This article concerns the challenge of reliable broadband passive sonar target detection and tracking in complex acoustic environments. Addressing this challenge is becoming increasingly crucial for safeguarding underwater infrastructure, monitoring marine life, and providing defense during seabed warfare. To that end, a solution is proposed based on a vector-autoregressive model for the ambient noise and a heavy-tailed statistical model for the distribution of the raw hydrophone data. These models are integrated into a Bernoulli track-before-detect (TkBD) filter that estimates the probability of target existence, target bearing, and signal-to-noise ratio (SNR). The proposed solution is evaluated on both simulated and real-world data, demonstrating the effectiveness of the proposed ambient noise modeling and the statistical model for the raw hydrophone data samples to obtain early target detection and robust target tracking. The simulations show that the SNR at which the target can be detected is reduced by 4 dB compared to when using the standard constant false alarm rate detector-based tracker. Further, the test with real-world data shows that the proposed solution increases the target detection distance from 250 to 390 m. The presented results illustrate that the TkBD technology, in combination with data-driven ambient noise modeling and heavy-tailed statistical signal models, can enable reliable broadband passive sonar target detection and tracking in complex acoustic environments and lower the SNR required to detect and track targets.

Typical iterated filters, such as the iterated extended Kalman filter (IEKF), KF (IUKF), and iterated posterior linearization filter (IPLF), have been developed to improve the linearization point (or density) of the likelihood linearization in the well-known extended KF (EKF) and unscented KF (UKF). A shortcoming of typical iterated filters is that they do not treat the linearization of the transition model of the system. To remedy this shortcoming, we introduce dynamically iterated filters (DIFs), a unified framework for iterated linearization-based nonlinear filters that deals with nonlinearities in both the transition model and the likelihood, thereby constituting a generalization of the aforementioned iterated filters. We further establish a relationship between the general DIF and the approximate iterated Rauch–Tung–Striebel smoother. This relationship allows for a Gauss–Newton interpretation, which in turn enables explicit step-size correction, leading to damped versions of the DIFs. The developed algorithms, both damped and non-damped, are numerically demonstrated in three examples, showing superior mean-squared error as well as improved parameter tuning robustness as compared to the analogous standard iterated filters.

Bearings-only target tracking using raw acoustic data typically achieves better tracking performance at lower signal-to-noise ratios (SNR) compared to approaches that rely on direction-of-arrival (DOA) preprocessing. However, using raw data directly as observations renders standard Kalman filter-type algorithms inapplicable, since the likelihood when using raw acoustic data depends only on second-order statistics. While particle filter-based methods can overcome this limitation, they are often computationally demanding, particularly in high-dimensional state spaces. To address this, we present a maximum a posteriori-based method to approximate the Bayesian filter recursions, which can handle likelihoods that depend only on the second-order statistics of the observations. The method formulates the observation update as an optimization problem and applies a Laplace approximation to estimate the posterior mean and covariance. This enables the direct use of raw observations while avoiding the computational cost associated with particle filtering. The method is validated through simulations and real-world data from a sea trial. Results show that the proposed approach achieves robust tracking performance at low SNR, outperforming the traditional target-tracking approach that uses DOA-based preprocessing of the acoustic data. Hence, it offers a computationally efficient alternative to particle filters for target tracking applications that utilize raw acoustic data.

Magnetic-field simultaneous localization and mapping (SLAM) using consumer-grade inertial and magnetometer sensors offers a scalable, cost-effective solution for indoor localization. However, the rapid error accumulation in the inertial navigation process limits the feasible exploratory phases of these systems. Advances in magnetometer array processing have demonstrated that odometry information, i.e., displacement and rotation information, can be extracted from local magnetic field variations and used to create magnetic-field odometry-aided inertial navigation systems. The error growth rate of these systems is significantly lower than that of standalone inertial navigation systems. This study seeks an answer to whether a magnetic-field SLAM system fed with measurements from a magnetometer array can indirectly extract odometry information - without requiring algorithmic modifications - and thus sustain longer exploratory phases. The theoretical analysis and simulation results show that such a system can extract odometry information and indirectly create a magnetic field odometry-aided inertial navigation system during the exploration phases. However, practical challenges related to map resolution and computational complexity remain significant.

