PRIMEX (PRIME-based Graph Encoding and Extraction for Information Fusion) is a novel framework designed to enhance distributed information fusion while minimizing communication overhead and computational complexity. Traditional information graph (IG)-based approaches require frequent synchronization and large-scale graph updates, leading to significant communication demands. PRIMEX overcomes these challenges by encoding information pedigree of state estimates as products of distinct prime numbers, allowing fusion to be performed using lightweight arithmetic operations such as greatest common divisor (GCD) for redundancy removal and least common multiple (LCM) for data integration. This eliminates the need for transmitting complex graph structures and instead leverages prime factorization-based queries to efficiently identify shared information, significantly improving scalability. PRIMEX is particularly well-suited for edge computing environments and decentralized systems, where reducing communication, computation, and memory overhead is crucial. By supporting federated learning principles, PRIMEX enhances system adaptability while preserving data privacy, making it a practical solution for scalable, distributed information fusion in applications such as autonomous systems, multi-agent networks, and large-scale sensing platforms.

In a realistic environment, where the target may be missed and false-alarms may be detected, it is prudent to capture such phenomena in the tracking algorithm. Two methods are considered: the maximum likelihood probabilistic data association (ML-PDA) algorithm and the maximum likelihood probabilistic multi-hypothesis tracker (ML-PMHT). In this paper we compare the ML-PDA and ML-PMHT based on their Cramer-Rao lower bounds (CRLBs), the key difference being the form of the scalar information reduction factor (IRF). The IRF is presented for ML-PMHT in a new form that makes it more computationally tractable and also easier to directly compare with that of the ML-PDA.

This paper deals with the identification of the stochastic Ornstein-Uhlenbeck (OU) process error model, which is characterized by an inverse time constant, and the unknown variances of the process and observation noises. Although the availability of the explicit expression of the log-likelihood function allows one to obtain the maximum likelihood estimator (MLE), this entails evaluating the nontrivial gradient and also often struggles with local optima. To address these limitations, we put forth a sample-efficient global optimization approach based on the Bayesian optimization (BO) framework, which relies on a Gaussian process (GP) surrogate model for the objective function that effectively balances exploration and exploitation to select the query points. Specifically, each evaluation of the objective is implemented efficiently through the Kalman filter (KF) recursion. Comprehensive experiments on various parameter scenarios and sampling intervals corroborate that BO-based estimator consistently outperforms MLE implemented by the steady-state KF approximation and the expectation-maximization algorithm (whose derivation is a side contribution) in terms of root meansquare error (RMSE) and statistical consistency, confirming the effectiveness and robustness of the$\mathbf{B O}$for identification of the stochastic OU process. Notably, the RMSE values produced by the BO-based estimator are smaller than the classical CramérRao lower bound, especially for the inverse time constant, estimating which has been a long-standing challenge. This seemingly counterintuitive result can be explained by the data-driven prior for the learning parameters indirectly injected by BO through the GP prior over the objective function.

The Interacting Multiple Model (IMM) estimator is well accepted as the best algorithm for tracking maneuvering targets, when the computational cost is considered. The IMM estimator includes a model-conditioned estimator for each kinematic model and the switching between modes or models is assumed to be a finite state Markov chain. The two-model configuration of the IMM estimator, the most commonly used version, typically includes either two nearly constant velocity (NCV) motion models or one NCV model and one nearly constant acceleration (NCA) model. In this paper, the design of these two configurations of the IMM estimator is considered. In this case, design refers to the selection of the motion models (i.e., NCV or NCA) and the corresponding process noise variances. The design methods are first considered for single coordinate tracking with measurements of position, and simulation results are given to illustrate the effectiveness of the design methods. Then, the design methods are applied to radar tracking, and simulation results are given to demonstrate the effectiveness of the design methods.

This paper applies Maximum Likelihood Estimation (MLE) to the identification of a stochastic error model of a gyroscope. The error model used for illustration features an Ornstein-Uhlenbeck process with an unknown time constant driven by a process noise with unknown variance, and a white measurement noise also with unknown variance. As the setup of MLE, the likelihood function ($L F)$ is derived in the steady-state Kalman filter framework and is defined in reference to the parameters of the Kalman filter gain and innovation variance. The resulting log-likelihood function (LLF) is a quadratic function of the measurements, facilitating the evaluation of the Cramér-Rao Lower Bound (CRLB) and makes it possible to confirm the statistical efficiency, i.e., optimality, of the ML estimator presented in this paper.

Electro-optical/Infrared (EO/IR) camera systems are commonly used in target detection and tracking applications. Such camera systems typically comprise a suite of sensors such as narrow/wide Field of View (FOV) cameras that provide target-originated angular measurements. To estimate the target position in Cartesian space, existing techniques in literature employ the non-linear measurement mapping from the Focal Plane Array (FPA) to azimuth and elevation space. A common assumption made in using this conversion is that azimuth and elevation measurement errors have the same standard deviation, are uncorrelated and are uniform across the camera’s FOV. This paper presents an approach to derive the azimuth and elevation statistics including the cross-correlation of their errors. This approach converts the raw target measurements and their covariance in the image space (FPA) to the angular space for subsequent use in Cartesian state filtering. This conversion has been validated to be unbiased and consistent, and results show that the Line of Sight (LOS) angle error variances and their correlations are in fact variable, with magnitudes dependent on the target’s location in the FPA. The correct LOS angle covariance matrices should be used in Cartesian state estimation and fusion rather than the assumed constant angle variances and uncorrelated errors between the azimuth and elevation.

