For automotive radar-based extended object tracking, this paper proposes a new approach, which jointly estimates the kinematic state and the extension of a vehicle. The vehicle’s shape is described as a rectangle with its vertices treated as the extension state. “Having a rectangular shape” is described as a quadratic equality constraint on the state. To deal with the challenging problem of modeling measurement (scattering center) distribution over a vehicle, we partition the rectangular area into multiple regions and assume that in each region the scattering centers have a simple distribution. An approach is proposed to associate measurements with these regions. Given an association, the target state is estimated in a linear minimum mean-square-error framework with the shape constraint treated as a pseudo measurement. The probabilities for these regions to generate measurements are updated online. The estimate is then projected into the constraint space. The effectiveness of the proposed approach is illustrated using both simulated and real data.

Extended object tracking (EOT) has attracted much attention in recent years. EOT approaches always assume that scattering centers are distributed on the boundary of or uniformly over the object extension. However, a practical distribution is complex and scattering centers can be concentrated on regions of the extension. To describe this phenomenon, a key-point-based model is proposed. It partitions a rectangular object extension into four regions that intersect at a key point. Over different regions scattering centers are assumed uniformly distributed with different densities related to the area of the regions. Thus, the overall complex distribution of regionally concentrated measurements can be described by combining the four local simple ones. The variation of the key point’s position on the object can affect the four regions in size and shape, and thus can characterize different overall distributions. Estimation of the extension amounts to that of the key point’s kinematic state, the object orientation, and the length and width of each region. Based on the proposed model, measurements are projected into two directions along with and perpendicular to the object orientation approximated by its prediction, respectively. Variances of the projected measurements in the two directions are derived to be Gamma distributed. Using the conjugate property of a Gamma and an inverse Gamma distributions, an analytical recursive estimator of the kinematic state and the length and width variables is obtained. The effectiveness of the proposed approach is illustrated using both simulated and real data.

This paper presents a new approach, named extension-deformation approach (EDA), to extended object tracking (EOT). It models the extension of an object as being deformed from a simple reference extension by moving several control points. Then, a complex object extension can be characterized by these control points given the reference extension. This greatly simplifies the problem of shape description. Thus, modeling and estimation of the extension reduce to those of the control points, which are treated as state components of the extension. A noiseless measurement is a point on the deformed extension that corresponds to a source on the reference extension. Once the source is given, the corresponding measurement model is linear in the state, making state estimation simple and direct. However, the source is unknown and hard to estimate accurately. To handle this problem, a multiple-source approach to kinematic state and extension estimation is proposed. Overall the proposed approach is simple and it can effectively track an object with an extension that can be non-star-convex. Simulation results are given to illustrate the effectiveness of the proposed approach.

For nonlinear estimation, the true joint distribution of the estimand and its nonlinear measurement corrupted by noises is very complex. The multiple conversion approach (MCA) matches the truth using a predesigned set of hypothesized non-Gaussian distributions. Each distribution corresponds to a non-linear conversion used by an uncorrelated conversion based filter (UCF), which is a linear minimum mean square error estimator using the measurement augmented by its nonlinear conversion. For dynamic problems, the predesigned set may not match the truth sufficiently because the true complex distribution varies over time. To solve this problem, we first prove that the estimation performance of the MCA can be improved by extending the set using a new distribution, if the estimator corresponding to it outperforms the MCA using the original set. This means that the underlying overall distribution given by the extended set matches the truth better. However, obtaining such an estimator is difficult. This paper proves that a UCF based estimator can meet the above requirement. The augmenting conversion in this UCF is the original MCA estimator, which is a nonlinear conversion of the original measurement. The conversion is then optimized and also simplified, and an optimized conversion (OC) and its simplification with analytical forms are obtained, respectively. For dynamic problems, two interacting multiple conversion algorithms using the OC and its simplification to extend the original set are proposed. The effectiveness of the proposed approach and algorithms is demonstrated by simulation results compared with other nonlinear filters for target tracking.

UAV swarms possess unique advantages in performing various tasks and have been successfully applied across multiple scenarios. Accurate navigation serves as the foundation and prerequisite for executing these tasks. Unlike single UAV localization, swarms enable the sharing and propagation of precise positioning information, which enhances overall swarm localization accuracy but also introduces the issue of uncertainty propagation. To address this challenge, this paper proposes an integrated navigation and positioning method that models, propagates, and mitigates uncertainties. To tackle the issue of uncertainty in information quality caused by outliers in external correction data, a robust integrated navigation method for nonlinear systems is derived based on a normal gamma distribution model. Considering uncertainty propagation, a statistical linearization model for nonlinear systems is developed. Building upon this model, an augmented measurement nonlinear least squares positioning method is applied, achieving further improvements in localization accuracy. Simulation experiments demonstrate that the proposed method, which thoroughly accounts for the effects of multiple uncertainties, can achieve robust tracking and provide relatively accurate positioning results.