Complex and nonlinear dynamical systems often involve parameters that change with time, accurate tracking of which is essential to tasks such as state estimation, prediction, and control. Existing machine-learning methods require full state observation of the underlying system and tacitly assume adiabatic changes in the parameter. Formulating an inverse problem and exploiting reservoir computing, we develop a model-free and fully data-driven framework to accurately track time-varying parameters from partial state observation in real time. In particular, with training data from a subset of the dynamical variables of the system for a small number of known parameter values, the framework is able to accurately predict the parameter variations in time. Low- and high-dimensional, Markovian and non-Markovian nonlinear dynamical systems are used to demonstrate the power of the machine-learning based parameter-tracking framework. Pertinent issues affecting the tracking performance are addressed.
The traditional GNSS-aided inertial navigation system (INS) usually exploits the extended Kalman filter (EKF) for state estimation, and the initial attitude accuracy is key to the filtering performance. To spare the reliance on the initial attitude, this work generalizes the previously proposed trident quaternion within the framework of Clifford algebra to represent the extended pose, IMU biases and lever arms on the Lie group. Consequently, a quasi-group-affine system is established for the low-cost INS/GNSS integrated navigation system, and the right-error Clifford algebra-based EKF (Clifford-RQEKF) is accordingly developed. The iterated filtering approach is further applied to significantly improve the performances of the Clifford-RQEKF and the previously proposed trident quaternion-based EKFs. Numerical simulations and experiments show that all iterated filtering approaches fulfill the fast and global convergence without the prior attitude information, whereas the iterated Clifford-RQEKF performs much better than the others under especially large IMU biases.
In this work, an innovative data-driven moving horizon state estimation is proposed for model dynamic-unknown systems based on Bayesian optimization. As long as the measurement data is received, a locally linear dynamics model can be obtained from one Bayesian optimization-based offline learning framework. Herein, the learned model is continuously updated iteratively based on the actual observed data to approximate the actual system dynamic with the intent of minimizing the cost function of the moving horizon estimator until the desired performance is achieved. Meanwhile, the characteristics of Bayesian optimization can guarantee the closest approximation of the learned model to the actual system dynamic. Thus, one effective data-driven moving horizon estimator can be designed further on the basis of this learned model. Finally, the efficiency of the proposed state estimation algorithm is demonstrated by several numerical simulations.
In this paper, we present a novel Reduced Robustified NMPC (R$^2$NMPC) algorithm that has the same complexity as an equivalent nominal NMPC while enhancing it with robustified constraints based on the dynamics of ellipsoidal uncertainty sets. This promises both a closed-loop- and constraint satisfaction performance equivalent to common Robustified NMPC approaches, while drastically reducing the computational complexity. The main idea lies in approximating the ellipsoidal uncertainty sets propagation over the prediction horizon with the system dynamics' sensitivities inferred from the last optimal control problem (OCP) solution, and similarly for the gradients to robustify the constraints. Thus, we do not require the decision variables related to the uncertainty propagation within the OCP, rendering it computationally tractable. Next, we illustrate the real-time control capabilities of our algorithm in handling a complex, high-dimensional, and highly nonlinear system, namely the trajectory following of an autonomous passenger vehicle modeled with a dynamic nonlinear single-track model. Our experimental findings, alongside a comparative assessment against other Robust NMPC approaches, affirm the robustness of our method in effectively tracking an optimal racetrack trajectory while satisfying the nonlinear constraints. This performance is achieved while fully utilizing the vehicle's interface limits, even at high speeds of up to 37.5m/s, and successfully managing state estimation disturbances. Remarkably, our approach maintains a mean solving frequency of 144Hz.
