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This paper proposes a Poisson multi-Bernoulli mixture (PMBM) filter on the space of sets of tree trajectories for multiple target tracking with spawning targets. A tree trajectory contains all trajectory information of a target and its descendants, which appear due to the spawning process. Each tree contains a set of branches, where each branch has trajectory information of a target or one of the descendants and its genealogy. For the standard dynamic and measurement models with multi-Bernoulli spawning, the posterior is a PMBM density, with each Bernoulli having information on a potential tree trajectory. To enable a computationally efficient implementation, we derive an approximate PMBM filter in which each Bernoulli tree trajectory has multi-Bernoulli branches, obtained by minimising the Kullback-Leibler divergence. The resulting filter improves tracking performance of state-of-the-art algorithms in a simulated scenario. [ABSTRACT FROM AUTHOR]

This paper derives the optimal Bayesian processing of an out-of-sequence (OOS) set of measurements in continuous-time for multiple target tracking. We consider a multi-target system modelled in continuous time that is discretised at the time steps when we receive the measurements, which are distributed according to the standard point target model. All information about this system at the sampled time steps is provided by the posterior density on the set of all trajectories. This density can be computed via the continuous-discrete trajectory Poisson multi-Bernoulli mixture (TPMBM) filter. When we receive an OOS measurement, the optimal Bayesian processing performs a retrodiction step that adds trajectory information at the OOS measurement time stamp followed by an update step. After the OOS measurement update, the posterior remains in TPMBM form. We also provide a computationally lighter alternative based on a trajectory Poisson multi-Bernoulli filter. The effectiveness of the two approaches to handle OOS measurements is evaluated via simulations. [ABSTRACT FROM AUTHOR]

We propose a solution of the multiple target tracking (MTT) problem based on sets of trajectories and the random finite set framework. A full Bayesian approach to MTT should characterize the distribution of the trajectories given the measurements, as it contains all information about the trajectories. We attain this by considering multiobject density functions in which objects are trajectories. For the standard tracking models, we also describe a conjugate family of multitrajectory density functions. [ABSTRACT FROM AUTHOR]

This manuscript experimentally validates a thin-film polymer and multimode fiber optic interaction-based low-cost optical fiber displacement sensor. The sensing setup is operated by deflecting a commercially Mylar Ⓡ polymer film using multimode optical fiber. The sensor exhibits a higher sensitivity of 24nm/ $\mu \text{m}$ and resolution of 41.6nm. The sensor’s analyses also demonstrate good polynomial approximation, with a maximal adjusted square of $\text {R}={0.9801}$ , and high stability, in which minimal power (0.4dB-Hour) and wavelength (< 2nm-Hour) variations are observed. Moreover, thermal experiments prove that the sensor has lower temperature traits ($0.05~\mu \text{m}/^{\circ }\text{C}$), and this parameter can be distinguished considering the wavelength shifting direction. The simplicity of the scheme, as well as the cost of the elements involved, make this technique a reliable alternative to detect micro-displacements. [ABSTRACT FROM AUTHOR]

In this letter, we consider Gaussian approximations of the optimal importance density in sequential importance sampling for nonlinear, non-Gaussian state-space models. The proposed method is based on generalized statistical linear regression and posterior linearization using conditional expectations. Simulation results show that the method outperforms the compared methods in terms of the effective sample size and provides a better local approximation of the optimal importance density. [ABSTRACT FROM AUTHOR]

This paper presents the probability hypothesis density filter (PHD) and the cardinality PHD (CPHD) filter for sets of trajectories, which are referred to as the trajectory PHD (TPHD) and trajectory CPHD (TCPHD) filters. Contrary to the PHD/CPHD filters, the TPHD/TCPHD filters are able to produce trajectory estimates from first principles. The TPHD filter is derived by recursively obtaining the best Poisson multitrajectory density approximation to the posterior density over the alive trajectories by minimising the Kullback-Leibler divergence. The TCPHD is derived in the same way but propagating an independent identically distributed (IID) cluster multitrajectory density approximation. We also propose the Gaussian mixture implementations of the TPHD and TCPHD recursions, the Gaussian mixture TPHD (GMTPHD) and the Gaussian mixture TCPHD (GMTCPHD), and the $L$ -scan computationally efficient implementations, which only update the density of the trajectory states of the last $L$ time steps. [ABSTRACT FROM AUTHOR]

This paper proposes a novel algorithm for target tracking with direction-of-arrival measurements, modeled by von Mises–Fisher distributions. The algorithm makes use of the assumed density framework with Gaussian distributions, in which the posterior probability density of the target state is approximated by a Gaussian density. A key component of this algorithm is that the proposed Bayesian model of the measurements takes into account the specific characteristics of angular measurements by using a von Mises–Fisher distribution. We propose two implementations of the algorithm, one based on first-order Taylor series expansion and another one based on sigma points. Simulation results show the benefits of the proposed algorithms in relation to other Gaussian filters in the literature. [ABSTRACT FROM AUTHOR]

This paper proposes the posterior linearization backward simultaneous localization and mapping (PLB-SLAM) algorithm for batch SLAM problems. Based on motion and landmark measurements, we aim to estimate the trajectory of the mobile agent and the landmark positions using an approximate Rao-Blackwellized Monte Carlo solution, as in FastSLAM. PLB-SLAM improves the accuracy of current FastSLAM solutions due to two key aspects: smoothing of the trajectory distribution via backward trajectory simulation and the use of iterated posterior linearization to obtain Gaussian approximations of the distribution of the landmarks. PLB-SLAM is assessed via numerical simulations and real experiments for indoor localization and mapping of radio beacons using a smartphone, Bluetooth beacons, and Wi-Fi access points. [ABSTRACT FROM AUTHOR]

This letter proposes a new algorithm for Gaussian process classification based on posterior linearization (PL). In PL, a Gaussian approximation to the posterior density is obtained iteratively using the best possible linearization of the conditional mean of the labels and accounting for the linearization error. PL has some theoretical advantages over expectation propagation (EP): all calculated covariance matrices are positive definite and there is a local convergence theorem. In experimental data, PL has better performance than EP with the noisy threshold likelihood and the parallel implementation of the algorithms. [ABSTRACT FROM AUTHOR]