoreq..tau..sub..alpha..

37. A program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine to perform method steps, the method steps comprising:

1) filtering input data to partition Rayleigh input data from non-Rayleigh input data;

2) estimating the intensity level of the Rayleigh input data;

3) determining the probability distributions of the non-Rayleigh input data.

4) determining the background noise level of the input data;

5) estimating noise parameters of the input data;

6) estimating the residual intensity of the input data using the noise parameters;

7) determining a detection statistic M.sub.i from the input data, estimated noise parameters, and the residual intensity of the input data;

8) determining the standard deviation N.sub.i of the detection statistic, M.sub.i ;

9) determining a normalized detection statistic S.sub.i, where S.sub.i =M.sub.i /N.sub.i,

10) determining a maximum value, S.sub.imax of S.sub.i ;

11) determining a mean value S.sub.Mean and a standard deviation S.sub.Std dev of all S.sub.i excluding S.sub.imax ;

12) determining a threshold .tau..sub..alpha. of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where .alpha. is a predetermined false alarm probability; and

13) generating an output signal if [S.sub.i -S.sub.Mean ]/S.sub.Std dev .gtoreq..tau..sub..alpha..

38. A program storage device readable by a machine, tangibly embodying a program of instructions executable by the machine to perform method steps, the method steps comprising:

1) filtering input data to partition exponential input data from non-exponential input data;

2) estimating the intensity level of the exponential input data;

3) determining the probability distributions of the non-exponential input data.

4) determining the background noise level of the input data;

5) estimating noise parameters of the input data;

6) estimating the residual intensity of the input data using the noise parameters;

7) determining a detection statistic M.sub.i from the input data, estimated noise parameters, and the residual intensity of the input data;

8) determining the standard deviation N.sub.i of the detection statistic, M.sub.i ;

9) determining a normalized detection statistic S.sub.i, where S.sub.i =M.sub.i /N.sub.i,

10) determining a maximum value, S.sub.imax of S.sub.i ;

11) determining a mean value S.sub.Mean and a standard deviation S.sub.Std dev of all S.sub.i excluding S.sub.imax ;

12) determining a threshold .tau..sub..alpha. of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where .alpha. is a predetermined false alarm probability; and

13) generating an output signal if [S.sub.i -S.sub.Mean ]/S.sub.Std dev .gtoreq..tau..sub..alpha..
ОПИСАНИЕ ИЗОБРЕТЕНИЯ


BACKGROUND OF THE INVENTION

The present invention relates to the field of signal processing, and more particularly to a method for detecting weak signals in a non-Gaussian, non-stationary background.

Many signal detection schemes in use today, including intensity-only and Doppler processors, are based on optimal detection formulas derived from Gaussian noise models. For example, signal detection schemes employing constant false alarm rate (CFAR) algorithms use the power detector, which is obtained from optimal detection theory by assuming a random signal and Gaussian noise, with an adaptive noise power estimator.

FIG. 1 shows the components of a basic CFAR detector. The input data is a collection of successive intensities (norm squared) of baseband demodulated radar returns from a set of range bins organized into a range-by-pulse matrix X=(x.sub.ij), where R is the number of range bins, P is the number of pulses and 1.ltoreq.i.ltoreq.R, 1.ltoreq.j.ltoreq.P. The steps in the processing include estimating the power in the i.sup.th bin using the formula: ##EQU1## The noise power estimate for the

where g is the number of guard bins on either side of the test bin, and L is the number of range bins used to form the estimate of the noise power.

The detection statistic for the i.sup.th bin, t.sub.i, may be calculated for each range bin by normalizing and summing the input data according to the formula: ##EQU2##

The threshold may be set as a fixed number, T, calculated using a predetermined false alarm rate and the assumption that under the noise only hypothesis the statistics, t.sub.i, are unit chi-squared random variables on 2P degrees of freedom. Alternatively, the threshold for the i.sub.th bin may be set using a function of the values of t.sub.l for l near i or determined by an operator.

