arXiv subjects

Arpan Chattopadhyay

Publications and source records attributed to Arpan Chattopadhyay.

At least 19 recordsLinked to original sources

arXiv2026

Multi-Target Micro-Motion Parameter Estimation using MIMO-FMCW Radar with Limited Measurements

This work presents a compressive sensing-based approach for estimating the micro-motion parameters of targets with rotating components, such as small unmanned aerial vehicles (UAVs) with propellers, using fewer measurements than conventional methods. A multiple-input-multiple-output (MIMO) frequency-modulated continuous-wave (FMCW) radar employing a randomly spaced sparse linear antenna array is utilized. Random sequences of linear frequency-modulated (LFM) chirps are transmitted to enable random sampling in the slow-time domain. At first, the range, velocity, and angle of arrival (AoA) of the targets are estimated to identify the bulk motion. A three-dimensional point target response (3D-PTR) is then constructed using the estimated parameters and subtracted from the total radar return to extract the micro-Doppler signatures associated with target rotation. These residual signals are processed within a compressive sensing (CS) framework using the one-dimensional orthogonal matching pursuit (1D-OMP) algorithm to jointly estimate the propellers' rotation frequencies and blade lengths with the help of a parametric dictionary. The proposed approach is also extended to a multi-target scenario. Simulation results demonstrate that the proposed approach accurately estimates micro-motion parameters with limited measurements in the slow-time and the spatial dimensions, validating its potential for UAV detection applications. These estimated parameters are then used to distinguish among various UAV motion types using a classification framework based on a set of decision rules.

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arXiv2026

Low-Complexity Super-Resolution Signature Estimation of XL-MIMO FMCW Radar

Extremely Large-Scale (XL) multiple input multiple output (MIMO) antenna systems combined with ultra-wide signal bandwidth (BW) offer the potential for ultra-high-resolution sensing in frequency modulated continuous wave (FMCW) radars. However, the use of ultra-wide BW results in significant spatial delays across the array aperture, comparable to the range resolution, leading to the spatial wideband effect (SWE). SWE introduces coupling between the range and angle domains, rendering conventional narrowband signal processing techniques ineffective for target signature estimation. In this paper, we propose an efficient super-resolution signature estimation technique for XL-MIMO FMCW radars operating under SWE, leveraging compressive sensing (CS) methods. The proposed 2D CS-based approach offers low computational complexity, making it highly suitable for real-time applications in large-scale radar systems. Numerical simulation results validate the superior performance of the proposed method compared to existing wideband and narrowband estimation techniques.

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arXiv2025

Quickest Change Point Detection with Measurements over a Lossy Link

Motivated by Industry 4.0 applications, we consider quickest change detection (QCD) of an abrupt change in a process when its measurements are transmitted by a sensor over a lossy wireless link to a decision maker (DM). The sensor node samples measurements using a Bernoulli sampling process, and places the measurement samples in the transmit queue of its transmitter. The transmitter uses a retransmit-until-success transmission strategy to deliver packets to the DM over the lossy link, in which the packet losses are modeled as a Bernoulli process, with different loss probabilities before and after the change. We pose the QCD problem in the non-Bayesian setting under Lorden's framework, and propose a CUSUM algorithm. By defining a suitable Markov process, involving the DM measurements and the queue length process, we show that the problem reduces to QCD in a Markov process. Characterizing the information measure per measurement sample at the DM, we establish the asymptotic optimality of our algorithm when the false alarm rate tends to zero. Further, when the DM receives incomplete data due to channel loss, we present asymptotically optimal QCD algorithms by suitably modifying the CUSUM algorithm. We then explore the last-come-first-served (LCFS) queuing discipline at the sensor transmit queue to lower detection delay in the non-asymptotic case. Next, we consider the case of multiple sensors, each with its own wireless transmitter queue, and show that our analysis extends to the case of multiple homogeneous sensors. When the sensors are heterogeneous, we present a sensor scheduling algorithm that minimizes detection delay by balancing the trade-off between the age of the observations and their information content. Numerical analysis demonstrate trade-offs that can be used to optimize system design parameters in the non-asymptotic regime.

