Search Results (23)

The highly dynamic properties of maneuvering targets make it intractable for radars to predict the target motion states accurately and quickly, and low-grade predicted states depreciate the efficiency of resource allocation. To overcome this problem, we introduce the modified current statistical (MCS) model, which incorporates the input-acceleration transition matrix into the augmented state transition matrix, to predict the motion state of a maneuvering target. Based on this, a robust resource allocation strategy is developed for maneuvering target tracking (MTT) in a netted opportunistic array radar (OAR) system under uncertain conditions. The mechanism of the strategy is to minimize the total transmitting power conditioned on the desired tracking performance. The predicted conditional Cramér–Rao lower bound (PC-CRLB) is deemed as the optimization criterion, which is derived based on the recently received measurement so as to provide a tighter lower bound than the posterior CRLB (PCRLB). For the uncertainty of the target reflectivity, we encapsulate the determined resource allocation model with chance-constraint programming (CCP) to balance resource consumption and tracking performance. A hybrid intelligent optimization algorithm (HIOA), which integrates a stochastic simulation and a genetic algorithm (GA), is employed to solve the CCP problem. Finally, simulations demonstrate the efficiency and robustness of the presented algorithm. Full article

The trajectory estimation of a highly maneuvering target is a challenging problem and has practical applications. The interacting multiple model (IMM) filter is a well-established filtering algorithm for the trajectory estimation of maneuvering targets. In this study, we present an overview of IMM filtering algorithms for tracking a highly-maneuverable fighter aircraft using an air moving target indicator (AMTI) radar on another aircraft. This problem is a nonlinear filtering problem due to nonlinearities in the dynamic and measurement models. We first describe single-model nonlinear filtering algorithms: the extended Kalman filter (EKF), unscented Kalman filter (UKF), and cubature Kalman filter (CKF). Then, we summarize the IMM-based EKF (IMM-EKF), IMM-based UKF (IMM-UKF), and IMM-based CKF (CKF). In order to compare the state estimation accuracies of the IMM-based filters, we present a derivation of the posterior Cramér-Rao lower bound (PCRLB). We consider fighter aircraft traveling with accelerations 3g, 4g, 5g, and 6g and present numerical results for state estimation accuracy and computational cost under various operating conditions. Our results show that under normal operating conditions, the three IMM-based filters have nearly the same accuracy. This is due to the accuracy of the measurements of the AMTI radar and the high data rate. Full article

With this follow-up paper, we continue developing a mathematical framework based on information geometry for representing physical objects. The long-term goal is to lay down informational foundations for physics, especially quantum physics. We assume that we can now model information sources as univariate normal probability distributions $\mathcal{N}$ ($\mu$, ${\sigma }_0)$, as before, but with a constant ${\sigma }_0$ not necessarily equal to 1. Then, we also relaxed the independence condition when modeling m sources of information. Now, we model m sources with a multivariate normal probability distribution ${\mathcal{N}}_m(\mathit{\mu },{\mathbf{\Sigma }}_0)$ with a constant variance–covariance matrix ${\mathbf{\Sigma }}_0$ not necessarily diagonal, i.e., with covariance values different to 0, which leads to the concept of modes rather than sources. Invoking Schrödinger’s equation, we can still break the information into m quantum harmonic oscillators, one for each mode, and with energy levels independent of the values of ${\sigma }_0$, altogether leading to the concept of “intrinsic”. Similarly, as in our previous work with the estimator’s variance, we found that the expectation of the quadratic Mahalanobis distance to the sample mean equals the energy levels of the quantum harmonic oscillator, being the minimum quadratic Mahalanobis distance at the minimum energy level of the oscillator and reaching the “intrinsic” Cramér–Rao lower bound at the lowest energy level. Also, we demonstrate that the global probability density function of the collective mode of a set of m quantum harmonic oscillators at the lowest energy level still equals the posterior probability distribution calculated using Bayes’ theorem from the sources of information for all data values, taking as a prior the Riemannian volume of the informative metric. While these new assumptions certainly add complexity to the mathematical framework, the results proven are invariant under transformations, leading to the concept of “intrinsic” information-theoretic models, which are essential for developing physics. Full article

