Ladar range rate estimation using pulse frequency shift

1. A method for forming a range rate estimate for a target with a laser detection and ranging system comprising a laser transmitter and an array detector, the method comprising:

transmitting a plurality of laser pulses at a pulse repetition frequency;

forming a one dimensional time series array corresponding to a time record of ladar return photons detected with the array detector;

fitting the time series array with a superposition of a sine and a cosine of an initial value of a tentative frequency;

iteratively fitting the time series array with a superposition of a sine and a cosine of the tentative frequency, and adjusting the tentative frequency until a completion criterion is satisfied at a final value of the tentative frequency; and

calculating the range rate estimate as the ratio of:

a product of the speed of light and a difference between a final value of the tentative frequency and the pulse repetition frequency; and

twice the pulse repetition frequency.

2. The method of claim 1 , wherein iteratively fitting the time series array with a superposition of a sine and a cosine of a tentative frequency comprises:

multiplying the time series array by the cosine of the tentative frequency and integrating the product numerically to calculate a cosine coefficient;

multiplying the time series array by the sine of the tentative frequency and integrating the product numerically to calculate a sine coefficient;

calculating an objective function from the cosine coefficient and the sine coefficient; and

adjusting the tentative frequency to an updated value at which a value of the objective function is increased.

3. The method of claim 2 , wherein the adjusting of the tentative frequency comprises adjusting the tentative frequency using a golden section search.

4. The method of claim 2 , wherein the objective function is equal to the sum of:

the square of the cosine coefficient; and

the square of sine coefficient.

5. The method of claim 2 , wherein the completion criterion is satisfied when the value of the objective function increases by less than a threshold amount during one iteration.

6. The method of claim 5 , wherein the threshold amount is 0.01 percent of the value of the objective function.

7. The method of claim 1 , wherein forming a one dimensional time series array comprises:

for each transmitted laser pulse:

detecting, with an array detector, a plurality of ladar return photons from the laser pulse, each detection producing an electrical pulse;

identifying, for each of the electrical pulses, a bin, of a plurality of time bins corresponding to the laser pulse, within which the electrical pulse was produced; and

forming a one dimensional range histogram array having, for each bin of the plurality of bins, an element with a value equal to the number of electrical pulses produced in the array detector during a time interval corresponding to the bin; and

concatenating:

respective portions of the range histogram arrays; and

a plurality of one dimensional arrays each consisting of a plurality of zeros,

to form the one dimensional time series array, each nonzero element of the time series array being the number of pulses produced in a time interval at a time corresponding to the position of the nonzero element in the time series array.

8. The method of claim 7 , wherein each respective portion of each range histogram array is a contiguous subset of the elements of the range histogram array selected to include a range of elements centered on an element corresponding to an initial estimate of a range to the target.

9. The method of claim 8 , wherein the contiguous subset is selected from a range histogram array by finding a first test subset of bins, having a left boundary satisfying

(mean(Test n )−mean(Background n ))/mean(signal n )<0.05

wherein:

Testn is a contiguous set of k bins, k being an integer greater than 1;

Signaln is a contiguous set of bins beginning immediately to the right of Testn and extending to a peak bin having the largest value in the range histogram array;

Backgroundn is a contiguous set of bins beginning immediately to the left of Testn and extending to the left edge of the range histogram array;

the mean( ) function refers to an average of a set of bins that is the argument of the function; and

left and right refer to earlier and later times, respectively.

10. A ladar system for forming a range rate estimate for a target, the system comprising:

a pulsed laser transmitter configured to transmit a sequence of laser pulses at a pulse repetition frequency;

a camera comprising an array detector; and

a processing circuit,

the camera and the processing circuit being together configured to form a one dimensional time series array corresponding to a time record of ladar return photons,

the processing unit being configured to:

fit the time series array with a superposition of a sine and a cosine of an initial value of a tentative frequency;

iteratively fit the time series array with a superposition of a sine and a cosine of the tentative frequency, and adjust the tentative frequency until a completion criterion is satisfied at a final tentative frequency; and

calculate the range rate estimate as the ratio of:

the product of the speed of light and the difference between a final value of the tentative frequency and the pulse repetition frequency; and

twice the pulse repetition frequency.

11. The system of claim 10 , wherein iteratively fitting the time series array with a superposition of a sine and a cosine of a tentative frequency comprises:

multiplying the time series array by the cosine of the tentative frequency and integrating the product numerically to calculate a cosine coefficient;

multiplying the time series array by the sine of the tentative frequency and integrating the product numerically to calculate a sine coefficient;

calculating an objective function from the cosine coefficient and the sine coefficient; and

adjusting the tentative frequency to an updated value at which a value of the objective function is increased.

12. The system of claim 11 , wherein the adjusting of the tentative frequency comprises adjusting the tentative frequency using a golden section search.

13. The system of claim 11 , wherein the objective function is equal to the sum of:

the square of the cosine coefficient; and

the square of sine coefficient.

14. The system of claim 11 , wherein the completion criterion is satisfied when the value of the objective function increases by less than a threshold amount during one iteration.

15. The system of claim 14 , wherein the threshold amount is 0.01 percent of the value of the objective function.

16. The system of claim 10 , wherein forming a one dimensional time series array comprises:

for each transmitted laser pulse:

detecting, by the array detector, of a plurality of ladar return photons from the laser pulse, each detection producing an electrical pulse;

identifying, by the camera, for each of the electrical pulses, a bin, of a plurality of time bins corresponding to the laser pulse, within which the electrical pulse was produced; and

forming, by the processing circuit, a one dimensional range histogram array having, for each bin of the plurality of bins, an element with a value equal to the number of electrical pulses produced in the array detector during a time interval corresponding to the bin; and

concatenating, by the processing circuit:

respective portions of the range histogram arrays; and

a plurality of one dimensional arrays each consisting of a plurality of zeros,

to form the one dimensional time series array, each nonzero element of the time series array being the number of pulses produced in a time interval at a time corresponding to the position of the nonzero element in the time series array.

17. The system of claim 16 , wherein each respective portion of each range histogram array is a contiguous subset of the elements of the range histogram array selected to include a range of elements centered on an element corresponding to an initial estimate of a range to the target.

18. The system of claim 17 , wherein the contiguous subset is selected from a range histogram array by finding a first test subset of bins, having a left boundary satisfying

(mean(Test n )−mean(Background n ))/mean(signal n )<0.05

wherein:

Testn is a contiguous set of k bins, k being an integer greater than 1;

Signaln is a contiguous set of bins beginning immediately to the right of Testn and extending to a peak bin having the largest value in the range histogram array;

Backgroundn is a contiguous set of bins beginning immediately to the left of Testn and extending to the left edge of the range histogram array;

the mean( ) function refers to an average of a set of bins that is the argument of the function; and

left and right refer to earlier and later times, respectively.