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arXiv2025

Multi-target Range, Doppler and Angle estimation in MIMO-FMCW Radar with Limited Measurements

Multiple-input multiple-output (MIMO) radar offers several performance and flexibility advantages over traditional radar arrays. However, high angular and Doppler resolutions necessitate a large number of antenna elements and the transmission of numerous chirps, leading to increased hardware and computational complexity. While compressive sensing (CS) has recently been applied to pulsed-waveform radars with sparse measurements, its application to frequency-modulated continuous wave (FMCW) radar for target detection remains largely unexplored. In this paper, we propose a novel CS-based multi-target localization algorithm in the range, Doppler, and angular domains for MIMO-FMCW radar, where we jointly estimate targets' velocities and angles of arrival. To this end, we present a signal model for sparse-random and uniform linear arrays based on three-dimensional spectral estimation. For range estimation, we propose a discrete Fourier transform (DFT)-based focusing and orthogonal matching pursuit (OMP)-based techniques, each with distinct advantages, while two-dimensional CS is used for joint Doppler-angle estimation. Leveraging the properties of structured random matrices, we establish theoretical uniform and non-uniform recovery guarantees with high probability for the proposed framework. Our numerical experiments demonstrate that our methods achieve similar detection performance and higher resolution compared to conventional DFT and MUSIC with fewer transmitted chirps and antenna elements.

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arXiv2025

Age-of-information minimization under energy harvesting and non-stationary environment

This work focuses on minimizing the age of information for multiple energy harvesting sources that sample data and transmit it to a sink node. At each time, the central scheduler selects one of the sources to probe the quality of its channel to the sink node, and then the assessed channel quality is utilized to determine whether a source will sample and send the packet. For a single source case, we assume that the probed channel quality is known at each time instant, model the problem of AoI minimization as a Markov decision process, and prove the optimal sampling policy threshold structure. We then use this threshold structure and propose an AEC-SW-UCRL2 algorithm to handle unknown and time varying energy harvesting rate and channel statistics, motivated by the popular SWUCRL2 algorithm for non stationary reinforcement learning. This algorithm is applicable when an upper bound is available for the total variation of each of these quantities over a time horizon. Furthermore, in situations where these variation budgets are not accessible, we introduce the AEC-BORL algorithm, motivated by the well known BORL algorithm. For the multiple source case, we demonstrate that the AoI minimization problem can be formulated as a constrained MDP, which can be relaxed using a Lagrange multiplier and decoupled into sub problems across source nodes. We also derive Whittle index based source scheduling policy for probing and an optimal threshold policy for source sampling. We next leverage this Whittle index and threshold structure to develop the WIT-SW-UCRL2 algorithm for unknown time varying energy harvesting rates and channel statistics under their respective variation budgets. Moreover, we also proposed a Whittle index and threshold based bandit over reinforcement learning (WIT-BORL) algorithm for unknown variation budgets. Finally, we numerically demonstrate the efficacy of our algorithms.

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arXiv2025

Quickest change detection for UAV-based sensing

This paper addresses the problem of quickest change detection (QCD) at two spatially separated locations monitored by a single unmanned aerial vehicle (UAV) equipped with a sensor. At any location, the UAV observes i.i.d. data sequentially in discrete time instants. The distribution of the observation data changes at some unknown, arbitrary time and the UAV has to detect this change in the shortest possible time. Change can occur at most at one location over the entire infinite time horizon. The UAV switches between these two locations in order to quickly detect the change. To this end, we propose Location Switching and Change Detection (LS-CD) algorithm which uses a repeated one-sided sequential probability ratio test (SPRT) based mechanism for observation-driven location switching and change detection. The primary goal is to minimize the worst-case average detection delay (WADD) while meeting constraints on the average run length to false alarm (ARL2FA) and the UAV's time-averaged energy consumption. We provide a rigorous theoretical analysis of the algorithm's performance by using theory of random walk. Specifically, we derive tight upper and lower bounds to its ARL2FA and a tight upper bound to its WADD. In the special case of a symmetrical setting, our analysis leads to a new asymptotic upper bound to the ARL2FA of the standard CUSUM algorithm, a novel contribution not available in the literature, to our knowledge. Numerical simulations demonstrate the efficacy of LS-CD.