To avoid an excessive false alarm rate when applied to non-Gaussian noise, many CFAR processors use a high threshold which makes it unlikely that weak signals will be discerned from the noise. Therefore, a need exists for a detector which can detect weak signals from a non-Gaussian noise background, yet which has a low false alarm rate.

SUMMARY OF THE INVENTION

The invention provides a method for detecting signals in non-Gaussian background clutter, comprising the steps of: 1) filtering input data to segregate Gaussian input data from non-Gaussian input data; 2) estimating the intensity level of the Gaussian input data; 3) determining the probability distributions of the non-Gaussian input data; 4) determining the background noise level of the input data; 5) estimating noise parameters of the input data; 6) estimating the residual intensity of the input data using the noise parameters; 7) determining a detection statistic M from the input data, estimated noise parameters, and the residual intensity of the input data; 8) determining a standard deviation N.sub.i of the detection statistic, M.sub.i ; 9) determining a normalized detection statistic S.sub.i, where S.sub.i =M.sub.i /N.sub.i,; 10) determining a maximum value, S.sub.imax of S.sub.i ; 11) determining a mean value S.sub.Mean and a standard deviation S.sub.Std dev of all S.sub.i excluding S.sub.imax ; 12) determining a threshold .tau..sub..alpha. of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where .alpha. is a predetermined false alarm probability; and 13) generating an output signal if [S.sub.i -S.sub.Mean ]/S.sub.Std dev .gtoreq..tau..sub..alpha..

The invention may also be characterized as providing a method for detecting signals in non-Gaussian background clutter, comprising the steps of: 1) filtering input data to partition Rayleigh input data from non-Rayleigh input data; 2) estimating the intensity level of the Rayleigh input data; 3) determining the probability distributions of the non-Rayleigh input data. 4) determining the background noise level of the input data; 5) estimating noise parameters of the input data; 6) estimating the residual intensity of the input data using the noise parameters; 7) determining a detection statistic M.sub.i from the input data, estimated noise parameters, and the residual intensity of the input data; 8) determining the standard deviation N.sub.i of the detection statistic, M.sub.i ; 9) determining a normalized detection statistic S.sub.i, where S.sub.i =M.sub.i /N.sub.i, 10) determining a maximum value, S.sub.imax of S.sub.i ; 11) determining a mean value S.sub.Mean and a standard deviation S.sub.Std dev of all S.sub.i excluding S.sub.imax ; 12) determining a threshold .tau..sub..alpha. of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where .alpha. is a predetermined false alarm probability; and 13) generating an output signal if [S.sub.i -S.sub.Mean ]/S.sub.Std dev .gtoreq..tau..sub..alpha..

The invention may further be implemented as a method for detecting signals in non-Gaussian background clutter, comprising the steps of: 1) filtering input data to partition exponential input data from non-exponential input data; 2) estimating the intensity level of the exponential input data; 3) determining the probability distributions of the non-exponential input data; 4) determining the background noise level of the input data; 5) estimating noise parameters of the input data; 6) estimating the residual intensity of the input data using the noise parameters; 7) determining a detection statistic M.sub.i from the input data, estimated noise parameters, and the residual intensity of the input data; 8) determining the standard deviation N.sub.i of the detection statistic, M.sub.i ; 9) determining a normalized detection statistic S.sub.i, where S.sub.i =M.sub.i /N.sub.i, 10) determining a maximum value, S.sub.imax of S.sub.i ; 11) determining a mean value S.sub.Mean and a standard deviation S.sub.Std dev of all S.sub.i excluding S.sub.imax ; 12) determining a threshold .tau..sub..alpha. of a zero mean unit variance normal distribution corresponding to a predetermined false alarm probability, where .alpha. is a predetermined false alarm probability; and 13) generating an output signal if [S.sub.i -S.sub.Mean ]/S.sub.Std dev .gtoreq..tau..sub..alpha.. The invention may also be implemented as computer program instructions written on a computer readable storage device. When executed, the program instructions cause the computer to perform the above-referenced method steps.

