A new TMA method for state estimation of underwater target

The article explores a passive target motion analysis (TMA) method for underwater unmanned vehicle (UUV) clusters to address challenges in information bandwidth, noise, and energy consumption due to weak underwater connectivity. The proposed approach utilizes passive sonar detection of adjacent UUVs’ radiated signals to obtain bearing information, combined with known platform features and planned operational speeds. Through simulations and real UUV data, the study demonstrates that incorporating speed information improves the trajectory tracking capability of both Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) TMA models. Specifically, for targets moving at constant velocity, planned speed information enhances tracking accuracy with relative distance errors around 5%. The results also show that relative speed can be effectively integrated into both EKF and UKF models to enable trajectory tracking in bearing only TMA. Future research directions include incorporating more platform information into TMA and improving algorithm robustness and accuracy.

The problem is target motion analysis (TMA) in situations where the variance (standard deviation) of additive white Gaussian measurement noise is unknown and time-varying. In particular, the paper examines a somewhat surprising result from the theoretical analysis based on the Cramer-Rao bound, which suggests that the best-achievable (second-order) error in target state estimation is unaffected by the lack of knowledge of the measurement noise variance. In order to examine this result, the paper develops three recursive Bayesian filters for TMA, which jointly estimate the target state and the measurement variance. The basis of all filters is the Cubature Kalman filter for bearings-only tracking, combined with (i) the variational Bayesian approach, (ii) the Rao-Blackwellised particle filter, and (iii) the interactive multiple-model (IMM), to deal with the unknown time-varying measurement variance. The paper presents extensive numerical simulation results and comparisons, which confirm that the lack of knowledge of the measurement noise variance is by no means a handicap for TMA.

Bearing and frequency measurements of TMA (Target Motion Analysis) in passive line array SONAR have lower bearing rate and frequency doppler, and are not detected or tracked continuously because of various ocean environments. This is a main reason to effect the TMA performance and it takes a long time to get TMA solutions. We propose the bearing and frequency TMA(BFTMA) using accumulative batch estimation to solve the TMA problem of line array passive SONAR. The accumulative batch estimation structure is based on MLE (Maximum Likelihood Estimation) but used accumulative measurements. The accumulative batch estimation is applied for the BFTMA with nonlinear Kalman filter to estimate the target range, speed and course. Simulation and sea data analysis were carried out to verify the performance and applicability of the proposed techniques.

A Newton-type method is used to solve the target motion analysis (TMA) problem with respect to bearing and frequency measurements from a passive sonar system. In many long-range sonar situations the TMA problem is ill conditioned and suffers from a small signal-to-noise ratio. Although Kalman filters have been investigated extensively it is known that maximum likelihood (ML) estimation is superior in these cases. The main reason for the good performance of the ML method is that the underlying numerical optimization problem deals with the ill conditioning of the problem. This work illustrates how the conditioning depends on the geometry of the tracks and the signal-to-noise ratio. Monte Carlo simulations with respect to the measurement noise show the influence on the ML estimation performance for three specific cases concerning multileg situations and bottom bounce measurements.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Introduction: Moyamoya is a progressive cerebrovascular disease leading to arterial stenosis of the circle of Willis. Using diffusion tensor imaging (DTI), adults with moyamoya have significantly decreased white matter fractional anisotropy (FA) compared to controls even when conventional imaging is normal. This raises concern for under recognized white matter injury. Children with moyamoya have been shown to have significantly increased whole brain apparent diffusion coefficient (ADC) values. However, to our knowledge the involvement of specific white matter tracts in children with moyamoya, relevant to specific cognitive domains, has not been evaluated. Methods: We present a cohort of 16 children with moyamoya with 25 affected hemispheres without stroke compared to 25 children controls. We analyzed DTI data using unscented Kalman filter (UKF) tractography and extracted major white matter pathways with a fiber clustering method. We compared the FA, ADC, AD, and RD globally as well as within each white matter tract using ANOVA. Results: Age and sex were not significantly different between children with moyamoya and controls. For all white matter tracts, children with moyamoya had significantly lower FA (-7.0%, p=0.04) as well as higher ADC (5.7%, p=0.002) and RD (9.5%, p=0.002). AD was also higher but not significant (2.3%, p=0.21). Specific white matter tracts that were significantly affected included: inferior fronto-occipital fasciculus, inferior longitudinal fasciculus, superior longitudinal fasciculus and thalamo-frontal tract (Table 1). Discussion: Lower FA with higher ADC and RD is consistent with decreased axonal myelination. Tracts in watershed regions were especially affected in children with moyamoya. These findings are also consistent with concerns that children with moyamoya are chronically hypoperfused. In conclusion, future research is needed to determine whether these findings are reversible.

