arXiv subjects

Shovan Bhaumik

Publications and source records attributed to Shovan Bhaumik.

16 recordsLinked to original sources

arXiv2026

Risk Sensitive Filtering for Singular Systems subject to Round-Robin Protocol

This paper develops a risk sensitive (RS) Kalman filtering framework for discrete-time linear stochastic singular systems operating under communication constraints imposed by a round-robin protocol. Due to limited network bandwidth, only a subset of the available measurements can be transmitted at each sampling instant, resulting in a periodically varying measurement structure. By employing the Weierstrass canonical form (WCF), the singular system is transformed into an equivalent augmented state space model, yielding a round-robin induced periodic system (RRIPS). A recursive risk sensitive Kalman filter (RSKF) is then developed for the RRIPS through a Bayesian formulation and the minimization of an exponential quadratic cost function, from which the recursive filtering equations are obtained for the original singular system. To enhance robustness against modeling uncertainties and disturbances, an adaptive RS mechanism is introduced in which the risk parameter is adjusted online according to the available covariance information. This adaptive strategy guarantees the positive definiteness of the predicted covariance matrix while adjusting the degree of risk sensitivity to the prevailing estimation uncertainty. Furthermore, sufficient conditions ensuring the filter stability are established using the observability and controllability concepts of periodic systems. The proposed framework reduces to the standard KF for singular systems when the RS parameter vanishes and recovers the standard RSKF when the singular matrix reduces to the identity matrix. Finally, numerical results are presented to demonstrate the effectiveness, robustness, and improved estimation performance of the proposed approach in comparison with the standard KF.

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arXiv2025

Consensus Tracking of an Underwater Vehicle Using Weighted Harmonic Mean Density

This paper addresses an underwater target tracking problem in which a large number of sonobuoy sensors are deployed on a surveillance region. The region is divided into several sub-regions, where a single tracker, capable of generating track is installed. Each sonobuoy can measure the direction of arrival of acoustic signals (known as bearing angles) and communicate the measurements with the local tracker. Further, each local tracker can communicate with all other trackers, where each of them can exchange their estimate and finally a consensus is reached. We propose a weighted harmonic mean density (HMD) based tracking to reach a consensus and provide a solution for the fusion of Gaussian densities. In this approach, optimal weights are assigned by minimizing the Kullback-Leibler divergence measure. Performance of the proposed method is measured using root mean square error, percentage of track divergence, and normalized estimation error squared. Simulation results demonstrate that the optimized HMD-based fusion outperforms existing fusion methods during a distributed tracking.

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arXiv2025

Bearing-only Tracking using Towed Sensor-Array with Non-Gaussian Measurement Noise Statistics

Passive bearing-only tracking (BOT) estimates the target states by utilising noisy bearing measurements captured by a sensor array. The sensor array is often towed behind the ship, using a long flexible cable to reduce interference from the own-ship's inherent noises. This forms a towed cable sensor-array system (TCSAS). During BOT, the tow-ship has to perform a manoeuvre to make the tracking system observable. Such a manoeuvre destabilises the TCSAS, thus making its exact location unknown \emph{w.r.t.} tow-ship. However, it is very crucial to know the exact location of the towed sensor-array to perform efficient and reliable target state estimation. The existing BOT approaches perform TMA during own-ship manoeuvre either by pausing the measurement updation step of the estimation algorithm or assuming a fixed aft position for the towed sensor-array. These assumptions lead to unreliable state estimation. To address this, we propose a dynamic model for TCSAS, using a lumped mass approach, which will provide the location of the sensor array during the own-ship manoeuvre. This location will be fed to the state estimation algorithm. The dynamic of TCSAS in 3D space is obtained by solving the equations obtained from the moment balance condition and quasi-static equilibrium condition at the lumped mass points. Moreover, the bearing data captured by the towed sensor-array is corrupted with non-Gaussian noise. It is handled using the maximum correntropy criterion based Kalman filter with a kernel bandwidth selection technique, proposed in this paper. The proposed sensor-array dynamic model is verified for a real-world BOT engagement scenario.