Another advantage of the invention is that the detector may optionally estimate the highest state variance using global data, and the combination of the high state parameters with the parameters estimated for each range bin.

Still another advantage of the invention is that it uses an estimate of the signal strength to modify the locally optimal detector so that the resulting detector will be able to detect signals that are not vanishingly small.

A further advantage of the invention is that it sets thresholds using the moments calculated from the multi-state mixture parameters used to process the data.

These and other advantages of the invention will become more apparent upon review of the accompanying drawings and specification, including the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of the basic components of a constant false alarm rate (CFAR) detector.

FIG. 2 is a block diagram of the basic components of a system for detecting signals in non-gaussian background clutter which embodies various features of the present invention.

FIG. 3 is a block diagram showing the basic components of another embodiment of a system for detecting signals in non-gaussian background clutter embodying various features of the present invention.

FIG. 4 is a block diagram of the hardware elements which may be used to implement the invention.

Throughout the several figures, like references refer to like elements.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The following description is of the best mode presently comtemplated for carrying out the invention. This description is not to be taken in a limiting sense, but is made merely for the purpose of describing the general principles of the invention. The scope of the invention should be determined with reference to the claims.

The present invention provides a method for detecting weak signals in a non-Gaussian and non-stationary background, such as radar sea clutter, acoustic data containing moving interferers, and seismic data. The invention preferably may be implemented as computer readable program instructions which may be encoded onto a program storage device such as magentic tape, a floppy disk, magnetooptical disk, compact disk, or the like. The storage device embodies the program of computer executable instructions for implementing the function of detecting weak signals in non-Gaussian and non-stationary backgrounds.

Referring to FIG. 2, input data 20 is provided to a computer readable program instructions referenced as a filter 24 of a detector 10. The filter 24 divides the input data 20 into data 26 which may include Gaussian data, Rayleigh data, or exponential data, and into data 30 which may include non-Gaussian data, non-Rayleigh data, and non-exponential data 30. If data 26 includes Gaussian data, then data 30 includes non-Gaussian data. If data 26 includes Rayleigh data, then data 30 includes non-Rayleigh data. If data 26 includes exponential data, then data 30 includes non-exponential data. The input data may be partitioned into groups of data 26 and 30 using a suitable statistical goodness of fit test, such as the Kolmogorov-Smirnov (KS1) test or Chi-Square test to reduce computational requirement. Next, the data 26 is provided to computer readable program instructions referenced as an intensity estimator 28 which generates estimates 29 of the intensity level of the input data 26. The input data 30 is received by computer readable program instructions referenced as a density estimator 32 which fits the data 30 to a family of first functions by estimating first parameters of the functions to determine the probability distributions of the data which are provided as output 34. The functions may be exponential mixture probability density functions. An example of an m-state exponential mixture probability density function with parameters (p.sub.1, . . . , p.sub.m, v.sub.1, . . . , v.sub.m) such that ##EQU3## and v.sub.1 <. . .<v.sub.m is: ##EQU4## The expectation maximization (EM) density estimator 32 estimates for the i.sup.th range bin, p.sub.k.sup.i and w.sub.k.sup.i for prescribed values of m, wherein different values of m may be used to suit the requirements of a particular application. The values of p.sub.k.sup.i and v.sub.k.sup.i are provided as output 34 from the EM density estimator 32. The first functions may also be Gaussian mixture probability density functions. Alternatively, the EM density estimator 32 may apply a quasi-Newton optimization algorithm to the output of the expectation and maximization algorithm to possibly speed the parameter estimation procedure.