This paper presents a method for extracting the digital elevation model (DEM) of forested areas from polarimetric interferometric synthetic aperture radar (PolInSAR) data. The method models the ground phase as a Von Mises distribution, with a mean of the topographic phase computed from an external DEM. By combining the prior distribution of the ground phase with the complex Wishart distribution of the observation covariance matrix, we derive the maximum a posterior (MAP) inversion method based on the RVoG model and analyze its Cramer–Rao Lower Bound (CRLB). Furthermore, considering the characteristics of the objective function, this paper introduces a Four-Step Optimization (FSO) method based on gradient optimization, which solves the inefficiency problem caused by exhaustive search in solving ground phase using the MAP method. The method is validated using spaceborne L-band repeat-pass SAOCOM data from a test forest area. The test results for FSO indicate that it is approximately 5.6 times faster than traditional methods without compromising accuracy. Simultaneously, the experimental results demonstrate that the method effectively solves the problem of elevation jumps in DEM inversion when modeling the ground phase with the Gaussian distribution. ICESAT-2 data are used to evaluate the accuracy of the inverted DEM, revealing that our method improves the root mean square error (RMSE) by about 23.6% compared to the traditional methods. Full article

This work addresses J.A. Wheeler’s critical idea that all things physical are information-theoretic in origin. In this paper, we introduce a novel mathematical framework based on information geometry, using the Fisher information metric as a particular Riemannian metric, defined in the parameter space of a smooth statistical manifold of normal probability distributions. Following this approach, we study the stationary states with the time-independent Schrödinger’s equation to discover that the information could be represented and distributed over a set of quantum harmonic oscillators, one for each independent source of data, whose coordinate for each oscillator is a parameter of the smooth statistical manifold to estimate. We observe that the estimator’s variance equals the energy levels of the quantum harmonic oscillator, proving that the estimator’s variance is definitively quantized, being the minimum variance at the minimum energy level of the oscillator. Interestingly, we demonstrate that quantum harmonic oscillators reach the Cramér–Rao lower bound on the estimator’s variance at the lowest energy level. In parallel, we find that the global probability density function of the collective mode of a set of quantum harmonic oscillators at the lowest energy level equals the posterior probability distribution calculated using Bayes’ theorem from the sources of information for all data values, taking as a prior the Riemannian volume of the informative metric. Interestingly, the opposite is also true, as the prior is constant. Altogether, these results suggest that we can break the sources of information into little elements: quantum harmonic oscillators, with the square modulus of the collective mode at the lowest energy representing the most likely reality, supporting A. Zeilinger’s recent statement that the world is not broken into physical but informational parts. Full article

The variational Bayesian method solves nonlinear estimation problems by iteratively computing the integral of the marginal density. Many researchers have demonstrated the fact its performance depends on the linear approximation in the computation of the variational density in the iteration and the degree of nonlinearity of the underlying scenario. In this paper, two methods for computing the variational density, namely, the natural gradient method and the simultaneous perturbation stochastic method, are used to implement a variational Bayesian Kalman filter for maneuvering target tracking using Doppler measurements. The latter are collected from a set of sensors subject to single-hop network constraints. We propose a distributed fusion variational Bayesian Kalman filter for a networked maneuvering target tracking scenario and both of the evidence lower bound and the posterior Cramér–Rao lower bound of the proposed methods are presented. The simulation results are compared with centralized fusion in terms of posterior Cramér–Rao lower bounds, root-mean-squared errors and the 3$\sigma$ bound. Full article

Reasonable allocation of space-based radar resources is a crucial aspect of improving the accuracy of space multi-target tracking and enhancing spatial awareness. The conventional resource allocation algorithm fails to exploit the high dynamic radar cross-section (RCS) characteristics, resulting in poor tracking robustness, tracking divergence, or even loss of tracking. However, the RCS of space targets fluctuates considerably in actual tracking scenarios, which cannot be disregarded for space target tracking tasks. To address this issue, we propose an adaptive allocation method that considers the dynamic RCS fluctuation characteristic for space-based radar tracking assignments. The proposed method exploits the predictable orbital information of space target to calculate the real-time observation angle of radar, and then obtains the multi-target dynamic RCS through the target RCS dataset. By combining the obtained RCS sequence, radar power, and bandwidth, an optimal model for radar tracking accuracy is established based on the multi-target posterior Cramér–Rao lower bound (PCRLB) to evaluate the tracking performance. By resolving the aforementioned multivariance optimization problem, we eventually acquire the results of power and bandwidth pre-allocation for tracking multiple space targets. Simulation results validate that, compared with the traditional methods, the proposed joint dynamic RCS power and bandwidth allocation (JRPBA) method can achieve superior tracking accuracy and minimize instances of missed tracking. Full article