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arXiv2025

Gaussian Integral based Bayesian Smoother

This work introduces the Gaussian integration to address a smoothing problem of a nonlinear stochastic state space model. The probability densities of states at each time instant are assumed to be Gaussian, and their means and covariances are evaluated by utilizing the odd-even properties of Gaussian integral, which are further utilized to realize Rauch-Tung-Striebel (RTS) smoothing expressions. Given that the Gaussian integration provides an exact solution for the integral of a polynomial function over a Gaussian probability density function, it is anticipated to provide more accurate results than other existing Gaussian approximation-based smoothers such as extended Kalman, cubature Kalman, and unscented Kalman smoothers, especially when polynomial types of nonlinearity are present in the state space models. The developed smoothing algorithm is applied to the Van der Pol oscillator, where the nonlinearity associated with their dynamics is represented using polynomial functions. Simulation results are provided to demonstrate the superiority of the proposed algorithm.

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arXiv2024

On Pooling-Based Track Fusion Strategies : Harmonic Mean Density

In a distributed sensor fusion architecture, using standard Kalman filter (naive fusion) can lead to degraded results as track correlations are ignored and conservative fusion strategies are employed as a sub-optimal alternative to the problem. Since, Gaussian mixtures provide a flexible means of modeling any density, therefore fusion strategies suitable for use with Gaussian mixtures are needed. While the generalized covariance intersection (CI) provides a means to fuse Gaussian mixtures, the procedure is cumbersome and requires evaluating a non-integer power of the mixture density. In this paper, we develop a pooling-based fusion strategy using the harmonic mean density (HMD) interpolation of local densities and show that the proposed method can handle both Gaussian and mixture densities without much changes to the framework. Mathematical properties of the proposed fusion strategy are studied and simulated on 2D and 3D maneuvering target tracking scenarios. The simulations suggest that the proposed HMD fusion performs better than other conservative strategies in terms of root-mean-squared error while being consistent.

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arXiv2024

Trigonometric Moments of a Generalized von Mises Distribution in 2-D Range-Only Tracking

A 2D range-only tracking scenario is non-trivial due to two main reasons. First, when the states to be estimated are in Cartesian coordinates, the uncertainty region is multi-modal. The second reason is that the probability density function of azimuth conditioned on range takes the form of a generalized von Mises distribution, which is hard to tackle. Even in the case of implementing a uni-modal Kalman filter, one needs expectations of trigonometric functions of conditional bearing density, which are not available in the current literature. We prove that the trigonometric moments (circular moments) of the azimuth density conditioned on range can be computed as an infinite series, which can be sufficiently approximated by relatively few terms in summation. The solution can also be generalized to any order of the moments. This important result can provide an accurate depiction of the conditional azimuth density in 2D range-only tracking geometries. We also present a simple optimization problem that results in deterministic samples of conditional azimuth density from the knowledge of its circular moments leading to an accurate filtering solution. The results are shown in a two-dimensional simulation, where the range-only sensor platform maneuvers to make the system observable. The results prove that the method is feasible in such applications.

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arXiv2024

Maximum Correntropy Polynomial Chaos Kalman Filter for Underwater Navigation

This paper develops an underwater navigation solution that utilizes a strapdown inertial navigation system (SINS) and fuses a set of auxiliary sensors such as an acoustic positioning system, Doppler velocity log, depth meter, attitude meter, and magnetometer to accurately estimate an underwater vessel's position and orientation. The conventional integrated navigation system assumes Gaussian measurement noise, while in reality, the noises are non-Gaussian, particularly contaminated by heavy-tailed impulsive noises. To address this issue, and to fuse the system model with the acquired sensor measurements efficiently, we develop a square root polynomial chaos Kalman filter based on maximum correntropy criteria. The filter is initialized using acoustic beaconing to accurately locate the initial position of the vehicle. The computational complexity of the proposed filter is calculated in terms of flops count. The proposed method is compared with the existing maximum correntropy sigma point filters in terms of estimation accuracy and computational complexity. The simulation results demonstrate an improved accuracy compared to the conventional deterministic sample point filters.

