Bearings-only Target Motion Analysis Research Articles

Passive ranging of a moving target in the direct-arrival zone in deep sea using a single vector hydrophone.

The vector hydrophone covers more comprehensive sound field information over the sound pressure hydrophone. The passive target ranging method based on the shallow-located unmanned platform equipped with vector hydrophones is explored based on the measured surface ship data acquired in the deep-sea area in December 2021. First, a bearings-only target motion analysis (TMA) algorithm is proposed, determining the motion state of a moving target (e.g., azimuth angle, abeam time, heading angle, and the ratio of velocity to initial distance) in accordance with its horizontal bearing time recording (BTR) data. Subsequently, the loss function is built following the situation information and the average complex acoustic intensity to determine the real-time grazing angle of the target. Last, the real-time range of the target is determined in accordance with the situation information and the grazing angle. As revealed by the comparison of the calculated value of the sea trial data with the GPS trajectory, the average distance error of the target reaches 11.6%, the root mean square error (RMSE) of the grazing angle is 1.99°, the RMSE of the velocity is 1.9 kn, and the RMSE of the abeam time reaches 51.4 s.

Non-Gaussian Pseudolinear Kalman Filtering-Based Target Motion Analysis with State Constraints

For the bearing-only target motion analysis (TMA), the pseudolinear Kalman filter (PLKF) solves the complex nonlinear estimation of the motion model parameters but suffers serious bias problems. The pseudolinear Kalman filter under the minimum mean square error framework (PL-MMSE) has a more accurate tracking ability and higher stability compared to the PLKF. Since the bearing signals are corrupted by non-Gaussian noise in practice, we reconstruct the PL-MMSE under Gaussian mixture noise. If some prior information, such as state constraints, is available, the performance of the PL-MMSE can be further improved by incorporating state constraints in the filtering process. In this paper, the mean square and estimation projection methods are used to incorporate PL-MMSE with linear constraints, respectively. Then, the linear approximation and second-order approximation methods are applied to merge PL-MMSE with nonlinear constraints, respectively. Simulation results demonstrate that the constrained PL-MMSE algorithms result in lower mean square errors and bias norms, which demonstrates the superiority of the constrained algorithms.

A Hybrid Newton-Raphson and Particle Swarm Optimization Method for Target Motion Analysis by Batch Processing.

Bearing-only target motion analysis (BO-TMA) by batch processing remains a challenge due to the lack of information on underwater target maneuvering and the nonlinearity of sensor measurements. Traditional batch estimation for BO-TMA is mainly performed based on deterministic algorithms, and studies performed with heuristic algorithms have recently been reported. However, since the two algorithms have their own advantages and disadvantages, interest in a hybrid method that complements the disadvantages and combines the advantages of the two algorithms is increasing. In this study, we proposed Newton–Raphson particle swarm optimization (NRPSO): a hybrid method that combines the Newton–Raphson method and the particle swarm optimization method, which are representative methods that utilize deterministic and heuristic algorithms, respectively. The BO-TMA performance obtained using the proposed NRPSO was tested by varying the measurement noise and number of measurements for three targets with different maneuvers. The results showed that the advantages of both methods were well combined, which improved the performance.

A Cramér-Rao Lower Bound Derivation for Passive Sonar Track-Before-Detect Algorithms

Track-before-detect (TkBD) algorithms have been shown to greatly abate measurement-to-track association (MTA) challenges. These simplifications are aptly relevant for reducing operator workload in deployed sonar systems that require a human “in-the-loop.” In a prior manuscript a case study of a passive bearings-only target motion analysis TkBD algorithm was demonstrated in complex sonar scenarios relevant to advanced fielded sonar systems. In this manuscript, a Cramer-Rao Lower Bound (CRLB) is derived for the algorithm previously developed. The approximations used in developing the CRLB are validated with a real data set. The CRLB itself, as a predictor of state estimation error performance, is validated with single- and multi-contact simulated data scenarios. The prior algorithm and CRLB derived herein is applicable to passive sonar, active sonar, radar, and optical applications through a change of point spread functions and Jacobians. The CRLB derived is simple to implement, requires minimal statistical assumptions, and is applicable to similarly implemented TkBD algorithms.

Batch Processing through Particle Swarm Optimization for Target Motion Analysis with Bottom Bounce Underwater Acoustic Signals.