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arXiv2025

Inverse Particle Filter

In cognitive systems, recent emphasis has been placed on studying the cognitive processes of the subject whose behavior was the primary focus of the system's cognitive response. This approach, known as inverse cognition, arises in counter-adversarial applications and has motivated the development of inverse Bayesian filters. In this context, a cognitive adversary, such as a radar, uses a forward Bayesian filter to track its target of interest. An inverse filter is then employed to infer the adversary's estimate of the target's or defender's state. Previous studies have addressed this inverse filtering problem by introducing methods like the inverse Kalman filter (KF), inverse extended KF, and inverse unscented KF. However, these filters typically assume additive Gaussian noise models and/or rely on local approximations of non-linear dynamics at the state estimates, limiting their practical application. In contrast, this paper adopts a global filtering approach and presents the development of an inverse particle filter (I-PF). The particle filter framework employs Monte Carlo (MC) methods to approximate arbitrary posterior distributions. Moreover, under mild system-level conditions, the proposed I-PF demonstrates convergence to the optimal inverse filter. Additionally, we propose the differentiable I-PF to address scenarios where system information is unknown to the defender. Using the recursive Cramer-Rao lower bound and non-credibility index (NCI), our numerical experiments for different systems demonstrate the estimation performance and time complexity of the proposed filter.

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arXiv2025

Minimizing Age of Detection for a Markov Source over a Lossy Channel

Monitoring a process/phenomenon of specific interest is prevalent in Cyber-Physical Systems (CPS), remote healthcare, smart buildings, intelligent transport, industry 4.0, etc. A key building block of the monitoring system is a sensor sampling the process and communicating the status updates to a monitor for detecting events of interest. Measuring the freshness of the status updates is essential for the timely detection of events, and it has received significant research interest in recent times. In this paper, we propose a new freshness metric, Age of Detection (AoD), for monitoring the state transitions of a Discrete Time Markov Chain (DTMC) source over a lossy wireless channel. We consider the pull model where the sensor samples DTMC state whenever the monitor requests a status update. We formulate a Constrained Markov Decision Problem (CMDP) for optimising the AoD subject to a constraint on the average sampling frequency and solve it using the Lagrangian MDP formulation and Relative Value Iteration (RVI) algorithm. Our numerical results show interesting trade-offs between AoD, sampling frequency, and transmission success probability. Further, the AoD minimizing policy provides a lower estimation error than the Age of Information (AoI) minimizing policy, thus demonstrating the utility of AoD for monitoring DTMC sources.

cs.IT↗

arXiv2024

Whittle's index-based age-of-information minimization in multi-energy harvesting source networks

We consider the problem of source sampling and transmission scheduling for age-of-information minimization in a system consisting of multiple energy harvesting (EH) sources and a sink node. At each time, one of the sources is selected by the scheduler and the quality of its channel to the sink is measured. This probed channel quality is then used to decide whether a source will sample an observation and transmit the packet to the sink in that time slot. We formulate this problem as a constrained Markov decision process (CMDP) assuming i.i.d. energy arrival and channel fading processes, and relax it using a Lagrange multiplier. We apply a near optimal Whittle's index policy to decide the node to be probed. Next, for the probed node, we derive an optimal threshold policy, which recommends source sampling and observation transmission from the probed source only when the measured channel quality is above a threshold. Our proposed policy is called Whittle's index and threshold based source scheduling and sampling (WITS3) policy. However, in order to calculate Whittle's indices, one must be aware of the underlying processes' transition matrices, which are occasionally concealed from the scheduler. Therefore, we further propose a variant Q-WITS3 of WITS3 based on Q-learning assisted by two timescale asynchronous stochastic approximation, which seeks to learn Whittle's indices and optimal policies for the case with unknown channel states and EH characteristics. Numerical results demonstrate the efficacy of our algorithms over two baseline policies.

