Performance of shockwave-based shooter localization under model misspecification

This paper considers the estimation of shooter locations using a sensor network where each sensor measures the time difference between receptions of a firearm´s muzzle blast and a bullet´s shockwave. This recently proposed approach has the advantages of reduced hardware complexity and not requiring time synchronization between sensors. The disadvantages are increased computational complexity and a requirement to know the bullet´s velocity at all points along the trajectory. This paper proposes to eliminate these disadvantages by intentionally adopting an incorrect model that assumes a constant bullet velocity. The model misspecification naturally induces bias in subsequent maximum likelihood estimates (MLEs). We explore the performance impact of the model misspecification through analytical derivation of the bias and variance of the pseudo MLE. The analytic results are applied to several realistic firearm models and corroborated with simulations.