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arXiv2024

Dynamics of a Towed Cable with Sensor-Array for Underwater Target Motion Analysis

During a war situation, many times an underwater target motion analysis (TMA) is performed using bearing-only measurements, obtained from a sensor array, which is towed by an own-ship with the help of a connected cable. It is well known that the own-ship is required to perform a manoeuvre in order to make the system observable and localise the target successfully. During the maneuver, it is important to know the location of the sensor array with respect to the own-ship. This paper develops a dynamic model of a cable-sensor array system to localise the sensor array, which is towed behind a sea-surface vessel. We adopt a lumped-mass approach to represent the towed cable. The discretized cable elements are modelled as an interconnected rigid body, kinematically related to one another. The governing equations are derived by balancing the moments acting on each node. The derived dynamics are solved simultaneously for all the nodes to determine the orientation of the cable and sensor array. The position of the sensor array obtained from this proposed model will further be used by TMA algorithms to enhance the accuracy of the tracking system.

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arXiv2023

Tracking an Underwater Target with Unknown Measurement Noise Statistics Using Variational Bayesian Filters

This paper considers a bearings-only tracking problem using noisy measurements of unknown noise statistics from a passive sensor. It is assumed that the process and measurement noise follows the Gaussian distribution where the measurement noise has an unknown non-zero mean and unknown covariance. Here an adaptive nonlinear filtering technique is proposed where the joint distribution of the measurement noise mean and its covariance are considered to be following normal inverse Wishart distribution (NIW). Using the variational Bayesian (VB) method the estimation technique is derived with optimized tuning parameters i.e, the confidence parameter and the initial degree of freedom of the measurement noise mean and the covariance, respectively. The proposed filtering technique is compared with the adaptive filtering techniques based on maximum likelihood and maximum aposteriori in terms of root mean square error in position and velocity, bias norm, average normalized estimation error squared, percentage of track loss, and relative execution time. Both adaptive filtering techniques are implemented using the traditional Gaussian approximate filters and are applied to a bearings-only tracking problem illustrated with moderately nonlinear and highly nonlinear scenarios to track a target following a nearly straight line path. Two cases are considered for each scenario, one when the measurement noise covariance is static and another when the measurement noise covariance is varying linearly with the distance between the target and the ownship. In this work, the proposed adaptive filters using the VB approach are found to be superior to their corresponding adaptive filters based on the maximum aposteriori and the maximum likelihood at the expense of higher computation cost.

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arXiv2023

Modeling and Estimation for Systems with Randomly Delayed Measurements and Packet Dropouts

A networked system often uses a shared communication network to transmit the measurements to a remotely located estimation center. Due to the limited bandwidth of the channel, a delay may appear while receiving the measurements. This delay can be arbitrary step random, and packets are sometimes dropped during transmission as it exceeds a certain permissible number. In this paper, such measurements are modeled with the Poisson distribution, which allows the user to determine the maximum delay the system might suffer. When the measurement delay exceeds the permissible number, the packet dropout happens. Based on the proposed model, we solve the problem by assuming that the prior and posterior densities of states are Gaussian and derive the expression of the estimated state and the error covariance. Later, relaxing the Gaussian assumption for densities, we propose a solution with the help of the sequential Monte Carlo (SMC) approach. The proposed SMC method divides the set of particles into several groups, where each group supports the possibility that the received measurement is delayed by a certain number of steps. The strength of an individual group is determined by the probability of a measurement being delayed with the same number of steps that the group represents. This approach estimates the states and also assesses the amount of delay from the received measurements. Finally, the developed estimators are implemented on two nonlinear estimation problems, and the simulation results are compared. The proposed SMC approach shows better results compared to the designed Gaussian delay filters and existing particle filters with delay.

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arXiv2023

Risk Sensitive Filtering with Randomly Delayed Measurements

Conventional Bayesian estimation requires an accurate stochastic model of a system. However, this requirement is not always met in many practical cases where the system is not completely known or may differ from the assumed model. For such a system, we consider a scenario where the measurements are transmitted to a remote location using a common communication network and due to which, a delay is introduced while receiving the measurements. The delay that we consider here is random and one step maximum at a given time instant. For such a scenario, this paper develops a robust estimator for a linear Gaussian system by minimizing the risk sensitive error criterion that is defined as an expectation of the accumulated exponential quadratic error. The criteria for the stability of the risk sensitive Kalman filter (RSKF) are derived and the results are used to study the stability of the developed filter. Further, it is assumed that the latency probability related to delay is not known and it is estimated by maximizing the likelihood function. Simulation results suggest that the proposed filter shows acceptable performance under the nominal conditions, and it performs better than the Kalman filter for randomly delayed measurements and the RSKF in presence of both the model uncertainty and random delays.