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arXiv2024

Age-of-information minimization via opportunistic sampling by an energy harvesting source

Herein, minimization of time-averaged age-of-information (AoI) in an energy harvesting (EH) source setting is considered. The EH source opportunistically samples one or multiple processes over discrete time instants and sends the status updates to a sink node over a wireless fading channel. Each time, the EH node decides whether to probe the link quality and then decides whether to sample a process and communicate based on the channel probe outcome. The trade-off is between the freshness of information available at the sink node and the available energy at the source node. We use infinite horizon Markov decision process (MDP) to formulate the AoI minimization problem for two scenarios where energy arrival and channel fading processes are: (i) independent and identically distributed (i.i.d.), (ii) Markovian. In i.i.d. setting, after channel probing, the optimal source sampling policy is shown to be a threshold policy. Also, for unknown channel state and EH characteristics, a variant of the Q-learning algorithm is proposed for the two-stage action model, that seeks to learn the optimal policy. For Markovian system, the problem is again formulated as an MDP, and a learning algorithm is provided for unknown dynamics. Finally, numerical results demonstrate the policy structures and performance trade-offs.

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arXiv2024

Inverse Unscented Kalman Filter

Rapid advances in designing cognitive and counter-adversarial systems have motivated the development of inverse Bayesian filters. In this setting, a cognitive 'adversary' tracks its target of interest via a stochastic framework such as a Kalman filter (KF). The target or 'defender' then employs another inverse stochastic filter to infer the forward filter estimates of the defender computed by the adversary. For linear systems, the inverse Kalman filter (I-KF) has been recently shown to be effective in these counter-adversarial applications. In the paper, contrary to prior works, we focus on non-linear system dynamics and formulate the inverse unscented KF (I-UKF) to estimate the defender's state based on the unscented transform, or equivalently, statistical linearization technique. We then generalize this framework to unknown systems by proposing reproducing kernel Hilbert space-based UKF (RKHS-UKF) to learn the system dynamics and estimate the state based on its observations. Our theoretical analyses to guarantee the stochastic stability of I-UKF and RKHS-UKF in the mean-squared sense show that, provided the forward filters are stable, the inverse filters are also stable under mild system-level conditions. We show that, despite being a suboptimal filter, our proposed I-UKF is a conservative estimator, i.e., I-UKF's estimated error covariance upper-bounds its true value. Our numerical experiments for several different applications demonstrate the estimation performance of the proposed filters using recursive Cramér-Rao lower bound and non-credibility index (NCI).

math.OC↗

arXiv2024

Inverse Cubature and Quadrature Kalman filters

Recent research in inverse cognition with cognitive radar has led to the development of inverse stochastic filters that are employed by the target to infer the information the cognitive radar may have learned. Prior works addressed this inverse cognition problem by proposing inverse Kalman filter (I-KF) and inverse extended KF (I-EKF), respectively, for linear and non-linear Gaussian state-space models. However, in practice, many counter-adversarial settings involve highly non-linear system models, wherein EKF's linearization often fails. In this paper, we consider the efficient numerical integration techniques to address such non-linearities and, to this end, develop inverse cubature KF (I-CKF), inverse quadrature KF (I-QKF), and inverse cubature-quadrature KF (I-CQKF). For the unknown system model case, we develop reproducing kernel Hilbert space (RKHS)-based CKF. We derive the stochastic stability conditions for the proposed filters in the exponential-mean-squared-boundedness sense and prove the filters' consistency. Numerical experiments demonstrate the estimation accuracy of our I-CKF, I-QKF, and I-CQKF with the recursive Cramér-Rao lower bound as a benchmark.