A target angular information in 3-dimensional space consists of an elevation angle and azimuth angle. Acoustic signals propagating along multiple paths in underwater environments usually have different elevation angles. Target motion analysis (TMA) uses the underwater acoustic signals received by a passive horizontal line array to track an underwater target. The target angle measured by the horizontal line array is, in fact, a conical angle that indicates the direction of the signal arriving at the line array sonar system. Accordingly, bottom bounce paths produce inaccurate target locations if they are interpreted as azimuth angles in the horizontal plane, as is commonly assumed in existing TMA technologies. Therefore, it is necessary to consider the effect of the conical angle on bearings-only TMA (BO-TMA). In this paper, a target conical angle causing angular ambiguity will be simulated using a ray tracing method in an underwater environment. A BO-TMA method using particle swarm optimization (PSO) is proposed for batch processing to solve the angular ambiguity problem.

A Closed-Form Estimator for Bearings-Only Fusion of Heterogeneous Passive Sensors

Bearings-only target motion analysis with fusion of heterogeneous passive sensors with and without propagation delay attempts to estimate a target trajectory by fusing bearings from two sensors: a sensor whose measurements have negligible propagation delay and a sensor with measurements that have non-negligible propagation delay. This problem is highly nonlinear and challenging, particularly due to the fact that the propagation delay is unknown and is highly coupled with the unknown target states. This paper proposes a novel closed-form instrumental variable based batch estimator for this problem that is computationally fast. The estimator is derived by writing pseudolinear type equations for the error vector-difference between the true target state and a nominal solution. A theoretical bias and mean square error analysis of the proposed estimator is carried out which provides insight into the performance of this estimator. Results indicate that this is a computationally efficient algorithm that is able to produce comparable performance to the maximum likelihood estimator and achieves the Cramer Rao lower bound.

An Algebraic Closed-Form Solution for Bearings-Only Maneuvering Target Motion Analysis From a Nonmaneuvering Platform

In bearings-only target motion analysis (TMA), the observer is often required to outmaneuver the target. However, under specific conditions, an observer moving with constant velocity is sufficient to compute the state of a target that changes its course. A maximum likelihood estimator (MLE) has been developed for this problem in the literature. Unfortunately, the MLE is not only computationally expensive but also prone to divergence problems when poorly initialised. To overcome these shortcomings, this paper proposes a novel quadratically constrained weighted instrumental variable (QC-WIV) estimator. Being a closed-form algorithm, the proposed QC-WIV is inherently more stable than the MLE while at the same time being computationally much more efficient. Moreover, it is shown analytically to be asymptotically unbiased. Numerical simulation studies are presented to corroborate the performance advantage of the proposed QC-WIV, where it is observed to be asymptotically efficient as well. In addition, the QC-WIV performance is on par with the MLE in small noise scenarios for both cases of known and unknown maneuver time. More importantly, the QC-WIV is observed to produce stable estimation performance in large noise levels at which the MLE suffers from divergence.

Bayesian WIV Estimators for 3-D Bearings-Only TMA With Speed Constraints

This paper develops Bayesian weighted instrumental variable (WIV) estimators under equality and inequality speed constraints for the three-dimensional (3-D) bearings-only target motion analysis (TMA) problem, which show improved estimation accuracies compared to their unconstrained counterpart. Incorporating the speed constraint information into our previously proposed Bayesian WIV estimator imposes a quadratic constraint on this problem. Finding an optimal solution for the resulting non-convex problem is by no means straightforward. The main problem with iterative optimization methods such as the maximum a posteriori is that they require initialization and may converge to a local minimum if poorly initialized. Using advanced linear and nonlinear algebra techniques, non-iterative accurate estimators under equality and inequality constraints are developed for this problem. Furthermore, it is proven that the proposed equality constrained estimator is approximately asymptotically unbiased and that the inequality constrained estimator is the optimal solution. An approximate covariance matrix has also been developed for the constrained WIV under equality constraint. Simulation results indicate that the equality and inequality constrained estimators outperform their unconstrained counterpart in the simulated scenarios.

Track-Before-Detect Bearings-Only Localization Performance in Complex Passive Sonar Scenarios: A Case Study

Track-before-detect (TkBD) algorithms have been shown to greatly abate measurement-to-track association (MTA) challenges. These simplifications are aptly relevant for reducing operator workload in deployed sonar systems that require a human “in the loop.” This paper presents a case study of a passive bearings-only target motion analysis TkBD algorithm using two complex data sets: one simulated and one obtained at sea, which are representative of scenario characteristics typically encountered with advanced operational sonar systems. The simulated data set exhibits crossing contacts of differing signal-to-noise ratios and short data gaps. The at-sea data, obtained from an open ocean exercise, are used to assess performance under realistic conditions that exhibit high levels of clutter, varying background noise levels, fading contacts, a high bearing-rate contact, and large data gaps. The TkBD algorithm is designed for the general complexities encountered in the examined data sets and employs a particle filter that defines its likelihood function as the accumulation of raster bin values from the output of the sonar beamformer conditioned on the particle's state trajectory. For the scenarios examined the localization performance of the algorithm is encouraging. The paper briefly reviews the chief motivation for using a TkBD approach, which is to circumvent MTA.

