In this paper, a novel tensor operator is introduced that directly solves the prediction step of the Bayes recursion for multi-dimensional discretized probability densities in Canonical Polyadic Decomposition form. The proposed operator combines computational efficiency with the possibility for non-linear and non-Gaussian scenarios. Based on the Continuous White Noise Velocity model, it enables a broad range of application in target tracking.

Distributed Accumulated State Density (DASD) filtering is an effective strategy for optimal multi-sensor fusion. However, the fusion of Accumulated State Densitys (ASDs) with unequal window lengths, as occurs in typical multi-sensor multiobject applications, has not yet been covered in the literature. This paper aims to fill that gap by exploring various approaches, which range from ASD cutting to more sophisticated ASD adaptation and ASD zero-padding. In consequence, we arrive at the optimal ASD-Information Matrix Fusion or ASD-Tracklet Fusion, respectively. Both provide the optimal and full ASD result with full-rate transmission of standard (single state) densities only, thus reducing the communication load compared to a corresponding transmission of full ASDs. These methods perform particularly well in practical scenarios where the models are not perfectly adapted. All approaches are discussed theoretically and are thoroughly evaluated in simulation.

This paper focuses on state prediction for stochastic dynamic models with linear dynamics, emphasizing a recently proposed efficient and robust Lagrangian approach for solving the Chapman–Kolmogorov equation. In contrast to the standard Eulerian perspective, the Lagrangian method separates the solution into two sequential steps: advection and diffusion. Advection is handled by moving a carefully designed grid, while diffusion is addressed using the convolution theorem. This approach significantly reduces computational complexity while preserving the same accuracy. In this paper, we propose formulating diffusion as a continuous-time process, leading to a partial differential equation (PDE). Various methods for solving this PDE are presented and compared within a unified framework, along with evaluations of their properties and example implementations. We demonstrate that the continuous formulation can yield substantial reductions in computational complexity with only marginal loss in accuracy.

This paper presents the application of a novel target tracking technique employing tensor decompositions for discretizing the target state space. The time evolution of the conditional probability density is realized by a Fokker-Planck equation solver and the measurement update, as usual, by applying Bayes’ rule. The method is applicable to non-Gaussian and non-linear system equations and enables the treatment of complex non-Gaussian target state densities. In addition, the efficient tensor decomposition scheme, in principle, allows for high-dimensional target states. The new tracking filter is applied to the problem of tracking an agile air target using bearing measurements from distributed acoustic and electromagnetic array sensors based on real data. It is shown that the new filter is able to initiate and maintain the target track with localization errors comparable to those of a standard particle filter.

The prediction step is a crucial element of the Bayesian recursion for target tracking and state estimation in general. Discrete representations of the probability density function (pdf) can deal with non-linear models and nonGaussian noise, however, the prediction step is challenging to solve on classical computers. In this paper, a novel concept of quantum simulation to solve the application of a continuous noise motion model to a pdf is presented. The pdf is prepared as the squared amplitudes for the basis states spanned by the number of used qubits. The number of required qubits grows linearly in the number of time steps to simulate in a prediction phase. One step performs a single Brownian motion, which is used to generate the diffusion of the Wiener increments. A drift function can be implemented based on a separate register, which holds the pdf on the velocity information for an adequate discretization. The approach will be visualized in terms of quantum circuits and evaluated based on a quantum simulator.

In extended object tracking, random matrices are commonly used to filter the mean and covariance matrix from measurement data. However, the relation from mean and covariance matrix to the extension parameters can become challenging when a lidar sensor is used. To address this, we propose virtual measurement models to estimate those parameters iteratively by adapting them, until the statistical moments of the measurements they would cause, match the random matrix result. While previous work has focused on 2D shapes, this paper extends the methodology to encompass 3D shapes such as cones, ellipsoids and rectangular cuboids. Additionally, we introduce a classification method based on Chamfer distances for identifying the best-fitting shape when the object’s shape is unknown. Our approach is evaluated through simulation studies and with real lidar data from maritime scenarios. The results indicate that a cone is the best representation for sailing boats, while ellipsoids are optimal for motorboats.

The increasing advances in Unmanned Systems are transforming the type of threats traditional defence systems are designed to tackle. One significant advancement is in artificial intelligence capability which allows a group of agents to perform complex collective behaviors. As consequence, providing defence systems with threat intelligence capability is becoming a necessity, where identifying collective behaviours and coordinated targets can significantly increase the effectiveness of the system. In this work, we propose a probabilistic approach to identify certain types of coordinated targets. A scoring function that utilizes accumulated state densities (ASDs) over a sliding time window is proposed to compute the likelihood of a pair of targets being coordinated. A simulation scenario including different types of coordination is used to test the performance of this proposed method.

Random matrices are used to filter the center of gravity (CoG) and the covariance matrix of measurements. However, these quantities do not always correspond directly to the position and the extent of the object, e.g. when a lidar sensor is used.In this paper, we propose a Gaussian processes regression model (GPRM) to predict the position and extension of the object from the filtered CoG and covariance matrix of the measurements. Training data for the GPRM are generated by a sampling method and a virtual measurement model (VMM). The VMM is a function that generates artificial measurements using ray tracing and allows us to obtain the CoG and covariance matrix that any object would cause. This enables the GPRM to be trained without real data but still be applied to real data due to the precise modeling in the VMM. The results show an accurate extension estimation as long as the reality behaves like the modeling and e.g. lidar measurements only occur on the side facing the sensor.

Non-linear filtering arises in many sensor applications such as for instance robotics, military reconnaissance, advanced driver assistance systems and other safety and security data processing algorithms. Since a closed-form of the Bayesian estimation approach is intractable in general, approximative methods have to be applied. Kalman or particle based approaches have the drawback of either a Gaussian approximation or a curse of dimensionality which both leads to a reduction in the performance in challenging scenarios. An approach to overcome this situation is state estimation using decomposed tensors. In this paper, a novel method to compute a non-linear likelihood function in Canonical Polyadic Decomposition form is presented, which avoids the full expansion of the discretized state space for each measurement. An exemplary application in a radar scenario is presented.

Gaussian mixtures (GM) provide a flexible and numerically robust means for the treatment of nonlinearities as well as for the integration of context knowledge into target tracking algorithms. Contextual information lead to constraints on the target state which can be incorporated in the time prediction step of a tracking filter (model of the target dynamics) as well as in the measurement update step in terms of a constraint likelihood function. In this paper, we present examples for each possibility: road-map assisted target tracking and integration of terrain map data for target localization. The algorithms are applied to the problem of airborne passive emitter localization and demonstrate enhanced tracking and localization precision for moving and for stationary ground based emitters.

With the ubiquity of information distributed in networks, performing recursive Bayesian estimation using distributed calculations is becoming more and more important. There are a wide variety of algorithms catering to different applications and requiring different degrees of knowledge about the other nodes involved. One recently developed algorithm is the distributed Kalman filter (DKF), which assumes that all knowledge about the measurements, except the measurements themselves, are known to all nodes. If this condition is met, the DKF allows deriving the optimal estimate if all information is combined in one node at an arbitrary time step. In this paper, we present an information form of the distributed Kalman filter (IDKF) that allows the use of explicit system inputs at the individual nodes while still yielding the same results as a centralized Kalman filter.