The performance of traditional direction of arrival (DOA) estimation methods always deteriorates at a low signal-to-noise ratio (SNR) or without sufficient observations. This paper investigates the Bayesian DOA estimation problem aided by the prior knowledge from the target tracker. The Bayesian Cramér–Rao lower bounds (CRLB) and the expected CRLB are first derived to evaluate the theoretical performance of Bayesian DOA estimation. Based on the maximum a posterior (MAP) estimator in the Bayesian framework, two methods are proposed. One is a two-step grid search method for a single target DOA case. The other is a gradient-based iterative solution for multiple targets DOA case, which extends the traditional Newton method by incorporating the prior knowledge. We also propose a minimum mean square error (MMSE) estimator using a Monte Carlo method, which requires trading off accuracy against computational complexity. By comparing with the maximum likelihood (ML) estimators and the MUSIC algorithm, the proposed three Bayesian estimators improve the DOA estimation performance in low SNR or with limited snapshots. Moreover, the performance is not affected by the correlation between sources. Full article

The simultaneous multi-beam working mode of the collocated multiple-input and multiple-output (MIMO) radar enables the radar to track multiple targets simultaneously. A joint power and bandwidth allocation algorithm in a collocated MIMO radar based on the quality of service (QoS) framework is proposed for the multi-target tracking problem with different threat levels. Firstly, a posterior Cramer–Rao lower bound (PCRLB) concerning the power and bandwidth is derived. In addition, the optimal objective functions of power and bandwidth are designed based on the QoS framework, and the problem is solved using the convex relaxation technique and the cyclical minimization algorithm. The numerical results show that the proposed algorithm has better tracking accuracy and achieves more reasonable resource allocation compared to strategies such as average allocation. Full article

Gravity-aided inertial navigation system (GAINS) is an important development in autonomous underwater vehicle (AUV) navigation. An effective path planning algorithm plays an important role in the performance of navigation in long-term underwater missions. By combining the gravity information obtained at each position with the error information from the INS, the posterior Cramér-Rao bound (PCRB) of GAINS is derived in this paper. The PCRB is the estimated lower bound of position variance for navigation along the planned trajectory. And the sum of PCRB is used as the minimum cost from the initial state to the current state in the state space, and the position error prediction variance of inertial navigation system (INS) is used as the minimum estimated cost of the path from the current state to the goal state in the A* algorithm. Thus, a path planning method with optimal navigation accuracy is proposed. According to simulation results, traveling along the path planned by the proposed method can rapidly improve the positioning accuracy while consuming just slightly more distance. Even when measuring noise changes, the planned path can still maintain optimal positioning accuracy, and high positioning accuracy is possible for any trajectory located within a certain range of the planned path. Full article

In view of the decline of filtering accuracy caused by measured outliers in target tracking application, a novel reweighted robust particle filter is proposed to acquire accurate state estimates in an automotive radar system. To infer the importance of each entry in the multidimensional contaminated measurement vector, we employ a weight vector, which follows a Gamma distribution, to model the measured noise and carry out accurate state estimates. Additionally, the particle filter method is employed to perform approximate posterior inference of state estimates in the nonlinear model. The Cramer–Rao lower bound is provided for the performance evaluation of the proposed method. Both simulation and experimental results demonstrate the superiorities of the proposed algorithm over other robust solutions. Full article

Antenna distribution plays an important role for the performance gain in multiple-input–multiple-output (MIMO) radar target tracking. Since to meet the requirements of the low probability of interception, especially in a hostile environment, only a finite number of antennas can be activated at each step. This naturally leads to a performance-driven resource management problem. In this paper, a dynamic antenna selection strategy is proposed for tracking targets in colocated MIMO radar. The derived posterior Cramér–Rao lower bound (PCRLB) of joint direction-of-arrival (DOA) and Doppler estimate were chosen as the optimization criteria. Furthermore, in the deviation, the target radar cross-section (RCS) as the determining variable and the random variable are both discussed. The objective function is related to the antenna allocation and non-convex, and an efficient fast discrete particle swarm optimization (FDPSO) algorithm is proposed for the solution exploration. Additionally, a closed-loop feedback system is established, where the main idea is that the tracking information from the current time epoch is utilized to predict the PCRLB and to guide the antenna adjustment for the next time epoch. The simulation results demonstrate the performance improvement compared with the three fixed-antenna configurations. Moreover, the FDPSO can provide close-to-optimal solutions while satisfying the real-time demand. Full article