math.OC↗

arXiv2024

Quickest Detection of False Data Injection Attack in Distributed Process Tracking

This paper addresses the problem of detecting false data injection (FDI) attacks in a distributed network without a fusion center, represented by a connected graph among multiple agent nodes. Each agent node is equipped with a sensor, and uses a Kalman consensus information filter (KCIF) to track a discrete time global process with linear dynamics and additive Gaussian noise. The state estimate of the global process at any sensor is computed from the local observation history and the information received by that agent node from its neighbors. At an unknown time, an attacker starts altering the local observation of one agent node. In the Bayesian setting where there is a known prior distribution of the attack beginning instant, we formulate a Bayesian quickest change detection (QCD) problem for FDI detection in order to minimize the mean detection delay subject to a false alarm probability constraint. While it is well-known that the optimal Bayesian QCD rule involves checking the Shriyaev's statistic against a threshold, we demonstrate how to compute the Shriyaev's statistic at each node in a recursive fashion given our non-i.i.d. observations. Next, we consider non-Bayesian QCD where the attack begins at an arbitrary and unknown time, and the detector seeks to minimize the worst case detection delay subject to a constraint on the mean time to false alarm and probability of misidentification. We use the multiple hypothesis sequential probability ratio test for attack detection and identification at each sensor. For unknown attack strategy, we use the window-limited generalized likelihood ratio (WL-GLR) algorithm to solve the QCD problem. Numerical results demonstrate the performances and trade-offs of the proposed algorithms.

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arXiv2023

Design and Detection of Controller Manipulation Attack on RIS Assisted Communication

In this paper, we introduce a new attack called controller manipulation attack (CMA) on a Reconfigurable Intelligent Surface (RIS) assisted communication system between a transmitter and a receiver. An attacker has the capability to manipulate the RIS controller and modify the phase shift induced by the RIS elements. The goal of the attacker is to minimize the data rate at the receiver, subject to a constraint on the attack detection probability at the receiver. We consider a number of attack detection models: (i) composite hypothesis testing based attack detection in a given fading block for known channel gains, (ii) sequential quickest detection of CMA in a given fading block for known channel gains, (iii) nonparametric hypothesis test to detect CMA for unknown channel gains over a fading block, and (iv) signal-to-noise-ratio (SNR) moment based detection over possibly multiple fading blocks. In the first case, a simple energy detector turns out to be uniformly most powerful (UMP). In the second case, simplification of the standard CUSUM test and its performance bounds are obtained. In the third case, non-parametric Kolmogorov-Smirnov test is further simplified to a simple per-sample double threshold test. The attack against these three detectors are designed via novel optimization formulations and semidefinite relaxation based solutions. In the fourth case, we consider threshold detection using moments of SNR; various SNR moments under no attack are obtained analytically for large RIS and then used to formulate the attack design problem as a linear program. Finally, numerical results illustrate the performance and trade-offs associated with the attack schemes, and also demonstrate their efficacy.

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arXiv2023

Inverse Extended Kalman Filter -- Part I: Fundamentals

Recent advances in counter-adversarial systems have garnered significant research attention to inverse filtering from a Bayesian perspective. For example, interest in estimating the adversary's Kalman filter tracked estimate with the purpose of predicting the adversary's future steps has led to recent formulations of inverse Kalman filter (I-KF). In this context of inverse filtering, we address the key challenges of non-linear process dynamics and unknown input to the forward filter by proposing an inverse extended Kalman filter (I-EKF). The purpose of this paper and the companion paper (Part II) is to develop the theory of I-EKF in detail. In this paper, we assume perfect system model information and derive I-EKF with and without an unknown input when both forward and inverse state-space models are non-linear. In the process, I-KF-with-unknown-input is also obtained. We then provide theoretical stability guarantees using both bounded non-linearity and unknown matrix approaches and prove the I-EKF's consistency. Numerical experiments validate our methods for various proposed inverse filters using the recursive Cramér-Rao lower bound as a benchmark. In the companion paper (Part II), we further generalize these formulations to highly non-linear models and propose reproducing kernel Hilbert space-based EKF to handle incomplete system model information.