Robust target motion analysis using the possibility particle filter

Bearings-only target motion analysis (TMA) is the process of estimating the state of a moving emitting target from noisy measurements collected by a single passive observer. The focus of this study is on recursive TMA, traditionally solved using the Bayesian filters (e.g. extended or unscented Kalman filters, particle filters). The TMA is a difficult problem and may result in track divergence, especially when the assumed probabilistic models are imperfect or mismatched. As a robust alternative to Bayesian filters for TMA, the authors present a recently proposed stochastic filter referred to as the possibility filter. The filter is implemented in the sequential Monte Carlo framework, and named the possibility particle filter. This study demonstrates its superior performance against the standard (Bayesian) particle filter in the presence of a model mismatch, while in the case of the exact model match, its performance equals that of the standard particle filter.

Bearing and range tracking with a two-hydrophone ocean glider

A Slocum glider fitted with two hydrophones separated by a distance of approximately 3 feet recorded sperm whale sounds during an experiment off the west coast of the island of Sardinia, Italy, in the summer of 2014. Time difference of arrival analysis of their echolocation clicks provided bearing tracks. It was also found that the left-right ambiguity inherent of the bearing estimation process could be broken by the natural oscillation in glider heading. More recently, a controlled experiment on a quiet lake with a known fixed acoustic source was devised to investigate unambiguous bearing estimation and possible ranging. Simple target motion analysis (TMA) using the glider’s position data resulted in range estimates of only a few hundred meters short of the true source location. Analysis of the acoustic data on the other hand, presented challenges to satisfactory TMA performance. Overall, it was found that simple bearing-only TMA analysis is possible with two-hydrophone acoustic data and small angular change of a few degrees in the heading of the observing platform. Results will be discussed with implications to marine mammal population density estimation studies, since the ability to estimate direction and range of sound-producing animals could improve estimation of detection probabilities.

Geometric Approach to Passive Ranging in Underwater Localization Systems

The use of underwater surveillance systems is critical for effective command of maritime power. Ships or submarines equipped with active sonar systems emit sounds to obtain range or angle information. Unfortunately, security issues may occur in this situation. To meet the security considerations for obtaining location information, a passive tracking or localization technique, the bearings-only target motion analysis (BO-TMA), was developed along with a given direction of arrival (DOA) estimation. With limited resources, a passive ranging approach with only a single passive array is practical, and is considered in this paper. In this paper, we propose a new geometric approach and derive a closed-form solution, which can be implemented in BO-TMA algorithms for initiation and updating the range of targets with a single passive sensor. Finally, analysis and simulation results showed that the proposed scheme can achieve good performance and is effective for a short operation time, such that an observer can move with more flexibility in combat scenarios. The proposed algorithm can further be performed by trackers to generate the initiation information and hence reduce the estimation bias.

Observability: Range-Only Versus Bearings-Only Target Motion Analysis When the Observer Maneuvers Smoothly

Range-only target motion analysis (ROTMA) consists of estimating the trajectory of a target using a single platform collecting range-only measurements. Observability analysis is carried out when the target is in constant-velocity motion and the observer maneuvers gently (a constant turn motion or a constant acceleration motion). We compare observability in bearings-only target motion analysis and ROTMA throughout the paper, together with the rank of the Fisher information matrix. In each case, we establish necessary and sufficient observability conditions and we identify the virtual (or ghost) targets giving the same measurements when the system is not observable.

Bearings‐only target motion analysis of a highly manoeuvring target

In this study, the authors tackle the bearings-only target motion analysis problem, which is to estimate the position and velocity of a target using bearing measurements. They consider a target which is highly manoeuvrable. This study introduces the modified range-parameterised extended Kalman filter (MRPEKF), which consists of a number of independent EKFs, each with a different initial range estimate. The MRPEKF uses the filter re-initialisation strategy to track a highly manoeuvring target. They further introduce the method to improve the efficiency of the MRPEKF. They verify the effectiveness of their MRPEKF by comparing it with the IMM KF using simulations.