Recently, we demonstrated success of a time-synchronized state estimator using deep neural networks (DNNs) for real-time unobservable distribution systems. In this letter, we provide analytical bounds on the performance of that state estimator as a function of perturbations in the input measurements. It has already been shown that evaluating performance based on only the test dataset might not effectively indicate a trained DNN's ability to handle input perturbations. As such, we analytically verify robustness and trustworthiness of DNNs to input perturbations by treating them as mixed-integer linear programming (MILP) problems. The ability of batch normalization in addressing the scalability limitations of the MILP formulation is also highlighted. The framework is validated by performing time-synchronized distribution system state estimation for a modified IEEE 34-node system and a real-world large distribution system, both of which are incompletely observed by micro-phasor measurement units.
This paper identifies and addresses the problems with naively combining (reinforcement) learning-based controllers and state estimators for robotic in-hand manipulation. Specifically, we tackle the challenging task of purely tactile, goal-conditioned, dextrous in-hand reorientation with the hand pointing downwards. Due to the limited sensing available, many control strategies that are feasible in simulation when having full knowledge of the object's state do not allow for accurate state estimation. Hence, separately training the controller and the estimator and combining the two at test time leads to poor performance. We solve this problem by coupling the control policy to the state estimator already during training in simulation. This approach leads to more robust state estimation and overall higher performance on the task while maintaining an interpretability advantage over end-to-end policy learning. With our GPU-accelerated implementation, learning from scratch takes a median training time of only 6.5 hours on a single, low-cost GPU. In simulation experiments with the DLR-Hand II and for four significantly different object shapes, we provide an in-depth analysis of the performance of our approach. We demonstrate the successful sim2real transfer by rotating the four objects to all 24 orientations in the $\pi/2$ discretization of SO(3), which has never been achieved for such a diverse set of shapes. Finally, our method can reorient a cube consecutively to nine goals (median), which was beyond the reach of previous methods in this challenging setting.
State estimation for discrete-time linear systems with quantized measurements is addressed. By exploiting the set-theoretic nature of the information provided by the quantizer, the problem is cast in the set membership estimation setting. Motivated by the possibility of suitably tuning the quantizer thresholds in sensor networks, the optimal design of adaptive quantizers is formulated in terms of the minimization of the radius of information associated to the state estimation problem. The optimal solution is derived for first-order systems and the result is exploited to design adaptive quantizers for generic systems, minimizing the size of the feasible output signal set. Then, the minimum number of sensor thresholds for which the adaptive quantizers guarantee asymptotic boundedness of the state estimation uncertainty is established. Threshold adaptation mechanisms based on several types of outer approximations of the feasible state set are also proposed. The effectiveness of the designed adaptive quantizers is demonstrated on numerical tests involving a specific case study and randomly generated systems, highlighting the trade off between the resulting estimation uncertainty and the computational burden required by recursive set approximations.
Employing Stochastic Nonlinear Model Predictive Control (SNMPC) for real-time applications is challenging due to the complex task of propagating uncertainties through nonlinear systems. This difficulty becomes more pronounced in high-dimensional systems with extended prediction horizons, such as autonomous vehicles. To enhance closed-loop performance in and feasibility in SNMPCs, we introduce the concept of the Uncertainty Propagation Horizon (UPH). The UPH limits the time for uncertainty propagation through system dynamics, preventing trajectory divergence, optimizing feedback loop advantages, and reducing computational overhead. Our SNMPC approach utilizes Polynomial Chaos Expansion (PCE) to propagate uncertainties and incorporates nonlinear hard constraints on state expectations and nonlinear probabilistic constraints. We transform the probabilistic constraints into deterministic constraints by estimating the nonlinear constraints' expectation and variance. We then showcase our algorithm's effectiveness in real-time control of a high-dimensional, highly nonlinear system-the trajectory following of an autonomous passenger vehicle, modeled with a dynamic nonlinear single-track model. Experimental results demonstrate our approach's robust capability to follow an optimal racetrack trajectory at speeds of up to 37.5m/s while dealing with state estimation disturbances, achieving a minimum solving frequency of 97Hz. Additionally, our experiments illustrate that limiting the UPH renders previously infeasible SNMPC problems feasible, even when incorrect uncertainty assumptions or strong disturbances are present.
