Future cellular networks that utilize millimeter wave signals provide new opportunities in positioning and situational awareness. Large bandwidths combined with large antenna arrays provide unparalleled delay and angle resolution, allowing high accuracy localization but also building up a map of the environment. Even the most basic filter intended for simultaneous localization and mapping exhibits high computational overhead since the methods rely on sigma point or particle-based approximations. In this paper, a first order Taylor series based Gaussian approximation of the filtering distribution is used and it is demonstrated that the developed extended Kalman probability hypothesis density filter is computationally very efficient. In addition, the results imply that efficiency does not come with the expense of estimation accuracy since the method nearly achieves the position error bound.
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