A Gaussian Process based Method for Multiple Model Tracking

Sun, Mengwei; Davies, Mike E.; Proudler, Ian K.; Hopgood, James R.

doi:10.1109/sspd47486.2020.9272174

Cited by 9 publications

(7 citation statements)

References 12 publications

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“…Point target [15] No Centralized Data-driven [16] No Centralized Data-driven (hybrid) [18] No Centralized Data-driven (hybrid) [19] No Centralized Data-driven (hybrid) [20] No Distributed Date-driven [52] No Distributed Model-driven [27] Yes Distributed Model-driven [43] No Distributed Data-driven [53] No Distributed Data-driven [25] No Centralized Data-driven (hybrid) [26] Yes Centralized Data-driven [54] No Centralized Date-driven (hybrid)…”

Section: Target Typementioning

confidence: 99%

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Gaussian Process Upper Confidence Bounds in Distributed Point Target Tracking Over Wireless Sensor Networks

Liu

Mihaylova

George

et al. 2023

IEEE J. Sel. Top. Signal Process.

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Uncertainty quantification plays a key role in the development of autonomous systems, decision-making, and tracking over wireless sensor networks (WSNs). However, there is a need of providing uncertainty confidence bounds, especially for distributed machine learning-based tracking, dealing with different volumes of data collected by sensors. This paper aims to fill in this gap and proposes a distributed Gaussian process (DGP) approach for point target tracking and derives upper confidence bounds (UCBs) of the state estimates. A unique aspect of the proposed approach consists in the theoretical results are derived that prove its maximum accuracy for tracking with and without clutter measurements. Particularly, the developed approaches with uncertainty bounds are generic and can provide trustworthy solutions with an increased level of reliability. A novel hybrid Bayesian filtering method is proposed to enhance the DGP approach by adopting a Poisson measurement likelihood model. The proposed approaches are validated over a WSN case study, whose sensors have limited sensing ranges. Numerical results demonstrate the tracking accuracy and robustness of the proposed approaches. The derived UCBs constitute a tool for trustworthiness evaluation of DGP approaches and the simulation results reveal that it characterizes the presence of the target states in the error bound with 88% and 42% higher probability in X and Y coordinates, respectively, than the confidence intervalbased method.

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Section: Target Typementioning

confidence: 99%

“…According to (18), (19), Lemma 1 and the analysis as in Theorem 1, the deviation of the true function value from the aggregated predictive mean by RBCM can be written as…”

Section: Appendix Amentioning

confidence: 99%

Gaussian Process Upper Confidence Bounds in Distributed Point Target Tracking Over Wireless Sensor Networks

Liu

Mihaylova

George

et al. 2023

IEEE J. Sel. Top. Signal Process.

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“…There are also works studying using GP to represent the state-space model [5]. GP was used to learn the whole or part of the state-space model and the learned functions can be integrated into a particle filter or extended Kalman filter [6]- [8]. Inference and learning for GP state-space model were also discussed with theoretical bounds derived in [9].…”

Section: A Related Workmentioning

confidence: 99%

A Learning Distributed Gaussian Process Approach for Target Tracking over Sensor Networks

Liu

Lyu

George

et al. 2022

2022 25th International Conference on Information Fusion (FUSION)

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Tracking manoeuvring targets often relies on complex models with non-stationary parameters. Gaussian process (GP) based model-free methods can achieve accurate performance in a data-driven manner but face scalability challenges. Aiming to address such challenges, this paper proposes a distributed GP-based tracking approach able to learn the kernel hyperparameters in an online manner, to improve the tracking performance and scalability. It caters to the inherent distributed feature of sensor networks and does not need measurements to be transmitted among sensors for target states predictions. Theoretical upper confidence bounds about the tracking error are derived within the regret bound setting. Through this theoretical analysis, the tracking error per time step is upper bounded as a function of predictive variances from local sensors. The theoretical results are supported by simulation based ones over a case study for tracking over wireless sensor networks. With evaluation on challenging target trajectories, a comparison on state-of-theart centralised and distributed GP approaches, numerical results demonstrate that the proposed approach achieves competitively high and robust tracking performance.

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“…Historically, the main focus of sequential Bayesian filters has been on model-based systems where there exists an explicit formulation of the DSSM [1], [4]. More recently data-driven Bayesian filters have been proposed where the DSSM is unknown or partially known but training data examples are provided [5]- [7]. In both scenarios the filters are broken down into essentially two stages, i.e.…”

Section: A State Of the Art -Non-linear Filtersmentioning

confidence: 99%

“…As it is rare to have access to the true underlying distributions mentioned above, we can alternatively estimate the KMEs using a finite number of samples drawn from the corresponding distributions. The empirical KME of the distribution in (7) is approximated as the average of the feature mappings of the sample set D X = {x {1} , . .…”

Section: B Practicalities Of Kmementioning

confidence: 99%

Adaptive Kernel Kalman Filter

Sun¹,

Davies²,

Proudler³

et al. 2022

Preprint

Self Cite

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Sequential Bayesian filters in non-linear dynamic systems require the recursive estimation of the predictive and posterior distributions. This paper introduces a Bayesian filter called the adaptive kernel Kalman filter (AKKF). With this filter, the arbitrary predictive and posterior distributions of hidden states are approximated using the empirical kernel mean embeddings (KMEs) in reproducing kernel Hilbert spaces (RKHSs). In parallel with the KMEs, some particles, in the data space, are used to capture the properties of the dynamical system model. Specifically, particles are generated and updated in the data space, while the corresponding kernel weight mean vector and covariance matrix associated with the feature mappings of the particles are predicted and updated in the RKHSs based on the kernel Kalman rule (KKR). Simulation results are presented to confirm the improved performance of our approach with significantly reduced particle numbers, by comparing with the unscented Kalman filter (UKF), particle filter (PF) and Gaussian particle filter (GPF). For example, compared with the GPF, the proposed approach provides around 5% logarithmic mean square error (LMSE) tracking performance improvement in the bearing-only tracking (BOT) system when using 50 particles.

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A Gaussian Process based Method for Multiple Model Tracking

Cited by 9 publications

References 12 publications

Gaussian Process Upper Confidence Bounds in Distributed Point Target Tracking Over Wireless Sensor Networks

Gaussian Process Upper Confidence Bounds in Distributed Point Target Tracking Over Wireless Sensor Networks

A Learning Distributed Gaussian Process Approach for Target Tracking over Sensor Networks

Adaptive Kernel Kalman Filter

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