Target angular information in a 3-dimensional space consists of an elevation angle and an azimuth angle. The azimuth angle indicates the direction of the target in a horizontal plane while the elevation angle indicates the direction of target signal in a vertical plane established from a passive line array sonar. The acoustic signals gathered by the line array sonar have different elevation angles as they propagate through multiple paths. The target angle measured by the line array sonar is, in fact, a conical angle that indicates the direction of incoming signal to the line array sonar system. Therefore, bottom bounce path produces an inaccurate target location if it is interpreted as the azimuth angle in the horizontal plane as is commonly used in exiting Target Motion Analysis (TMA) technologies. Therefore, it is necessary to consider the conical angle effect on bearings-only TMA (BO-TMA). In this paper, the conical angle of target that causes angular ambiguity will be simulated, and the BO-TMA method using Particle Swarm Optimization (PSO) is proposed to solve the angular ambiguity problem.

It is well known that passive target tracking by a single observer, commonly referred to as target motion analysis (TMA), can be done using angle and/or frequency measurements. Depending on the measurement set, different passive tracking procedures result: angle-only tracking (AOT), frequency-only tracking (FOT), and angle/frequency tracking (AFT). Whereas the two-dimensional passive tracking problem has been solved for a multitude of scenarios, thus giving a good insight into the parametric dependences, the three-dimensional problem has been discussed only in a few specific cases. To get a deeper insight into the parametric dependences of three-dimensional TMA, this work analyzes AOT and AFT in typical three-dimensional Airborne Warning and Control System (AWACS) scenarios. A Cramer Rao (CR) analysis of the problem reveals the parametric dependences of both methods and gives a clear idea of the increase in estimation accuracy by using AFT instead of AOT. The results obtained in this way are well confirmed by Monte Carlo simulations taking maximum likelihood (ML) as estimation procedure.

When tracking maneuvering targets with a nearly constant acceleration (NCA) Kalman filter with discrete white noise acceleration (DWNA), the selection of the process noise variance is complicated by the fact that the process noise errors are modeled as white Gaussian, while target maneuvers are deterministic or highly correlated in time. In recent years for nearly constant velocity (NCV) Kalman filters, the deterministic tracking index was introduced and used to develop a relationship between the maximum acceleration of the target and the process noise variance that minimizes the maximum mean squared error (MMSE) in position. A lower bound on the process noise variance was also expressed in terms of the maximum acceleration and deterministic tracking index. In this paper, the design methods for NCV Kalman filters with DWNA are extended to develop design methods for NCA Kalman filters with DWNA tracking maneuvering targets. The effectiveness of the design methods are illustrated via Monte Carlo simulations.

In this study, the target motion analysis methods, especially used for passive target tracking in submarines, are implemented using evolutionary algorithms. In target motion analysis problem, using a time sequence of transmitted noise directions of a sound source in an acoustic environment; the range, course and speed of the corresponding source are estimated. Size of the search space; ambient noise on the transmission and noise on sensor measurements; decreased observability in different problem scenarios and the need of fast and exact solution, evolutionary strategies, a strong variant of the evolutionary search algorithms, is applied to the problem and efficiency of the results are presented for selected scenarios.

In this paper, according to the characteristics of underwater target tracking, extended Kalman filter (EKF) algorithm was applied to address underwater bearing-only non-maneuverable target tracking problem. To ensure the observability in bearing-only passive target tracking, we use two sensor arrays in uniform rectilinear motion to track the single target. EKF is recursive Bayesian filter algorithm based on the linearization of the nonlinearities in the state and the measurement system. And the simulation experiment shows that, to the constant velocity single target, the bearings-only EKF algorithm with dual-array has good results, also the EKF has lower computation complexity than unscented Kalman filter and particle filter. It confirms the effectiveness of the EKF algorithm in solving the underwater bearing-only target tracking problem.

