Compact supersonic projectile tracking
A tracking system including: a plurality of acoustic sensors rigidly held apart from each other and from an acoustically reflective surface; a processor configured to: receive spatial relationships between the plurality of acoustic sensors and between the plurality of acoustic sensors and the acoustically reflective surface; receive a plurality of measurement signals; identify: in the plurality of measurement signals, timing of arrival of a supersonic shockwave of a projectile to the respective sensor; and timing of arrival of a reflection of the supersonic shockwave from the acoustically reflective surface to the respective sensor; determine at least a portion of a trajectory of the projectile, using: the timing of arrival of the supersonic shockwave; the timing of arrival of the reflection; the spatial relationship between the plurality of acoustic sensors; and the spatial relationship between sensors and the spatial relationship between sensors and the acoustically reflective surface.
1 . A projectile tracking system comprising:
a plurality of acoustic sensors rigidly held apart from each other and each acoustic sensor of the plurality of acoustic sensors is held apart from an acoustically reflective surface by a respective shortest straight line distance selected so that, for the respective acoustic sensor a time between arrival of a supersonic shockwave of a projectile at the respective acoustic sensor and arrival of a reflection of said supersonic shockwave from said acoustically reflective surface at the respective acoustic sensor is at least a sensing relaxation time of the respective acoustic sensor, said respective shortest straight line distance being at least double said sensing relaxation time multiplied by a speed of sound, the sensing relaxation time defined as a time delay after sensing of a first shockwave at which a sensor is able to detect a second shockwave;
a processor configured to:
receive a spatial relationship between said plurality of acoustic sensors and a spatial relationship between said plurality of acoustic sensors and said acoustically reflective surface;
receive a plurality of measurement signals comprising a measurement signal corresponding to each of said plurality of acoustic sensors;
identify:
in at least one single measurement signal of said plurality of measurement signals, timing of arrival of a supersonic shockwave of a projectile to the respective sensor; and
in said at least one single, timing of arrival of a reflection of said supersonic shockwave from said acoustically reflective surface to the respective sensor;
determine at least a portion of a trajectory of the projectile, using:
said timing of arrival of said supersonic shockwave;
said timing of arrival of said reflection;
said spatial relationship between said plurality of acoustic sensors; and
said spatial relationship between said plurality of acoustic sensors and said acoustically reflective surface.
2 . The system according to claim 1 , wherein said acoustically reflective surface is a target.
3 . The system according to claim 1 , wherein said projectile is a bullet.
4 . The system according to claim 1 , wherein said processor is configured to:
receive a spatial relationship between said plurality of acoustic sensors and an additional acoustically reflective surface positioned away from said plurality of acoustic sensors;
identify, in said at least one single measurement signal, timing of arrival of a second reflection of said supersonic shockwave from said additional acoustically reflective surface to the respective sensor;
determine at least a portion of a trajectory of the projectile, using
said timing of arrival of said second reflection; and
said spatial relationship between said sensors and said additional acoustically reflective surface.
5 . The system according to claim 4 , wherein said plurality of acoustic sensors are each spaced apart from said additional acoustically reflective surface by a distance selected based on a sensing relaxation time of said plurality of acoustic sensors.
6 . The system according to claim 1 , wherein said plurality of acoustic sensors comprises three acoustic sensors and wherein said processor is configured to receive three measurement signals one from each of said three acoustic sensors.
7 . The system according to claim 6 , wherein said sensors are positioned so that, for a range of projectile trajectories, each of said three acoustic sensors senses said supersonic shockwave and said reflection;
wherein said processor is configured, for said range of projectile trajectories to:
identify, in each of said three sensor signals, separately identifiable timing of arrival of said supersonic shockwave and timing of arrival of said reflection in the respective sensor signal;
determine a position at which said projectile intersects with a plane of said acoustically reflective surface to an accuracy of 1 cm.
8 . The projectile tracking system according to claim 7 , wherein said range of trajectories includes projectiles on trajectories which hit said acoustically reflective surface.