Distributed sensor networks have gained interest thanks to the developments in processing power and communications. Event-triggering mechanisms can be useful in reducing communication between the nodes of the network, while still ensuring an adequate behaviour of the system. However, very little attention has been given to continuous-time systems in this context. In this work, we propose a strategy for distributed state estimation in sensor networks, based on average dynamic consensus of the continuous measurements. While communication between nodes is discrete and heavily reduced due to the event-triggering mechanism, our method ensures that the nodes are still able to produce a continuous estimate of the global average measurement and the state of the plant, within some tuneable error bounds.
The optimality of Bayesian filtering relies on the completeness of prior models, while deep learning holds a distinct advantage in learning models from offline data. Nevertheless, the current fusion of these two methodologies remains largely ad hoc, lacking a theoretical foundation. This paper presents a novel solution, namely an explainable gated Bayesian recurrent neural network specifically designed to state estimation under model mismatches. Firstly, we transform the non-Markov state-space model into an equivalent first-order Markov model with memory. It is a generalized transformation that overcomes the limitations of the first-order Markov property and enables recursive filtering. Secondly, by deriving a data-assisted joint state-memory-mismatch Bayesian filtering, we design a Bayesian gated framework that includes a memory update gate for capturing the temporal regularities in state evolution, a state prediction gate with the evolution mismatch compensation, and a state update gate with the observation mismatch compensation. The Gaussian approximation implementation of the filtering process within the gated framework is derived, taking into account the computational efficiency. Finally, the corresponding internal neural network structures and end-to-end training methods are designed. The Bayesian filtering theory enhances the interpretability of the proposed gated network, enabling the effective integration of offline data and prior models within functionally explicit gated units. In comprehensive experiments, including simulations and real-world datasets, the proposed gated network demonstrates superior estimation performance compared to benchmark filters and state-of-the-art deep learning filtering methods.
Precise relative navigation is a critical enabler for distributed satellites to achieve new mission objectives impossible for a monolithic spacecraft. Carrier phase differential GPS (CDGPS) with integer ambiguity resolution (IAR) is a promising means of achieving cm-level accuracy for high-precision Rendezvous, Proximity-Operations and Docking (RPOD), In-Space Servicing, Assembly and Manufacturing (ISAM) as well as satellite formation flying and swarming. However, IAR is sensitive to received GPS signal noise, especially under severe multi-path or high thermal noise. This paper proposes a sensor-fusion approach to achieve IAR under such conditions in two coupling stages. A loose coupling stage fuses through an Extended Kalman Filter the CDGPS measurements with on-board sensor measurements such as range from cross-links, and vision-based bearing angles. A second tight-coupling stage augments the cost function of the integer weighted least-squares minimization with a soft constraint function using noise-weighted observed-minus-computed residuals from these external sensor measurements. Integer acceptance tests are empirically modified to reflect added constraints. Partial IAR is applied to graduate integer fixing. These proposed techniques are packaged into flight-capable software, with ground truths simulated by the Stanford Space Rendezvous Laboratory's S3 library using state-of-the-art force modelling with relevant sources of errors, and validated in two scenarios: (1) a high multi-path scenario involving rendezvous and docking in low Earth orbit, and (2) a high thermal noise scenario relying only on GPS side-lobe signals during proximity operations in geostationary orbit. This study demonstrates successful IAR in both cases, using the proposed sensor-fusion approach, thus demonstrating potential for high-precision state estimation under adverse signal-to-noise conditions.