In this paper, we develop an approach for measurement-to-track association (M2TA) in the presence of (unknown) camera panning and zooming from drone-captured video. Standard M2TA methods assume that the target motion can be used to predict the “measurement association regions” for the bounding boxes. However, if there is a sudden state change due to camera shift (panning) and zooming, it will lead to incorrect associations and poor tracking results. To solve this, the zoom ratio and panning in 2D coordinates are used to describe the camera motion parameters in each frame. The estimated parameters are obtained by a grid search combined with global assignment or directly solved using the linear least squares method, which is also combined iteratively with assignment. The goal is to achieve correct M2TA by adjusting the predicted measurements using the estimated camera parameters. These “improved” predictions can also be used to update the target state with filtering algorithms. Frames with panning or/and zooming from real data are used to illustrate the effectiveness of the proposed methods and compared with the validation gate method based on inflated covariances.

The problem addressed in this paper is the tracking a maneuvering target in a distributed sensor network using a real-world-motivated fusion configuration. The local node SL receives a track from the remote node SR generated by its Interacting Multiple Model (IMM) estimator, and the “inside information” such as motion models, mode probabilities and mode-conditioned estimates of the remote track is unknown. The local node SL has its own measurements which need to be fused with the remote IMM track. This problem can be solved using an existing technique with the following steps: 1) generate a SL track based on its own measurements; 2) perform Track-to-Track Fusion (T2TF) on SR and SL tracks. This paper will develop an alternative approach to fuse the remote IMM track and the local measurements directly. We called it the IMM Cumulated information Fusion (IMM-CFusion). The IMM-CFusion estimates the cumulated information of the local SLmeasurements with multiple models, and then fuses this cumulated information with the remote IMM track state. The IMM-CFusion shows better performance than the T2TF approach in a test case.

It has been shown in previous works that the trajectory of a thrusting/ballistic object in three-dimensional space is observable with two-dimensional measurements from a stationary passive sensor. The measurements can either start from the launch point or start in flight, i.e., with delayed acquisition. The observability of the target trajectory was investigated by testing the invertibility of the Fisher Information Matrix (FIM) numerically. This work discusses the observability of the trajectory via the uniqueness of the target state vector for a certain sequence of 2-d angle-only measurements (azimuth and elevation angles) from a single fixed passive sensor. The discussion starts with polynomial motion from which the results are extended to nonlinear thrusting/ballistic motion. Two cases: (i) known thrust and drag coefficient, (ii) unknown thrust and drag coefficient are considered. The gravity acceleration is shown to be the crucial part that guarantees the observability in all the cases.

This paper considers the problem of target tracking using an asynchronous multistatic system with unknown transmitter positions. In such a system, the receiver is considered as the own sensor to perform passive tracking. It listens to the signals from at least two non-cooperative transmitters via direct and indirect (bouncing from targets) paths. The transmitters and targets are then tracked based on the measured bearings and the bistatic ranges (derived from the TDOA of the direct and indirect path signals). Since the transmitter positions are unknown, they have to be estimated, and their estimates will contain errors. To cope with these errors, we develop an iterated least squares estimator with covariance inflation (ILS-CI) for track initiation, and apply the covariance inflation filter (CIF) for track update. Four approaches, namely the optimal, simple, covariance inflation (CI) and combined approaches, with different strategies in track initiation and track update, are proposed to solve this tracking problem. Their performances are evaluated through simulation tests.

We consider the problem of point target detection on images and focal plane arrays (FPA). Imaging sensors are becoming ubiquitous tools in several applications, such as biomedical systems, autonomous surveillance systems, target tracking systems, and robotics. In these applications, matched filter and template matching are commonly used detection strategies, however, these approaches are unable to provide sub-pixel accuracy and avenues for adaptive pixel-width selection for computationally efficient image processing. In this paper, we derive the maximum likelihood estimator (MLE) of target location on images. The proposed MLE is optimal under the assumption that the FPA contains a point target that has its signal intensity spread in multiple image pixels in the form of a Gaussian point spread function (PSF) with known standard deviation. Further, we derive the Cramér-Rao lower bound (CRLB) of the estimate and present the hypothesis test for target acceptance, resulting in a novel maximum likelihood detector (MLD) for images. Simulation results are provided to validate the performance of the proposed MLE and MLD; it is shown that the MLE is efficient in very low SNR values, starting at -15 dB, and the MLD achieves probability of detection of near unity with zero false alarms starting at 0 dB.

