Likelihood function decomposition for multistatic tracking and field stabilization

An alternating directions method is presented for joint maximum a posteriori estimation of target track and sensor field using bistatic range data. The algorithm cycles over two sub-algorithms: one improves the target state estimate conditioned on sensor field state, and the other improves the sensor field state estimate conditioned on target state. Nonlinearities in the sub-algorithms are mitigated by decomposing their likelihood functions using integral representations. The kernels of these integrals are linear-Gaussian densities in the states to be estimated, a fact that facilitates the use of missing data methods. The resulting sub-algorithms are equivalent to linear-Gaussian Kalman smoothers. The alternating directions algorithm is guaranteed to converge to (at least) a local maximum of the joint target-field likelihood function.