Dynamic operation of biological processes, such as anaerobic digestion (AD), requires reliable process monitoring to guarantee stable operating conditions at all times. Unscented Kalman filters (UKF) are an established tool for nonlinear state estimation, and there exist numerous variants of UKF implementations, treating state constraints, improvements of numerical performance and different noise cases. So far, however, a unified comparison of proposed methods emphasizing the algorithmic details is lacking. The present study thus examines multiple unconstrained and constrained UKF variants, addresses aspects crucial for direct implementation and applies them to a simplified AD model. The constrained UKF considering additive noise delivered the most accurate state estimations. The long run time of the underlying optimization could be vastly reduced through pre-calculated gradients and Hessian of the associated cost function, as well as by reformulation of the cost function as a quadratic program. However, unconstrained UKF variants showed lower run times at competitive estimation accuracy. This study provides useful advice to practitioners working with nonlinear Kalman filters by paying close attention to algorithmic details and modifications crucial for successful implementation.
In this paper, we present a controller framework that synthesizes control policies for Jump Markov Linear Systems subject to stochastic mode switches and imperfect mode estimation. Our approach builds on safe and robust methods for Model Predictive Control (MPC), but in contrast to existing approaches that either optimize without regard to feasibility or utilize soft constraints that increase computational requirements, we employ a safe and robust control approach informed by the feasibility of the optimization problem. We formulate and encode finite horizon safety for multiple model systems in our MPC design using Control Barrier Functions (CBFs). When subject to inaccurate hybrid state estimation, our feasibility-guided MPC generates a control policy that is maximally robust to uncertainty in the system's modes. We evaluate our approach on an orbital rendezvous problem and a six degree-of-freedom hexacopter under several scenarios and benchmarks to demonstrate the utility of the framework. Results indicate that the proposed technique of maximizing the robustness horizon, and the use of CBFs for safety awareness, improve the overall safety and performance of MPC for Jump Markov Linear Systems.
Operating an active distribution network (ADN) in the absence of enough measurements, the presence of distributed energy resources, and poor knowledge of responsive demand behaviour is a huge challenge. This paper introduces systematic modelling of demand response behaviour which is then included in Forecasting Aided State Estimation (FASE) for better control of the network. There are several innovative elements in tuning parameters of FASE-based, demand profiling, and aggregation. The comprehensive case studies for three UK representative demand scenarios in 2023, 2035, and 2050 demonstrated the effectiveness of the proposed approach.
Distribution system state estimation (DSSE) is paramount for effective state monitoring and control. However, stochastic outputs of renewables and asynchronous streaming of multi-rate measurements in practical systems largely degrade the estimation performance. This paper proposes a deep reinforcement learning (DRL)-enabled adaptive DSSE algorithm in unbalanced distribution systems, which tackles hybrid measurements with different time scales efficiently. We construct a three-step forecasting-aided state estimation framework, including DRL-based parameter identification, prediction, and state estimation, with multi-rate measurements incorporating limited synchrophasor data. Furthermore, a DRL-based adaptive parameter identification mechanism is embedded in the prediction step. As a novel attempt at utilizing DRL to enable DSSE adaptive to varying operating conditions, this method improves the prediction performance and further facilitates accurate state estimation. Case studies in two unbalanced feeders indicate that our method captures state variation with multi-source multi-rate data efficiently, outperforming the traditional methods.
We propose an efficient solution to the state estimation problem in multi-scan multi-sensor multiple extended target sensing scenarios. We first model the measurement process by a doubly inhomogeneous-generalized shot noise Cox process and then estimate the parameters using a jump Markov chain Monte Carlo sampling technique. The proposed approach scales linearly in the number of measurements and can take spatial properties of the sensors into account, herein, sensor noise covariance, detection probability, and resolution. Numerical experiments using radar measurement data suggest that the algorithm offers improvements in high clutter scenarios with closely spaced targets over state-of-the-art clustering techniques used in existing multiple extended target tracking algorithms.
Augmented reality (AR) requires the seamless integration of visual, auditory, and linguistic channels for optimized human-computer interaction. While auditory and visual inputs facilitate real-time and contextual user guidance, the potential of large language models (LLMs) in this landscape remains largely untapped. Our study introduces an innovative method harnessing LLMs to assimilate information from visual, auditory, and contextual modalities. Focusing on the unique challenge of task performance quantification in AR, we utilize egocentric video, speech, and context analysis. The integration of LLMs facilitates enhanced state estimation, marking a step towards more adaptive AR systems. Code, dataset, and demo will be available at https://github.com/nguyennm1024/misar.