One regularity condition for the classical Cramér-Rao lower bound (CRLB) of an unbiased estimator to hold is that the support of the likelihood function (LF) should be independent of the parameter to be estimated. This has been shown to be too stringent and the CRLB has been shown to be valid for the case of parameter-dependent support as long as the LF is continuous at the boundary of its support. For the case where the LF is not continuous at the boundary of its support, a new modified CRLB - designated as the Cramér-Rao-Leibniz lower bound (CRLLB) as it relies on the Leibniz integral rule - has been presented for the scalar parameter and measurement case in [3]. The CRLLB for multidimensional parameter and measurements has been developed in [8]. The present work applies the multidimensional CRLLB to n-dimensional measurement noise with the raised fractional cosine and the truncated Laplace distributions inside an (n - 1)-sphere.

Acoustic propagation delay has not been investigated for a continuous wave multistatic sonar tracking system except for the recent study conducted by Jauffret et al. [4], which estimates the trajectory of a constant velocity target. The results showed that the estimate bias caused by the propagation delay is not negligible, especially for a bistatic system. This paper develops an interacting multiple model unscented Gauss-Helmert filter with numerical Jacobian (IMM-UGHF-NJ) to track a maneuvering target with propagation delay using a bistatic sonar system. The IMM-UGHF-NJ can overcome the two tracking challenges introduced by the delay, namely, implicit state transition model and lack of analytical expression of the Doppler shifted frequency in the measurement model. Simulation tests have been conducted, and the results show that the IMM-UGHF-NJ can reduce the estimation error significantly, especially for fast moving targets.

In previous works, it has been shown that the estimation problem of a thrusting/ballistic object in the three-dimensional space can be solved with two-dimensional measurements (azimuth and elevation angles starting from the launch time) assuming the launch point is perfectly known. In this paper, the problem is extended to estimate the target's trajectory with measurements starting after the launch time, i.e., delayed acquisition. Compared to the situation of acquisition at launch time, one has an additional unknown speed (magnitude of the velocity vector) and the unknown acquisition location. The 2D angle measurements are all obtained from a single fixed passive sensor. The parameter vector, in this case, has dimension 8 (velocity vector azimuth angle and elevation angle, drag coefficient, specific thrust, target speed and 3D acquisition position). The invertibility of the Fisher Information Matrix (FIM) of the parameter vector is investigated to test the observability (estimability) of the system. The simulation results prove the statistical efficiency and unbiasedness of the Maximum Likelihood estimator, that is, the Cramer-Rao lower bound (the inverse of the FIM if it is invertible) can be used as the actual covariance.

Summary form only given. The problem of track-to-track association and track fusion has been considered in the literature where the local trackers assume the same target motion model and send their local state estimates to the fusion center on demand. Many issues arise when local trackers use different target motion models or even operate on different target state spaces. In this case, selecting an appropriate track association method at the fusion center is essential to the performance of the overall tracking system. In this paper, we examine several track association methods with different assumptions on the target distribution in a surveillance region. We found that the track association performance can be very different among these methods even when they have the same desired significance level of the correct association probability. We recommend to use the track association method that best approximates the likelihood ratio test with complete knowledge of the target distribution. In addition, existing track fusion techniques have to be modified to account for the model mismatch among some of the local trackers. The track association and fusion problem is illustrated by a two dimensional tracking example with both radar tracks and electronic support measures (ESM) tracks.

Summary form only given. The topic of multisensor tracking has been of interest to researchers for more than 30 years. However, the development and successful fielding of multisensor tracking systems have lagged significantly behind the research activities. In this presentation, a historical perspective of the key algorithmic developments associated with multisensor tracking will be given and their significance will be discussed. The technological advancements that have enabled the recent realizations of multisensor tracking will be discussed along with technological shortfalls that are limiting the realization of better multisensor tracking systems. Some thoughts on the future direction for multisensor tracking will be summarized.

The problem of track-to-track association and track fusion has been considered in the literature where the fusion center has access to multiple track estimates and the associated estimation error covariances from local sensors, as well as their cross covariances. Due primarily to the communication constraints in real systems, some legacy trackers may only provide the local track estimates to the fusion center without any covariance information. In some cases, the local (sensor-level) trackers operate with fixed filter gain and do not have any self assessment of their estimation errors. In other cases, the network conveys a coarsely quantized root mean square (RMS) estimation error of each local tracker. Thus the fusion center needs to solve the track association and fusion problem with incomplete data from legacy local trackers. In this paper a robust track-to-track association and fusion algorithm is described for a distributed tracking system, which accounts for the cross correlation of the estimation error between local tracks in a practical way. Its applicability to real-time and different rate data sources is also discussed by generalizing the algorithms from the existing literature to the case of asynchronous sensors. The problem of track fusion with legacy track sources which lack covariance information is handled by approximating this information through a modified Lyapunov equation. The situation when a coarsely quantized RMS estimation error is available is also discussed. A two-sensor tracking example is used to illustrate the effectiveness of the proposed distributed track fusion algorithm and compared with a centralized interacting multiple model estimator