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arXiv2023

Robust Maximum Correntropy Kalman Filter

The Kalman filter provides an optimal estimation for a linear system with Gaussian noise. However when the noises are non-Gaussian in nature, its performance deteriorates rapidly. For non-Gaussian noises, maximum correntropy Kalman filter (MCKF) is developed which provides an improved result. But when the system model differs from nominal consideration, the performance of the MCKF degrades. For such cases, we have proposed a new robust filtering technique which maximize a cost function defined by exponential of weighted past and present errors along with the Gaussian kernel function. By solving this cost criteria we have developed prior and posterior mean and covariance matrix propagation equations. By maximizing the correntropy function of error matrix, we have selected the kernel bandwidth value at each time step. Further the conditions for convergence of the proposed algorithm is also derived. Two numerical examples are presented to show the usefulness of the new filtering technique.

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arXiv2023

Resolving Left-Right Ambiguity During Bearing Only Tracking of an Underwater Target Using Towed Array

In bearing only tracking using a towed array, the array can sense the bearing angle of the target but is unable to differentiate whether the target is on the left or the right side of the array. Thus, the traditional tracking algorithm generates tracks in both the sides of the array which create difficulties when interception is required. In this paper, we propose a method based on likelihood of measurement which along with the estimators can resolve left-right ambiguity and track the target. A case study has been presented where the target moves (a) in a straight line with a near constant velocity, (b) maneuvers with a turn, and observer takes a `U'-like maneuver. The method along with the various estimators has been applied which successfully resolves the ambiguity and tracks the target. Further, the tracking results are compared in terms of the root mean square error in position and velocity, bias norm, \% of track loss and the relative execution time.

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arXiv2019

Nonlinear State Estimation using Gaussian Integral

In this letter, a new filtering technique to solve a nonlinear state estimation problem has been developed. It is well known that for a nonlinear system, the prior and posterior probability density functions (pdf) are non-Gaussian in nature. However, in this work, they are assumed as Gaussian and subsequently mean, and covariance of them are calculated. In the proposed method, nonlinear functions of process dynamics and measurement are expressed in a polynomial form with the help of Taylor series expansion. In order to calculate the prior and the posterior mean and covariance, the functions are integrated over the Gaussian pdf with the help of Gaussian integral. The performance of the proposed method is tested in two nonlinear state estimation problems. The simulation results show that the proposed filter provides more accurate result than other existing deterministic sample point filters such as cubature Kalman filter, unscented Kalman filter, etc.

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arXiv2018

Adaptive Sparse-grid Gauss-Hermite Filter

In this paper, a new nonlinear filter based on sparse-grid quadrature method has been proposed. The proposed filter is named as adaptive sparse-grid Gauss-Hermite filter (ASGHF). Ordinary sparse-grid technique treats all the dimensions equally, whereas the ASGHF assigns a fewer number of points along the dimensions with lower nonlinearity. It uses adaptive tensor product to construct multidimensional points until a predefined error tolerance level is reached. The performance of the proposed filter is illustrated with two nonlinear filtering problems. Simulation results demonstrate that the new algorithm achieves a similar accuracy as compared to sparse-grid Gauss-Hermite filter (SGHF) and Gauss-Hermite filter (GHF) with a considerable reduction in computational load. Further, in the conventional GHF and SGHF, any increase in the accuracy level may result in an unacceptably high increase in the computational burden. However, in ASGHF, a little increase in estimation accuracy is possible with a limited increase in computational burden by varying the error tolerance level and the error weighting parameter. This enables the online estimator to operate near full efficiency with a predefined computational budget.

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arXiv2018

Particle Filter for Randomly Delayed Measurements with Unknown Latency Probability

This paper focuses on designing a particle filter for randomly delayed measurements with an unknown latency probability. A generalized measurement model is adopted which includes measurements that are delayed randomly by an arbitrary but fixed maximum number of the steps, along with random packet drops. Recursion equation for importance weights is derived under the presence of random delays. Offline and online algorithms for identification of the unknown latency parameter using the maximum likelihood criterion are proposed. Further, this work explores the conditions which ensure the convergence of the proposed particle filter. Finally, two numerical examples concerning problems of non-stationary growth model and the bearing-only tracking are simulated to show the effectiveness and superiority of the proposed filter.

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