Systems and methods for analyzing waveforms using pulse shape information

1. A method for operating a LiDAR system, comprising:

receiving, by the LiDAR system, a waveform representing light which was reflected off of a surface of at least one object;

generating, by the LiDAR system, a plurality of timestamp values for photon detection events triggered by pulses in the waveform;

generating, by a processor, a count histogram of the timestamp values;

inferring, by the processor, a trials histogram from the count histogram, the trials histogram representing a number of times a photodetector of the LiDAR system was available during reception of the waveform;

generating an estimated range distance from the LiDAR system to the at least one object and an estimated intensity value for a given pulse of the waveform, based on results from analyzing the count histogram and the trials histogram;

determining, by the processor, a position using the estimated range distance from the LiDAR system to the at least one object; and

producing, by the processor, a LiDAR dataset comprising a data point defined by the position and the estimated intensity value.

2. The method according to claim 1 , wherein the estimated intensity value represents an estimate value for a return strength of a pulse.

3. The method according to claim 1 , wherein the estimated intensity value is set equal to a maximum likelihood estimation of pulse intensity given a pulse shape, the count histogram and the trials histogram.

4. The method according to claim 3 , wherein the maximum likelihood estimation of pulse intensity is selected from a plurality of possible intensity values each determined using a linear combination of the count histogram and the trials histogram.

5. The method according to claim 4 , wherein each of the plurality of intensity values is determined in accordance with mathematical equation

λ

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=

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f

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(

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where s represents a span size of at least a portion of the count histogram, f(i, τ=j) represents a known pulse shape of a waveform at bin index i that has a centroid at waveform offset τ, n i represents a trials count at bin i, i represents a location of a bin index in the trials histogram that corresponds to a given pulse, and k i represents a count number of a given pulse detection event at bin index i.

6. The method according to claim 1 , wherein the estimated range distance is set equal to a maximum likelihood estimation of range distance given a plurality of possible intensity values.

7. The method according to claim 6 , wherein the maximum likelihood estimation of range distance is determined by performing comparison operations in which the count histogram is compared with a plurality of computed reference histograms given certain conditions.

8. The method according to claim 7 , wherein each of said comparison operations produces a probability score representing a probability that the timestamp values were caused by given possible values for parameters τ j and λ j .

9. The method according to claim 8 , wherein the probability score is defined by mathematical equation

L

j

(

score

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i

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k

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log

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(

1

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were s represents a span size of at least a portion of the count histogram, f(i, τ=j) represents a known pulse shape of a waveform at time index i that has a centroid at time index τ, n i represents a trials count at bin i, i represents a location of a timestamp value in the trials histogram that corresponds to a given pulse, k i represents a count number of a given pulse detection event, λ represents a given previously computed intensity value λ j , and τ represents a timestamp value which is set to a pre-defined value j associated with the given previously computed intensity value λ j .

10. The method according to claim 1 , further comprising using the LiDAR dataset to control operations of an autonomous vehicle.

11. A system, comprising:

a processor;

a non-transitory computer-readable storage medium comprising programming instructions that are configured to cause the processor to implement a method for operating a LiDAR system, wherein the programming instructions comprise instructions to:

generate a plurality of timestamp values for photon detection events triggered by pulses in a received waveform representing light which was reflected off of a surface of at least one object;

generate a count histogram of the timestamp values;

infer a trials histogram from the count histogram, the trials histogram representing a number of times a photodetector of the LiDAR system was available during reception of the waveform;

generate an estimated range distance from the LiDAR system to the at least one object and an estimated intensity value for a given pulse of the received waveform, based on results from analyzing the count histogram and the trials histogram;

determine a position using the estimated range distance from the LiDAR system to the at least one object; and

produce a LiDAR dataset comprising a data point defined by the position and the estimated intensity value.

12. The system according to claim 11 , wherein the estimated intensity value represents an estimate value for a return strength of a pulse.

13. The system according to claim 11 , wherein the estimated intensity value is set equal to a maximum likelihood estimation of pulse intensity given a pulse shape, the count histogram and the trials histogram.

14. The system according to claim 13 , wherein the maximum likelihood estimation of pulse intensity is selected from a plurality of possible intensity values each determined using a linear combination of the count histogram and the trials histogram.

15. The system according to claim 14 , wherein each of the plurality of intensity values is determined in accordance with mathematical equation

λ

j

=

∑

i

=

0

S

-

1

k

i

∑

i

=

0

S

-

1

(

n

i

-

k

i

2

)

⁢

f

⁡

(

i

,

τ

=

j

)

(

1

)

where s represents a span size of at least a portion of the count histogram, f(i, τ=j) represents a known pulse shape of a waveform at bin index i that has a centroid at waveform offset τ, n i represents a trials count at bin i, i represents a location of a bin index in the trials histogram that corresponds to a given pulse, and k i represents a count number of a given pulse detection event at bin index i.

16. The system according to claim 11 , wherein the estimated range distance is set equal to a maximum likelihood estimation of range distance given a plurality of possible intensity values.

17. The system according to claim 16 , wherein the maximum likelihood estimation of range distance is determined by performing comparison operations in which the count histogram is compared with a plurality of computed reference histograms given certain conditions.

18. The system according to claim 17 , wherein each of said comparison operations produces a probability score representing a probability that the timestamp values were caused by given possible values for parameters τ j and λ j .

19. The system according to claim 18 , wherein the probability score is defined by mathematical equation

L

j

(

score

)

=

∑

i

=

0

s

-

1

k

i

⁢

log

⁡

(

1

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-

λ

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f

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(

i

,

τ

=

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)

)

-

(

n

i

-

k

i

)

⁢

λ

⁢

f

⁡

(

j

,

τ

=

j

)

were s represents a span size of at least a portion of the count histogram, f(i, τ=j) represents a known pulse shape of a waveform at time index i that has a centroid at time index τ, n i represents a trials count at bin i, i represents a location of a timestamp value in the trials histogram that corresponds to a given pulse, k i represents a count number of a given pulse detection event, λ represents a given previously computed intensity value λ j , and τ represents a timestamp value which is set to a pre-defined value j associated with the given previously computed intensity value λ j .

20. The system according to claim 11 , further comprising using the LiDAR dataset to control operations of an autonomous vehicle.