9 . The system according to claim 8 , wherein said range of projectile trajectories comprises trajectories where said projectile passes through a plane of said acoustically reflective surface at a distance of less than 50 cm away from said acoustically reflective surface.
10 . The system according to claim 1 , wherein said plurality of acoustic sensors are hosted by a tracking device having an elongate body with a maximal extent of 30 cm perpendicular to a central longitudinal axis of said elongate device housing.
11 . The system according to claim 10 , wherein said maximal extent perpendicular to said central longitudinal axis of said elongate body is 10 cm.
12 . The system according to claim 11 , wherein a maximal extent of said elongate body is 50 cm.
13 . A method of supersonic projectile tracking comprising:
receiving a plurality of measurement signals from a plurality of acoustic sensors rigidly held apart from each other, each acoustic sensor being held apart from an acoustically reflective surface by a respective shortest straight-line distance selected so that, for the respective acoustic sensor, a time between arrival of a supersonic shockwave of a projectile at the respective acoustic sensor and arrival of a reflection of said supersonic shockwave from said acoustically reflective surface at the respective acoustic sensor is at least a sensing relaxation time of the respective acoustic sensor, said respective shortest straight-line distance being at least double said sensing relaxation time multiplied by a speed of sound, the sensing relaxation time defined as a time delay after sensing of a first shockwave at which a sensor is able to detect a second shockwave;
receiving a spatial relationship between said plurality of acoustic sensors and a spatial relationship between said plurality of acoustic sensors and said acoustically reflective surface;
identifying:
in at least one single measurement signal said plurality of measurement signals, timing of arrival of a supersonic shockwave of a projectile to the respective sensor; and
in said at least one single measurement signal, timing of arrival of a reflection of said supersonic shockwave from said acoustically reflective surface to the respective sensor;
determining at least a portion of a trajectory of the projectile, using:
said timing of arrival of said supersonic shockwave;
said timing of arrival of said reflection;
said known spatial relationship between said plurality of acoustic sensors; and
said spatial relationship between said plurality of acoustic sensors and said acoustically reflective surface.
14 . The method according to claim 13 , wherein said identifying includes identifying timing of a change in pressure above a pressure threshold change.
15 . The method according to claim 13 , wherein said identifying includes identifying timing of a differential of pressure above a differential threshold.
16 . The method according to claim 14 , wherein said identifying includes identifying timing of a second differential of pressure above a second differential threshold.
17 . The projectile tracking system according to claim 1 comprising:
a tracking device hosting the plurality of acoustic sensors, which comprise at least three acoustic sensors, wherein the tracking device rigidly holds the plurality of acoustic sensors spaced apart from each other;
a stand configured to rigidly hold said tracking device and the acoustically reflective surface so that said plurality of acoustic sensors are each separated by a respective shortest straight, line distance selected so that, for each respective acoustic sensor, a time delay between arrival of a projectile supersonic shockwave at the respective acoustic sensor and arrival of a reflection of said projectile supersonic shockwave from said acoustically reflective surface at the respective acoustic sensor is at least the sensing relaxation time of the respective acoustic sensor, said respective shortest straight line distance being at least double said sensing relaxation time multiplied by a speed of sound.
18 . The projectile tracking system according to claim 1 , wherein the processor is configured to determine from said timing of arrival of said supersonic shockwave, said timing of arrival of said reflection, said spatial relationship between said plurality of acoustic sensors, and said spatial relationship between said plurality of acoustic sensors and said acoustically reflective surface, a position at which said projectile intersects with a plane of said acoustically reflective surface.
19 . The projectile tracking system according to claim 18 , wherein the plane of the acoustically reflective surface is orientated generally extending vertically.
20 . The method according to claim 13 , wherein said determining said at least a portion of said trajectory of the projectile comprises determining from said timing of arrival of said supersonic shockwave, said timing of arrival of said reflection, said known spatial relationship between said plurality of acoustic sensors, and said spatial relationship between said plurality of acoustic sensors and said acoustically reflective surface, a position at which said projectile intersects with a plane of said acoustically reflective surface.