State Covariance Matrix Research Articles

Single trajectory-based policy optimization for discrete-time stochastic systems

Policy optimization has reemerged as an important approach for reinforcement learning and optimal control problems. A notable drawback is that even for linear quadratic problems, the execution of model-free policy optimization methods generally relies on multiple trajectories to estimate the cost gradient and state covariance matrix in each iteration. This paper proposes a novel single trajectory-based policy optimization algorithm for stochastic systems subject to multiplicative noises. Specifically, three variants of policy optimization methods are proposed to learn the optimal control policy in a model-free manner, all of which are supported with provable convergence results. In contrast with the existing work of policy optimization algorithms, the execution of our algorithm reuses a single system trajectory without regenerating system trajectories in each iteration. Our algorithm is evaluated through several numerical examples, which imply our algorithm outperforms other evaluated policy optimization algorithms.

An indoor positioning method based on bluetooth array/PDR fusion using the SVD-EKF

With the development of mobile internet and artificial intelligence, the core of current surveying and mapping science and technology is no longer confined solely to outdoor applications. High-precision indoor positioning technology is now one of the core technologies in the era of artificial intelligence. An angle measurement and positioning system based on wireless signal array antennas can achieve high accuracy in indoor unblocked conditions. However, indoor environment is unpredictable, and the user's behavior is also random. Inevitably, some signal reflection and other factors will affect the positioning accuracy. Considering all the aforementioned, this study analyzes the principles and characteristics of a Bluetooth signal based array antenna angle measurement and positioning system. In addition, aiming at the multi-phase problem caused by antenna switching, the frequency estimation method based on FFT (Fast Fourier Transform) is studied in this paper, achieving high-precision angle measurement and positioning. Aiming at the problem that the system positioning error increase in the complex and variable indoor environment, a fusion positioning method of Bluetooth array/PDR (Pedestrian Dead Reckoning) based on the SVD-EKF (Singular Value Decomposition–Extended Kalman Filter) is proposed. This study introduces a few improvements to the EKF (Extended Kalman Filter). First, the predicted state covariance matrix is decomposed by singular value decomposition, which improves the robustness of the EKF. Second, a Bluetooth array self-evaluation factor is introduced and combined with the Huber function to construct an adaptive factor, thus further enhancing filtering accuracy and environmental adaptability. Through static and dynamic data collected in indoor environment, the feasibility of the algorithm is verified. The results of static and dynamic experimental results show that the array angle measurement and positioning system can achieve high accuracy, the near point positioning maximum error is 0.3m and the far point positioning accuracy is 0.6m. The dynamic test results in the room show that after SVD-EKF algorithm optimization, the positioning error is reduced by 0.05m, which is equivalent to the EKF algorithm. However, in corridor areas, the improvement of accuracy of SVD-EKF algorithm is better than EKF, achieving an improvement of 0.373 m and a smoother positioning result compared to the traditional EKF algorithm. This study provides a new practical technology with a high precision and easy deployment for indoor positioning.

One-sided device-independent random number generation through fiber channels

Randomness is an essential resource and plays important roles in various applications ranging from cryptography to simulation of complex systems. Certified randomness from quantum process is ensured to have the element of privacy but usually relies on the device’s behavior. To certify randomness without the characterization for device, it is crucial to realize the one-sided device-independent random number generation based on quantum steering, which guarantees security of randomness and relaxes the demands of one party’s device. Here, we distribute quantum steering between two distant users through a 2 km fiber channel and generate quantum random numbers at the remote station with untrustworthy device. We certify the steering-based randomness by reconstructing covariance matrix of the Gaussian entangled state shared between distant parties. Then, the quantum random numbers with a generation rate of 7.06 Mbits/s are extracted from the measured amplitude quadrature fluctuation of the state owned by the remote party. Our results demonstrate the first realization of steering-based random numbers extraction in a practical fiber channel, which paves the way to the quantum random numbers generation in asymmetric networks.

Optimizing Consider-Covariance Models for Realistic Orbit Errors and Application to Collision Avoidance

Precise knowledge about the orbit state vectors and the associated uncertainties are crucial for reliable conjunction assessment and efficient mitigation of on-orbit collision risks through collision avoidance maneuvers by active satellites. The decision-making process heavily relies on the orbit accuracy and the uncertainty realism of the encountering objects, primarily space debris, and the maneuvering satellite itself. The process of determining an orbit creates an estimate of the orbit state and its associated state covariance matrix. This estimate serves as the initial value for predicting the orbit’s uncertainty at the time of closest approach. To determine and numerically propagate realistic orbit errors, the uncertainties of the dynamic model must be taken into account. One method that fulfils this purpose is consider covariance propagation, provided that suitable consider parameters and their variances have been established. This paper presents a novel method for optimizing the consider covariance parameters from past mission data. Real orbit data from multiple low Earth orbit satellites controlled by the DLR, German Aerospace Center’s German Space Operations Center are used to calibrate and evaluate different error models, including covariance parameters and other error terms. The results demonstrate improved uncertainty realism in orbit predictions and subsequent benefits for collision avoidance. Finally, this paper presents the required steps for integrating the new method into the existing collision avoidance system, along with initial results from conjunction assessment.

