Systems and methods for determining shooter locations with weak muzzle detection
Systems and methods for locating the shooter of supersonic projectiles are described. The system uses at least five, preferably seven, spaced acoustic sensors. Sensor signals are detected for shockwaves and muzzle blast, wherein muzzle blast detection can be either incomplete coming from less than 4 sensor channels, or inconclusive due to lack of signal strength. Shooter range can be determined by an iterative computation and/or a genetic algorithm by minimizing a cost function that includes timing information from both shockwave and muzzle signal channels. Disambiguation is significantly improved over shockwave-only measurements.
1. A method for determining an unambiguous projectile trajectory using an array of spaced acoustic sensors when a shockwave associated with a projectile is detected by at least five of the sensors but a muzzle blast associated with the projectile is detected by fewer than four of the sensors, comprising:
obtaining four or more shockwave TDOA measurements from the sensors detecting the shockwave, wherein the shockwave TDOA measurements are insufficient to compute the unambiguous projectile trajectory;
obtaining fewer than three muzzle blast TDOA measurements from the sensors detecting the muzzle blast; and
iteratively computing solutions to a ballistic model using the shockwave TDOA measurements and the muzzle blast TDOA measurements to obtain the unambiguous projectile trajectory.
2. The method of claim 1 , wherein one or two muzzle blast TDOA measurements are obtained from the sensors detecting the muzzle blast.
3. The method of claim 2 , wherein the unambiguous projectile trajectory is computed using a genetic algorithm.
4. The method of claim 3 , wherein performing the genetic algorithm comprises using a predefined number of generations with an initial population that includes a predetermined number of individuals, wherein each individual represented by a 4-tupel which includes shooter azimuth, shooter elevation, missed azimuth and missed elevation.
5. The method of claim 4 , wherein residuals are computed for the individuals in each generation, said residuals including a least-square fit of a combination of the shockwave TDOA measurements and the muzzle blast TDOA measurements.
6. The method of claim 5 , wherein if a ratio of the solution having the smallest residual and its ambiguous alternate solution is greater than a predefined value, designating the solution having the smallest computed residual as the unambiguous projectile trajectory.
7. The method of claim 6 , wherein performing the genetic algorithm comprises applying crossover and mutation operators to the initial population in a generation.
8. The method of claim 7 , wherein applying the crossover operator includes exchanging at least one of missed azimuth and missed elevation between two individuals from the population in a generation.
9. The method of claim 7 , wherein applying the crossover operator includes exchanging at least one of shooter azimuth and trajectory azimuth between two individuals from the population in a generation.
10. The method of claim 7 , wherein the mutation operator comprises field-mutation, incremental mutation, flip-mutation and no mutation.
11. The method of claim 10 , wherein the field-mutation operator replaces a value of the 4-tupel with a randomly selected value.
12. The method of claim 10 , wherein the incremental mutation operator induces a small mutation in all fields of the 4-tupel.
13. The method of claim 10 , wherein the flip-mutation operator changes the solution in a generation to its ambiguous alternate solution in the generation.
14. The method of claim 10 , wherein the no-mutation operator leaves the individuals in a generation unaltered.
15. The method of claim 1 , wherein iteratively computing solutions to a ballistic model is based at least in part on a value of a residual for the TDOA measurements obtained from the sensors detecting the shockwave and from the sensors detecting the muzzle blast.
16. The method of claim 15 , wherein the residual is a function of the differences between the calculated and measured TDOA measurements.