Observability: range-only vs. bearings-only target motion analysis for a leg-by-leg observer's trajectory

The aim of so-called range-only target motion analysis (ROTMA) is to estimate the trajectory of a target by a single platform collecting range-only measurements.We focus on the observability analysis when the target is in constant-velocity (CV) motion. More precisely, the observability conditions are established when the observer’s trajectory is composed of one or several legs. We establish a link between the Fisher information matrix (FIM) and the observability, after having proven the similarity of this matrix with the FIM encountered in bearings-only target motion analysis (BOTMA). We compare observability statuses in BOTMA and ROTMA in the paper.

Optimal design of the Own Ship maneuver in the bearing-only target motion analysis problem using a heuristically supervised Extended Kalman Filter

The state estimation algorithm and the Own Ship maneuvering specifications have great effects on the accuracy of the bearing-only tracking (BOT) method. In the BOT problem, the EKF algorithm is widely used as the nonlinear state estimation algorithm while it suffers from its sensitivity to the initial values of covariance matrixes. This paper aims at improving the accuracy of the BOT problem by using the metaheuristic evolutionary optimization algorithms as supervising algorithms. Three different optimization algorithms, Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and Cuckoo Search (CS) are used in finding the optimal initial values of the dynamic and the measurement process noise covariance matrixes of the Extended Kalman Filter (EKF). Moreover, the optimal path (leg) planning of the Own Ship maneuver is also done by minimizing the Fisher Information Matrix (FIM). The Monte Carlo analysis of the simulation results demonstrates the effectiveness of the evolutionary algorithms in improving the performance of the EKF in a BOT problem.

A Practical Method of Observer Velocity Optimization with Airborne ESM Sensor

In bearings-only target motion analysis, the observer trajectory has an important effect on the accuracy of target localization and tracking. This paper presented a practical method of observer velocity optimization based on Monte-Carlo run for airborne ESM measurement system. For verifying the validity of our method, the geometric dilution of precision (GDOP) is taken as the performance index. Finally, three scenarios are given and the GDOP values of the ESM measurement system in scenarios are calculated to illustrate the observer velocity optimization strategy.

Comparing passive source localization and tracking approaches with a towed horizontal receiver array in an ocean waveguide

Approaches for instantaneous passive source localization using a towed horizontal receiver array in a random range-dependent ocean waveguide are examined. They include: (1) Moving array triangulation, (2) array invariant, (3) bearings-only target motion analysis in modified polar coordinates via the extended Kalman filter, and (4) bearings-migration minimum mean-square error. These methods are applied to localize and track a vertical source array deployed in the far-field of a towed horizontal receiver array during the Gulf of Maine 2006 Experiment. The source transmitted intermittent broadband pulses in the 300 to 1200 Hz frequency range. A nonlinear matched-filter kernel designed to replicate the acoustic signal measured by the receiver array is applied to enhance the signal-to-noise ratio. The source localization accuracy is found to be highly dependent on source-receiver geometry and the localization approach. For a relatively stationary source drifting at speeds much slower than the receiver array tow-speed, the mean source position can be estimated by moving array triangulation with less than 3% error near broadside direction. For a moving source, the Kalman filter method gives the best performance with 5.5% error. The array invariant is the best approach for localizing sources within the endfire beam of the receiver array with 7% error.

Detection of Target Maneuver from Bearings-Only Measurements

An acceleration-based target maneuver detecting algorithm is proposed for bearings-only target motion analysis (BO-TMA). Firstly, compared with the existing bearing-based detectors, the acceleration-based detector is shown to have the same maneuver burden on the observer. Secondly, the algorithm stems from the instrumental variable method and gains desirable asymptotical properties. Numerical simulations are carried out to show the algorithm works well against the bearing- based detecting algorithms (e.g., the Shiryayev sequential probablility ratio test (SSPRT)-based detector).

Accuracy of passive source localization approaches with a single towed horizontal line-array in an ocean waveguide

Instantaneous passive source localization applying the (1) synthetic aperture tracking, (2) array invariant, (3) bearings-only target motion analysis in modified polar coordinates via the extended Kalman filter, and (4) bearings-migration minimum mean-square error methods to measurements made on a single towed horizontal receiver array in a random range-dependent ocean waveguide are examined. These methods are employed to localize and track a vertical source array deployed in the far-field of a towed horizontal receiver array during the Gulf of Maine 2006 Experiment. The source transmitted intermittent broadband pulses in the 300-1200 Hz frequency range. All four methods are found to be comparable with averaged error of between 9% to 13% in estimating the mean source position in a wide variety of source-receiver geometries. In the case of a relatively stationary source, the synthetic aperture tracking outperforms the other three methods by a factor of two with only 4% error. For a moving source, the Kalman filter method yields the best performance with 8% error. The array invariant is the best approach for localizing sources within the endfire beam of the receiver array with less than 10% error.