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arXiv2023

Inverse Extended Kalman Filter -- Part II: Highly Non-Linear and Uncertain Systems

Counter-adversarial system design problems have lately motivated the development of inverse Bayesian filters. For example, inverse Kalman filter (I-KF) has been recently formulated to estimate the adversary's Kalman-filter-tracked estimates and hence, predict the adversary's future steps. The purpose of this paper and the companion paper (Part I) is to address the inverse filtering problem in non-linear systems by proposing an inverse extended Kalman filter (I-EKF). The companion paper proposed the theory of I-EKF (with and without unknown inputs) and I-KF (with unknown inputs). In this paper, we develop this theory for highly non-linear models, which employ second-order, Gaussian sum, and dithered forward EKFs. In particular, we derive theoretical stability guarantees for the inverse second-order EKF using the bounded non-linearity approach. To address the limitation of the standard I-EKFs that the system model and forward filter are perfectly known to the defender, we propose reproducing kernel Hilbert space-based EKF to learn the unknown system dynamics based on its observations, which can be employed as an inverse filter to infer the adversary's estimate. Numerical experiments demonstrate the state estimation performance of the proposed filters using recursive Cramér-Rao lower bound as a benchmark.

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arXiv2023

A Low-Delay MAC for IoT Applications: Decentralized Optimal Scheduling of Queues without Explicit State Information Sharing

We consider a system of several collocated nodes sharing a time slotted wireless channel, and seek a MAC (medium access control) that (i) provides low mean delay, (ii) has distributed control (i.e., there is no central scheduler), and (iii) does not require explicit exchange of state information or control signals. The design of such MAC protocols must keep in mind the need for contention access at light traffic, and scheduled access in heavy traffic, leading to the long-standing interest in hybrid, adaptive MACs. Working in the discrete time setting, for the distributed MAC design, we consider a practical information structure where each node has local information and some common information obtained from overhearing. In this setting, "ZMAC" is an existing protocol that is hybrid and adaptive. We approach the problem via two steps (1) We show that it is sufficient for the policy to be "greedy" and "exhaustive". Limiting the policy to this class reduces the problem to obtaining a queue switching policy at queue emptiness instants. (2) Formulating the delay optimal scheduling as a POMDP (partially observed Markov decision process), we show that the optimal switching rule is Stochastic Largest Queue (SLQ). Using this theory as the basis, we then develop a practical distributed scheduler, QZMAC, which is also tunable. We implement QZMAC on standard off-the-shelf TelosB motes and also use simulations to compare QZMAC with the full-knowledge centralized scheduler, and with ZMAC. We use our implementation to study the impact of false detection while overhearing the common information, and the efficiency of QZMAC. Our simulation results show that the mean delay with QZMAC is close that of the full-knowledge centralized scheduler.

cs.NI↗

arXiv2023

Inverse Reinforcement Learning With Constraint Recovery

In this work, we propose a novel inverse reinforcement learning (IRL) algorithm for constrained Markov decision process (CMDP) problems. In standard IRL problems, the inverse learner or agent seeks to recover the reward function of the MDP, given a set of trajectory demonstrations for the optimal policy. In this work, we seek to infer not only the reward functions of the CMDP, but also the constraints. Using the principle of maximum entropy, we show that the IRL with constraint recovery (IRL-CR) problem can be cast as a constrained non-convex optimization problem. We reduce it to an alternating constrained optimization problem whose sub-problems are convex. We use exponentiated gradient descent algorithm to solve it. Finally, we demonstrate the efficacy of our algorithm for the grid world environment.

cs.LG↗