In the context of distributed defense, multi-sensor networks are required to be able to carry out reasonable planning and scheduling to achieve the purpose of continuous, accurate and rapid target detection. In this paper, a multi-sensor cooperative scheduling model based on the partially observable Markov decision process is proposed. By studying the partially observable Markov decision process and the posterior Cramer–Rao lower bound, a multi-sensor cooperative scheduling model and optimization objective function were established. The improvement of the particle filter algorithm by the beetle swarm optimization algorithm was studied to improve the tracking accuracy of the particle filter. Finally, the improved elephant herding optimization algorithm was used as the solution algorithm of the scheduling scheme, which further improved the algorithm performance of the solution model. The simulation results showed that the model could solve the distributed multi-sensor cooperative scheduling problem well, had higher solution performance than other algorithms, and met the real-time requirements. Full article

Accurate geolocation and tracking of Radio-Frequency Interference (RFI) sources, which affect wireless and satellite systems such as Global Navigation Satellite Systems (GNSS) and Satellite Communication (SatCom) systems, are considered to be a significant issue. Several studies connected to civil and military operations on this issue have been investigated recently. The literature review has surveyed many algorithm simulations for optimizing geolocation and target-tracking estimation. Although most of these algorithms have their own advantages, they have weaknesses, such as accuracy, mathematical complexity, difficulties in implementation, and validation in the real environment, etc. This study has been concerned with investigating the accuracy of geolocation and tracking under high speed and powerful rotation using extracted data from the Orolia Skydel simulator, which simulates the space environment involving Low Earth Orbit (LEO) satellites as sensors and Unmanned Aerial Vehicles (UAV) as RFI emitters. Various scenarios modeled using the Orolia Simulator for quasi-real dynamic trajectories of LEO satellites have been created. The assumed approaches have been verified by Cramer–Rao Lower Bound (CRLB) and Posterior CRLB (PCRLB) to determine the increase in Root Mean Square Error (RMSE) value. The simulation scenarios have been performed using the Monte Carlo iteration. Eventually, the overall achieved results of the considered approaches using data acquired from the Orolia Simulator were presented and compared with theoretical simulation. Full article

Airborne angle-only sensors can be used to track stationary or mobile ground targets. In order to make the problem observable in 3-dimensions (3-D), the height of the target (i.e., the height of the terrain) from the sea-level is needed to be known. In most of the existing works, the terrain height is assumed to be known accurately. However, the terrain height is usually obtained from Digital Terrain Elevation Data (DTED), which has different resolution levels. Ignoring the terrain height uncertainty in a tracking algorithm will lead to a bias in the estimated states. In addition to the terrain uncertainty, another common source of uncertainty in angle-only sensors is the sensor biases. Both these uncertainties must be handled properly to obtain better tracking accuracy. In this paper, we propose algorithms to estimate the sensor biases with the target(s) of opportunity and algorithms to track targets with terrain and sensor bias uncertainties. Sensor bias uncertainties can be reduced by estimating the biases using the measurements from the target(s) of opportunity with known horizontal positions. This step can be an optional step in an angle-only tracking problem. In this work, we have proposed algorithms to pick optimal targets of opportunity to obtain better bias estimation and algorithms to estimate the biases with the selected target(s) of opportunity. Finally, we provide a filtering framework to track the targets with terrain and bias uncertainties. The Posterior Cramer–Rao Lower Bound (PCRLB), which provides the lower bound on achievable estimation error, is derived for the single target filtering with an angle-only sensor with terrain uncertainty and measurement biases. The effectiveness of the proposed algorithms is verified by Monte Carlo simulations. The simulation results show that sensor biases can be estimated accurately using the target(s) of opportunity and the tracking accuracies of the targets can be improved significantly using the proposed algorithms when the terrain and bias uncertainties are present. Full article