Computer readable program instructions referenced as a robust parameter selector 36 employs the outputs 29 and 34 to determine the parameters 37 of the background noise of the input data 20. The input data 20 contains noise components and Therefore, noise parameters 37 of the input data 20 are estimated, and are determined in the robust parameter selector 36 which may be implemented as computer readable subroutine ROBPARSEL10.m (Appendix 1), written, by way of example, in MATLAB.TM.. The v.sub.k.sup.i, where if m=2, then k=1, and a "clutter plus noise parameter," cpn(.theta.), where ##EQU5## The robust parameter selector 36 mimimizes the generation of false alarms by detector 10.

ROBPARSEL10.m, presented by way of example, in APPENDIX 1, determines exponential mixture parameters 37 of the noise in the input data 20. For each range bin ROBPARSEL10.M determines robust estimates of the two-state exponential mixture density estimate the value of p.sub.2 of the noise component of the input data 20. Lines 106-115 of ROBPARSEL10.m calculate the value of v.sub.2 of the noise component of the input data. 20. Depending upon the value of v2oflag, lines 131-185 of ROBPARSEL10.m scale v.sub.2. At lines 187-196, ROBPARSEL10.m scales p.sub.1, depending upon the value of the input parameter pLflag,. The variable v.sub.1 is scaled at lines 197-210 of ROBPARSEL10.m depending upon the value of vlflag.

TABLE I ______________________________________ Input Parameters for ROBPARSEI 10.m Parameter Description ______________________________________ unempar2 exponentlal mixture parameters of the input data npow average intensity of the input scaling of v.sub.1 pLflag flag used to control the scaling of p.sub.1 ______________________________________

TABLE II ______________________________________ Output Parameters for ROBPARSEL 10.m Parameter Description ______________________________________ rnnpar estimates of the exponential mixture parameters of the noise data rnpow estimates of the intensity of the noise data ______________________________________

Still referring to FIG. 2, for the i.sup.th range bin, a residual variance calculator 40 transforms the output 37 from the robust parameter selector and the input data 20 into an estimate output 42 of the signal strength of any signal of interest which may be in the input data 20. The residual variance calculator 40 may produce the signal strength estimate v.sub.s.sup.i (residual intensity) used by the detection statistic M according to the formula: ##EQU6##

Next, computer readable program instructions referenced as detection statistic calculator 46 transforms the input data 20 and the outputs 37 and 42 into an exponential mixture amplitude detection statistic, M, or simply, "detection statistic" which may be determined as follows: Let .theta..sup.i =(p.sub.1.sup.i, . . . ,p.sub.m+1.sup.i,v.sub.1.sup.i, . . . ,v.sub.m+1.sup.i, v.sub.s.sup.i) be the outputs 37 and 42, then the detection statistic, M, for the i.sup.th range bin is calculated according to the formulas: ##EQU7##

Computer readable program instructions referenced as parameter dependent normalization factor calculater 50 uses output 37 to determine a normalization factor, N, for each range bin. The normalization factor may be obtained by determining k moments of the distribution of the detection statistic M, where k is a positive integer and preferably, where k=2. The moments may be calculated or obtained from a look-up table.

The k moments of the detection statistic may be determined in accordance with the following procedures: M may be approximated by a piecewise polynomial function obtained from piecewise polynomial approximations of the state weighting functions w.sub.k.sup.i (x.sub.ij)=p(k.vertline.x.sub.ij, .theta..sup.i). For an m-state mixture lim.sub.u.fwdarw..infin. w.sub.m (u)=1. Select K so that if u>K then w.sub.m (u).apprxeq.1. Select the degree, d, and number, p, of the polynomials to be used in the approximation. Define a partition:

Then for each 1.ltoreq.j.ltoreq.m-1 and each 1.ltoreq.l.ltoreq.p let P.sub.lj be the Lagrange interpolating polynomial of degree d defined by [u.sub.(l-1)d, . . . , u.sub.ld ] and [w.sub.j (u.sub.l-1)d, . . . , w.sub.j (v.sub.ld)]. Other i.e. .chi..sub.A (u)=1 if .mu..epsilon.A and 0 otherwise. Define the piecewise polynomial approximation of the weighting functions by: ##EQU9## and the approximate detector by ##EQU10## Since P M is piecewise polynomial, its moments are easily calculated for Gaussian mixture, Rayleigh mixture, or exponential mixture noise and a Gaussian signal having variance v.sub.s. Other signal models require appropriate modifications. For 1.ltoreq.l.ltoreq.p+1 define: ##EQU11## and define u.sub.(p+1)d =.infin.. Then, ##EQU12## Since Q.sub.l is a truncated polynomial, the integrals in (11) may be evaluated using the incomplete gamma function.

The normalization factor, N, of the detection statistic M for each time series is calculated as follows: Under the noise only hypothesis, the mean of the detection statistic, E(PM.sup.1), is zero, and the second moment, E(PM.sup.2) is obtained from equation (11). Therefore, N=[E(PM.sup.2)].sup.1/2.

Computer readable program instructions referenced as comparator 54 uses the detection statistic M and the normalization factor N to determine whether a signal is present and to generate an output signal A if a normalized detection statistic is greater than a threshold, as described below:

Given a false alarm probability, .alpha., and letting .PHI. be the unit normal distribution, the comparator 54, determines a threshold .tau..sub..alpha. for the zero-mean unit-variance normal density which is defined as

The probability of a false alarm is equal to a predetermined false alarm probability suitable for a particular application. A suitable false alarm probability is based on one's tolerance for investigating alarms, based on the cost of a misdetection. For example, if missing a signal of interest would be very costly in terms of man-hours, level of risk, severity of consequences, etc., then a higher false alarm rate would be tolerated. Conversely, if missing a signal of interest would not be very costly, one could tolerate a lower false alarm rate.

Then, the comparator 54 determines the first normalized detection statistic S.sub.i, where S.sub.i =M.sub.i /N.sub.i,, N.sub.i is the output of the parameter dependent normalization factor calculater 50, and M.sub.i is the detection statistic which is the output of detection statistic determinator 46, for each ith range bin, where i is an index. Then, the maximum value, S.sub.imax of S.sub.i is identified; the mean value S.sub.Mean of all S.sub.i except for S.sub.imax is determined; and the standard deviation S.sub.Std dev of all S.sub.i except for S.sub.imax is determined. Finally, a signal is declared present in range bin i if:

Referring to FIG. 4, if a signal is declared present, a computer 70 generates an output signal A The output signal A may be provided to an output device 72, such as a video monitor, printer, audio alarm or other output device capable of providing a human intelligible message indicating that a signal of interest has been detected.

The present invention may also be implemented to further include computer readable program instructions referenced as tail parameter estimator 60 and parameter combiner 64, shown in FIG. 3. The tail parameter estimator 60 receives the data 30 and provides parameter outputs (v.sub.m+1 and p.sub.m+1) 62 of an additional state of a Gaussian mixture model or exponential mixture model. The parameters v.sub.m+1 and p.sub.m+1 account for high intensity noise that might not otherwise be observed in the neighborhood of a particular range bin. The values v.sub.m+1 represents the average value of high intensity data 30, and p.sub.m+1 represents the probability of observing such high intensity input data 30. The values of v.sub.m+1 and p.sub.m+1 may be determined by fitting the K highest intensity values (the "tail") of the complementary cumulative distribution of the non-Guassian input data 30 to a decaying exponential function.

