Problems in sensor-level target tracking using filtering algorithms have been exhaustively studied in the literature. We are interested in two deeper ideas that go beyond sensor-level tracking to the meta-level:

*Inverse Filtering and Inference:*Given the response of a radar to our probe signal, how can we decide if the radar is cognitive? How can we estimate the radar’s accuracy? How can we reconstruct the tracked estimate of the enemy? How do we optimally probe the enemy’s radar to estimate its gain with minimum covariance? Such problems have significant relevance in electronic warfare.-
*Meta-level tracking:*Given track estimates, how do devise automated signal interpretation algorithms that assist a human operator to interpret the trajectory of a target? For example: How can one infer if a target is circling a building and therefore behaving suspiciously? A closed trajectory has long range dependencies – the beginning and end points coincide. Standard Markovian state space models cannot capture the long-range dependencies and spatial complexities of such trajectories. We have used natural language processing models such as stochastic context free grammars and reciprocal stochastic processes to model the trajectories of targets. Our meta-level target tracking goes beyond sensor-level tracking. We aim to infer the intent of the target – this constitutes the human-sensor interface (middleware).

### Relevant Presentations:

#### Rationalizing Youtube Commenting Behavior via Inverse Reinforcement Learning

#### Inverse Reinforcement Learning

#### Meta-Cognition: Inverse-Inverse Reinforcement Learning for Cognitive Radars

### Relevant Publications

**‘Identifying Coordination in a Cognitive Radar Network–A Multi-Objective Inverse Reinforcement Learning Approach‘**, L. Snow, V. Krishnamurthy, B. M. Sadler,*IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)*, 2023.**‘How can a Cognitive Radar Mask its Cognition?’**, K. Pattanayak, V. Krishnamurthy, C. Berry,*IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)*, 2022.**‘Adversarial radar inference: Inverse tracking, identifying cognition, and designing smart interference‘**, V. Krishnamurthy, K. Pattanayak, S. Gogineni, B. Kang, M. Rangaswamy,*IEEE Transactions on Aerospace and Electronic Systems,*2021.**‘Langevin Dynamics for Adaptive Inverse Reinforcement Learning of Stochastic Gradient Algorithms‘**, V. Krishnamurthy, G. Yin,*Journal of Machine Learning Research*, 2021.**‘Rationally inattentive inverse reinforcement learning explains youtube commenting behavior‘**, W. Hoiles, V. Krishnamurthy, K. Pattanayak,*Journal of Machine Learning Research*, 2020.**‘Inverse filtering for hidden Markov models with applications to counter-adversarial autonomous systems‘**, R. Mattila, C. R Rojas, V. Krishnamurthy, B. Wahlberg,*IEEE Transactions on Signal Processing*, 2020.**‘Identifying cognitive radars-inverse reinforcement learning using revealed preferences’**, V. Krishnamurthy, D. Angley, R. Evans, B. Moran,*IEEE Transactions on Signal Processing*, 2020.**‘Inverse Sequential Hypothesis Testing‘**, Kunal Pattanayak, Vikram Krishnamurthy, Erik Blasch,*2020 IEEE 23rd International Conference on Information Fusion (FUSION)*, 2020.**‘What did your adversary believeƒ Optimal filtering and smoothing in counter-adversarial autonomous systems‘**, R. Mattila, I. Lourenço, V. Krishnamurthy, C. R. Rojas, B. Wahlberg,*ICASSP 2020-2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)*, 2020.**‘Policy gradient using weak derivatives for reinforcement learning‘**, S. Bhatt, A. Koppel, V. Krishnamurthy,*2019 IEEE 58th Conference on Decision and Control (CDC)*, 2019.**‘How to calibrate your adversary’s capabilities? Inverse filtering for counter-autonomous systems‘**, V. Krishnamurthy, M. Rangaswamy,*IEEE Transactions on Signal Processing*, 2019.**‘Convex stochastic dominance in bayesian localization, filtering, and controlled sensing pomdps‘**, V. Krishnamurthy,*IEEE Transactions on Information Theory*, 2019.**‘Estimating private beliefs of Bayesian agents based on observed decisions‘**, R. Mattila, I. Lourenço, C. R Rojas, V. Krishnamurthy, B. Wahlberg,*IEEE Control Systems Letters*, 2019.**‘Inverse filtering for linear Gaussian state-space models‘**, R. Mattila, C. R Rojas, V. Krishnamurthy, B. Wahlberg,*2018 IEEE Conference on Decision and Control (CDC)*, 2018.**‘Syntactic enhancement to VSIMM for roadmap based anomalous trajectory detection: A natural language processing approach‘**, V. Krishnamurthy, S. Gao,*IEEE Transactions on Signal Processing*, 2018.**‘Spatiotemporal trajectory models for metalevel target tracking‘**, M. Fanaswala, V. Krishnamurthy,*IEEE Aerospace and Electronic Systems Magazine*, 2015.**‘Syntactic models for trajectory constrained track-before-detect’**, M. Fanaswala, V. Krishnamurthy,*IEEE Transactions on Signal Processing*, 2014.**‘Reduced complexity HMM filtering with stochastic dominance bounds: A convex optimization approach‘**, V. Krishnamurthy, C. R Rojas,*IEEE Transactions on Signal Processing*, 2014.**‘Tracking a Markov-modulated stationary degree distribution of a dynamic random graph‘**, M. Hamdi, V. Krishnamurthy, G. Yin,*IEEE Transactions on Information Theory*, 2014.**‘Stochastic context-free grammars for scale-dependent intent inference’**, B. Balaji, M. Fanaswala, V. Krishnamurthy,*Signal Processing, Sensor Fusion, and Target Recognition XXII,*2013.**‘Distributed energy-aware diffusion least mean squares: Game-theoretic learning‘**, O. N. Gharehshiran, V. Krishnamurthy, G. Yin,*IEEE Journal of Selected Topics in Signal Processing*, 2013.**‘Distributed tracking of correlated equilibria in regime switching noncooperative games‘**, O. N. Gharehshiran, V. Krishnamurthy, G. Yin,*IEEE Transactions on Automatic Control*, 2013.**‘Syntactic modeling and signal processing of multifunction radars: A stochastic context-free grammar approach’**,**‘Intent inference and syntactic tracking with GMTI measurements‘**, A. Wang, V. Krishnamurthy, B. Balaji,*IEEE Transactions on Aerospace and Electronic Systems*, 2011.**‘Syntactic modeling and signal processing of multifunction radars: A stochastic context-free grammar approach’**, N.