The majority of data assimilation (DA) methods in the geosciences are based on Gaussian assumptions. While these assumptions facilitate efficient algorithms, they cause analysis biases and subsequent forecast degradations. Non-parametric, particle-based DA algorithms have superior accuracy, but their application to high-dimensional models still poses operational challenges. Drawing inspiration from recent advances in the field of generative artificial intelligence (AI), this article introduces a new nonlinear estimation theory which attempts to bridge the existing gap in DA methodology. Specifically, a Conjugate Transform Filter (CTF) is derived and shown to generalize the celebrated Kalman filter to arbitrarily non-Gaussian distributions. The new filter has several desirable properties, such as its ability to preserve statistical relationships in the prior state and convergence to highly accurate observations. An ensemble approximation of the new theory (ECTF) is also presented and validated using idealized statistical experiments that feature bounded quantities with non-Gaussian distributions, a prevalent challenge in Earth system models. Results from these experiments indicate that the greatest benefits from ECTF occur when observation errors are small relative to the forecast uncertainty and when state variables exhibit strong nonlinear dependencies. Ultimately, the new filtering theory offers exciting avenues for improving conventional DA algorithms through their principled integration with AI techniques.
Anomaly detection in multivariate time series has emerged as a crucial challenge in time series research, with significant research implications in various fields such as fraud detection, fault diagnosis, and system state estimation. Reconstruction-based models have shown promising potential in recent years for detecting anomalies in time series data. However, due to the rapid increase in data scale and dimensionality, the issues of noise and Weak Identity Mapping (WIM) during time series reconstruction have become increasingly pronounced. To address this, we introduce a novel Adaptive Dynamic Neighbor Mask (ADNM) mechanism and integrate it with the Transformer and Denoising Diffusion Model, creating a new framework for multivariate time series anomaly detection, named Denoising Diffusion Mask Transformer (DDMT). The ADNM module is introduced to mitigate information leakage between input and output features during data reconstruction, thereby alleviating the problem of WIM during reconstruction. The Denoising Diffusion Transformer (DDT) employs the Transformer as an internal neural network structure for Denoising Diffusion Model. It learns the stepwise generation process of time series data to model the probability distribution of the data, capturing normal data patterns and progressively restoring time series data by removing noise, resulting in a clear recovery of anomalies. To the best of our knowledge, this is the first model that combines Denoising Diffusion Model and the Transformer for multivariate time series anomaly detection. Experimental evaluations were conducted on five publicly available multivariate time series anomaly detection datasets. The results demonstrate that the model effectively identifies anomalies in time series data, achieving state-of-the-art performance in anomaly detection.
In this work, we focus on analyzing vulnerability of nonlinear dynamical control systems to stealthy false data injection attacks on sensors. We start by defining the stealthiness notion in the most general form where an attack is considered stealthy if it would be undetected by any intrusion detector, i.e., any intrusion detector could not do better than a random guess. Depending on the level of attacker's knowledge about the plant model, controller, and the system states, two different attack models are considered. For each attack model, we derive the conditions for which the system will be vulnerable to stealthy impactful attacks, in addition to finding a methodology for designing such sequence of false data injection attacks. When the attacker has complete knowledge about the system, we show that if the closed loop system is incrementally exponentially stable while the open loop plant is incrementally unstable, then the system is vulnerable to stealthy yet impactful attacks on sensors. However, in the second attack model, with less knowledge about the system, additional conditions need to be satisfied and the level of stealthiness depends on the accuracy of attacker's knowledge about the system. We also consider the impact of stealthy attacks on state estimation, and show that if the closed loop control system including the estimator is incrementally stable, then the state estimation in the presence of attack converges to the attack free estimates. Finally, we illustrate our results on numerical case studies.