This paper describes a technique for combining state estimates from two nonlinear filters for the purpose of providing a global estimate that converges to the correct state value, while the estimates from the individual filters may not. The practical situation considered-occurs in target motion analysis. In this case, there are two extended Kalman filters in the tracking system, one processing bearing, and the other processing conical angle measurements provided by spatially separated sensors. Prior to an observer maneuver, the target parameters from each filter will not converge. However, by using the proposed technique, the global estimate-a combination of the two estimates--converges to the correct value without an observer maneuver, as the numerical results show.

Accurate contaminant prediction is very important for risk assessment and site remediation. Several predictive tools in the form of mathematical models have been used to model the movement and behavior of contaminants in groundwater. These deterministic models do not account for the heterogeneity and uncertainties in the subsurface environment. Discretization of the models spatially and temporally introduces approximation and truncation errors. In this research, to improve the accuracy of subsurface contaminant prediction in time and space and to assess the impact of first-order decay rate parameter estimation, Kalman filter coupled with Monte Carlo sampling was used in a specified three-dimensional domain space. The filter is perturbed with random Gaussian noise to reflect real life case of contaminant movement. Set of sparse observation points selected at specific locations are used to guide the filter at every time step to improve the accuracy of the prediction. The first-order decay rate parameter is estimated using Monte Carlo sampling method. The algorithms to generate the simulation results were run on Matlab 7.1. The efficacy of the Kalman filter coupled with Monte Carlo sampling, Kalman filter without Parameter Estimation and the numerical method were tested using Mean Absolute Error (MAE) and Maximum Absolute Error (Emax) equations. The results show that the Kalman filter coupled with Monte Carlo sampling performs better than both the Kalman filter without Parameter Estimation and the numerical method. Also, the Kalman filter coupled with Monte Carlo sampling is capable of reducing the error in the numerical solution by approximately 75% when Mean Absolute Error equation is used to estimate the prediction error. The error reduction is due to the adaptive nature of the Kalman filter to the observation data used in the simulation.

In bearings-only target motion analysis (BOTMA), the common hypothesis is that the observer maneuvers while the source is traveling according to a constant speed and course. But there is no reason that the roles of each protagonist cannot be exchanged. In this paper, we consider an uncommon scenario: the trajectory of the target is composed of two legs (i.e., a target brutally changes its heading while keeping its speed) and the observer does not maneuver. We prove that the trajectory of the target is observable under nonrestrictive conditions. A batch estimator is proposed, and its performance is compared with the classic Cramer-Rao lower bound (CRLB). Monte-Carlo simulations reveal the efficiency of the estimator. The robustness to a nonbrutal heading change is evaluated. Then an adhoc estimate taking the correct model into account is proposed and applied to simulated data. Again, its performance is compared with the CRLB, and its robustness is evaluated when the speed of the target changes. Finally, the respective performances of the target motion analysis (TMA) made by each mobile are compared.

The marine environmental noise formed by wind noise, rain noise, biological noise, sea surface waves, seismic disturbances, and so on is a kind of interference background field in underwater acoustic channels, which brings adverse effects to underwater acoustic target recognition. To improve the recognition accuracy of underwater targets under background noise interference, a bidirectional denoising autoencoder (BDAE) is proposed in this paper for underwater acoustic target signal denoising robust representation learning. The proposed bidirectional denoising autoencoder is an extension of the regular denoising autoencoder, which uses the original underwater acoustic target signals and their corresponding denoised signals to learn robust representations. We then measure the usefulness of the learned representations using a support vector machine classifier. Our proposed approach is verified on the ShipsEar database. Experimental results indicate that the proposed bidirectional denoising autoencoder can effectively learn the robust representations of underwater acoustic target signal denoising and is superior to the traditional methods.

Modern radars employ linear frequency modulated (LFM) waveforms for target tracking as the range-Doppler coupling enables better track accuracy in range. When tracking maneuvering targets with a nearly constant velocity (NCV) Kalman filter, the selection of the process noise variance is complicated by the fact that the process errors are modeled as white Gaussian, while target maneuvers are deterministic or highly correlated in time. In recent years, the deterministic tracking index was introduced and used to develop a relationship between the maximum acceleration of the target and the process noise variance that minimizes the maximum mean squared error (MMSE) in position. A lower bound on the process noise variance was also expressed in terms of the maximum acceleration and deterministic tracking index. In this paper, the design methods for NCV Kalman filters are extended to radar tracking with linear frequency modulation (LFM) waveforms. The effectiveness of the design methods are confirmed via Monte Carlo simulations.