arXiv subjects

Himali Singh

Publications and source records attributed to Himali Singh.

9 recordsLinked to original sources

arXiv2026

Inverse Stochastic Filtering for Inverse Cognition in Counter-adversarial systems

Recent advances in cognitive and counter-adversarial systems with the ability to infer their adversary's beliefs have garnered significant research interest in inverse filtering from a Bayesian perspective. Such counter-adversarial systems have potential applications where an autonomous system interacts with its environment, learns relevant information about it, and then adapts itself to achieve its goals optimally. An important example is the inverse cognition problem in cognitive radar-target dynamics. A cognitive radar adapts its waveform, beam pattern, and other parameters in real-time to accurately localize its target. An intelligent target can employ these inverse filtering results to evade detection and even deceive the adversarial radar. In this setting, a cognitive adversary or 'attacker' tracks its target of interest using a stochastic framework such as a Kalman filter (KF). The target or 'defender' then employs another inverse stochastic filter to infer the forward filter's estimates of the defender's state computed by the attacker. For instance, recently, inverse KF (I-KF) has been developed to predict the attacker's future steps by estimating its (forward) KF's estimates. Existing works on inverse stochastic filtering and inverse cognition consider either linear Gaussian or finite state-space models, which limits their applicability in many practical engineering problems. Hence, in this dissertation, we study inverse filtering in the general non-linear non-Gaussian system framework and develop inverse non-linear filters using different sub-optimal approaches.

eess.SP↗

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.

eess.SP↗

arXiv2024

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.

math.OC↗

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↗

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.

math.OC↗

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.

math.OC↗

arXiv2023

Counter-Adversarial Learning with Inverse Unscented Kalman Filter

In counter-adversarial systems, to infer the strategy of an intelligent adversarial agent, the defender agent needs to cognitively sense the information that the adversary has gathered about the latter. Prior works on the problem employ linear Gaussian state-space models and solve this inverse cognition problem by designing inverse stochastic filters. However, in practice, counter-adversarial systems are generally highly nonlinear. In this paper, we address this scenario by formulating inverse cognition as a nonlinear Gaussian state-space model, wherein the adversary employs an unscented Kalman filter (UKF) to estimate the defender's state with reduced linearization errors. To estimate the adversary's estimate of the defender, we propose and develop an inverse UKF (IUKF) system. We then derive theoretical guarantees for the stochastic stability of IUKF in the mean-squared boundedness sense. Numerical experiments for multiple practical applications show that the estimation error of IUKF converges and closely follows the recursive Cramér-Rao lower bound.

math.OC↗

arXiv2023

Multi-target Range and Angle detection for MIMO-FMCW radar with limited antennas

Multiple-input multiple-output (MIMO) radar has several advantages with respect to the traditional radar array systems in terms of performance and flexibility. However, in order to achieve high angular resolution, a MIMO radar requires a large number of transmit and receive antennas, which increases hardware design and computational complexities. Although spatial compressive sensing (CS) has been recently considered for a pulsed-waveform MIMO radar with sparse random arrays, such methods for the frequency-modulated continuous wave (FMCW) radar remain largely unexplored. In this context, we propose a novel multi-target localization algorithm in the range-angle domain for a MIMO FMCW radar with a sparse array of randomly placed transmit and receive elements. In particular, we first obtain the targets' range-delays using a discrete Fourier transform (DFT)-based focusing operation. The target angles are then recovered at each detected range using CS-based techniques exploiting the sparsity of the target scene. Our simulation results demonstrate the effectiveness of the proposed algorithm over the classical methods in detecting multiple targets with a sparse array.

eess.SP↗