Multiple target tracking based on homogeneous symmetric transformation of measurements

Symmetrical measurement equation, generated from homogeneous symmetric functions, has been proposed in this paper for tracking multiple targets. The observability condition, resultant measurement noise and its covariance for any number of particles arising from proposed symmetric transformation of measurement have been derived. The derived expression of resultant noise covariance is verified using Monte Carlo run. As a case study, three particles in motion are considered where positions and velocities of the particles are estimated using extended Kalman filter. From the simulation results it is found that the targetsʼ identity is lost during estimation. The target tracks have been labeled by minimizing the sum of square errors over the permutation of states. The performance of estimator in terms of root mean square error is compared with the two types of symmetric transformation of measurements, namely sum of power and sum of product form, existing in literature. Results are also compared with optimal state estimator which assumes that the correct association between measurements and targets is known. From simulation it is observed that RMSEs of position and velocity are small in homogeneous form compared to those obtained from sum of power and product form.