The tail parameters may be estimated in accordance with the following steps:

a. The cumulative distribution function, C(x), of the data 30 is calculated using well known techniques.

b. A limit, L, is defined so that the top p percent of the data 30 are greater than L.

c. Using a linear regression, a linear function is fitted to the function log (l-C(x)) for x>L, and the slope, d and y-intercept b of this line are returned.

d. The m+1-state parameters (v.sub.m+1, p.sub.m+1) are then defined as

The parameter combiner (as opposed to the parameter selector) 64 receives the robust estimated noise parameters 37 from the robust parameter selector 36 and the estimated tail parameters 62 from the tail parameter estimator 60, and adds the parameters p.sub.m+1, v.sub.m+1 of the data 30 in accordance with the rules set forth as follows to provide estimated noise parameters 68: If v.sub.m+1 >v.sub.m.sup.i, then the parameter combiner 64 combines the tail parameters 62 and the robust parameters 37, (p.sub.1.sup.i. . . , p.sub.m.sup.i, v.sub.1.sup.i, . . . , v.sub.m.sup.i) to produce estimated noise parameters 68 of an m+1 state exponential mixture density function for each ith range bin, (p.sub.1.sup.i, . . . ,p.sub.m+1.sup.i,v.sub.1.sup.i, . . . ,v.sub.m+1). The estimated noise parameters 68 generated by the parameter combiner 64 are defined and determined in accordance with the following formulas: ##EQU13##

Additionally, the parameter combiner 64 coalesces states of the exponential mixture density function or Gaussian mixture density function if its variance terms v.sub.k.sup.i are sufficiently close, i.e., within some predetermined limit, to be practically considered as one state.

Still referring to FIG. 3, for the i.sup.th range bin, the residual variance calculator 40 transforms the output 68 and the input data 20 (including both data 26 and data 30) into an estimate output 42 as described above with reference to FIG. 2. Next, the detection statistic calculator 46 transforms the input data 20 and the output 68 and 42 into an exponential mixture amplitude detection statistic, M. The parameter dependent normalization factor calculater 50 uses output 68 to determine a normalization factor, N, for each range bin. The comparator 54 uses the detection statistic M and the normalization factor N to determine whether a signal is present and to generate an output signal A if normalized detection statistic is greater than a threshold. In all other respects, the operations of the residual variance calculator 40, parameter normalization factor calculator 50, and comparator 54, are described above with reference to FIG. 2.

In one alternative embodiment of the invention, the robust parameter selector 36 may be replaced by a minimax parameter selector to provide the robust estimates of the noise parameters 37. The minimax parameters are calculated as follows.

a. Define uncertainty intervals for p.sub.j and v.sub.j denoted I.sub.pj and I.sub.vj respectively, for 1.ltoreq.j.ltoreq.m, and let .DELTA..theta.=I.sub.p1 .chi.. . . .chi.I.sub.pm .times.I.sub.v1 .chi.. . . .chi.I.sub.vm. For each range bin the endpoints of the intervals may be determined from the minimum and maximum values of the parameters of the input data on nearby range bins.

b. Select the minimax parameter vector, .theta..sub.mm, from .DELTA..theta. as follows. Let .mu.(.theta., .theta..sub.0, 0) and .sigma.(.theta., .theta..sub.0,0) be the mean and standard deviation in the noise-only case, as calculated from equation (11), of the processor that uses parameter vector .theta. when the true parameter vector is .theta..sub.0. The value of v.sub.s used in the weighting function (9) is

The threshold is set at the desired PFA, assuming that the processor parameters, .theta., are correct, i.e. if .lambda..sub..alpha. is the threshold of the standard unit normal distribution corresponding to PFA=.alpha., then since .mu.(.theta., .theta., 0)=0, the threshold is .tau.(.alpha., .theta.)=.lambda..sub..alpha. .tau.(.theta.,.theta., 0). The actual probability of false alarm is then ##EQU14## where .PHI. is the unit normal distribution. By definition, ##EQU15## Equation (14) may be substituted into equation (15) and the resulting equation may be solved numerically.

Obviously, many modifications and variations of the present invention are possible in light of the above teachings. It is therefore to be understood that within the scope of the appended claims, the invention may be practiced otherwise than as specifically described. ##SPC1##

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