The problem of geoacoustic inversion using acoustic transmission loss measurements is considered. A recursive Bayesian method based on the unscented Kalman filter is proposed to sequentially estimate the unknown sound propagation model parameters and select the measurement points that minimize the estimation uncertainty. The proposed method is evaluated in a simulation study emulating the estimation of geoacoustic seabed parameters in shallow waters. The results show that the proposed sequential measurement point selection method improves estimation performance compared to a fixed preplanned measurement point selection strategy. Moreover, the distribution of the selected measurement points over time shows that the proposed method tends to choose measurement points associated with a lower sound speed.

Current autonomous underwater vehicles generally use multibeam sonars and Doppler velocity logs to aid their inertial navigation systems. While effective, these active acoustic systems can reveal the presence of a vehicle, making them unsuitable for covert operations. This report presents the key findings from a research project investigating the feasibility of using a quantum magnetometer array as a substitute or complement to active sonar sensors in autonomous underwater vehicles. Field and sea trials demonstrate that the magnetic field near the Earth’s surface exhibits significant spatial variations, enabling speed estimation and absolute positioning using quantum magnetometer arrays. Theoretical analysis shows that temporal variations in the Earth’s magnetic field, rather than sensor noise, set the fundamental performance limit for estimating vehicle speed using a magnetometer sensor array. However, if a continuous forward communication link with a rate of ∼ 10 bits/s is available, the temporal variation can, to a large extent, be removed by transmission of correction data. Temporal variations also make map-matching-based positioning challenging. But by estimating the magnetic-field gradient using a magnetometer array, temporal variations can be effectively canceled, making gradient-based magnetic-field map-matching a promising approach. Further work is needed to quantify the effects of platform-induced disturbances and map imperfections. 

Basis Function (BF) expansions are a cornerstone of any engineer's toolbox for computational function approximation which shares connections with both neural networks and Gaussian processes. Even though BF expansions are an intuitive and straightforward model to use, they suffer from quadratic computational complexity in the number of BFs if the predictive variance is to be computed. We develop a method to automatically select the most important BFs for prediction in a sub-domain of the model domain. This significantly reduces the computational complexity of computing predictions while maintaining predictive accuracy. The proposed method is demonstrated using two numerical examples, where reductions up to 50-75% are possible without significantly reducing the predictive accuracy.

Maintaining consistent uncertainty estimates in localization systems is crucial as the perceived uncertainty commonly affects high-level system components, such as control or decision processes. A method for constructing an observability-constrained magnetic field-aided inertial navigation system is proposed to address the issue of erroneous yaw observability, which leads to inconsistent estimates of yaw uncertainty. The proposed method builds upon the previously proposed observability-constrained extended Kalman filter and extends it to work with a magnetic field-based odometry-aided inertial navigation system. The proposed method is evaluated using simulation and real-world data, showing that (i) the system observability properties are preserved, (ii) the estimation accuracy increases, and (iii) the perceived uncertainty calculated by the EKF is more consistent with the true uncertainty of the filter estimates.

We present an algorithm to estimate and quantify the uncertainty of the accelerometers' relative geometry in an inertial sensor array. We formulate the calibration problem as a Bayesian estimation problem and propose an algorithm that samples the accelerometer positions' posterior distribution using Markov chain Monte Carlo. By identifying linear substructures of the measurement model, the unknown linear motion parameters are analytically marginalized, and the remaining non-linear motion parameters are numerically marginalized. The numerical marginalization occurs in a low dimensional space where the gyroscopes give information about the motion. This combination of information from gyroscopes and analytical marginalization allows the user to make no assumptions of the motion before the calibration. It thus enables the user to estimate the accelerometer positions' relative geometry by simply exposing the array to arbitrary twisting motion. We show that the calibration algorithm gives good results on both simulated and experimental data, despite sampling a high dimensional space.

A maximum likelihood estimator is presented for self-calibrating both accelerometers and gyroscopes in an inertial sensor array, including scale factors, misalignments, biases, and sensor positions. By simultaneous estimation of the calibration parameters and the motion dynamics of the array, external equipment is not required for the method. A computational efficient iterative optimization method is proposed where the calibration problem is divided into smaller subproblems. Further, an identifiability analysis of the calibration problem is presented. The analysis shows that it is sufficient to know the magnitude of the local gravity vector and the average scale factor gain of the gyroscopes, and that the array is exposed to two types of motions for the calibration problem to be well defined. The proposed estimator is evaluated by real-world experiments and by Monte Carlo simulations. The results show that the parameters can be consistently estimated and that the calibration significantly improves the accuracy of the motion estimation. This enables on-the-fly calibration of small inertial sensors arrays by simply twisting them by hand.