An Investigation of Extended-Dimension Embedded CKF-SLAM Based on the Akaike Information Criterion.

Simultaneous localization and mapping (SLAM) faces significant challenges due to high computational costs, low accuracy, and instability, which are particularly problematic because SLAM systems often operate in real-time environments where timely and precise state estimation is crucial. High computational costs can lead to delays, low accuracy can result in incorrect mapping and localization, and instability can make the entire system unreliable, especially in dynamic or complex environments. As the state-space dimension increases, the filtering error of the standard cubature Kalman filter (CKF) grows, leading to difficulties in multiplicative noise propagation and instability in state estimation results. To address these issues, this paper proposes an extended-dimensional embedded CKF based on truncated singular-value decomposition (TSVD-AECKF). Firstly, singular-value decomposition (SVD) is employed instead of the Cholesky decomposition in the standard CKF to mitigate the non-positive definiteness of the state covariance matrix. Considering the effect of small singular values on the stability of state estimation, a method is provided to truncate singular values by determining the truncation threshold using the Akaike information criterion (AIC). Furthermore, the system noise is embedded into the state variables, and an embedding volume criterion is used to improve the conventional CKF while extending the dimensionality. Finally, the proposed algorithm was validated and analyzed through both simulations and real-world experiments. The results indicate that the proposed method effectively mitigates the increase in localization error as the state-space dimension grows, enhancing time efficiency by 55.54%, and improving accuracy by 35.13% compared to the standard CKF algorithm, thereby enhancing the robustness and stability of mapping.

A robust and efficient cubature Kalman filter based on the variational Bayesian method and its application in target tracking

Abstract In this paper, we propose a robust cubature Kalman filter (CKF) for nonlinear state-space models with unknown state and measurement noise covariance matrix. We study situations in which sensors are independent of each other. Therefore, the unknown measurement noise variance is modeled as an unknown inverse gamma (IG) distribution. The Gaussian-Student-t-inverse-Wishart (GSTIW) mixture distribution is used to model the one-step prediction distribution. Modeling generates numerous unknown parameters. Therefore, we adopt the statistical linearization method to linearize the observation function and then estimate the state and parameters separately to reduce the computational burden of estimating unknown parameters, significantly improving the algorithm’s efficiency. Finally, using the variational Bayesian method, a novel and efficient robust CKF based on the IG distribution and GSTIW mixture distributions (IG-GSTIW-CKF) is obtained. Simulation and experimental results show that the proposed method has better estimation accuracy than several advanced algorithms when sensors are independent. In addition, the efficiency of the proposed algorithm is significantly higher than that of other CKF-based methods.

Multimode squeezed state for reconfigurable quantum networks at telecommunication wavelengths

Continuous variable encoding of quantum information requires the deterministic generation of highly correlated quantum states of light in the form of quantum networks, which, in turn, necessitates the controlled generation of a large number of squeezed modes. In this paper, we present an experimental source of multimode squeezed states of light at telecommunication wavelengths. Generation at such wavelengths is especially important as it can enable quantum information processing, communication, and sensing beyond the laboratory scale. We use a single-pass spontaneous parametric down-conversion process in a nonlinear waveguide pumped with the second harmonic of a femtosecond laser. Our measurements reveal significant squeezing in more than 21 frequency modes, with a maximum squeezing value exceeding 2.5 dB. We demonstrate multiparty entanglement by measuring the state's covariance matrix. Finally, we show the source reconfigurability by preparing few-node cluster states and measure their nullifier squeezing level. These results pave the way for a scalable implementation of continuous variable quantum information protocols at telecommunication wavelengths, particularly for multiparty, entanglement-based quantum communications. Moreover, the source is compatible with additional pulse-by-pulse multiplexing, which can be utilized to construct the necessary three-dimensional entangled structures for quantum computing protocols. Published by the American Physical Society 2024

Real-time calibration of magnetometers based on the recursive least squares method

Abstract A real-time calibration method for magnetometers based on the recursive least squares (RLS) algorithm is proposed to address the issues of large data processing and lack of real-time performance in the calibration of magnetometers in complex magnetic environments using the traditional least squares (LS) algorithm. Firstly, an error model for the magnetometer is established. Then, using this error model as the measurement equation, the current measurement value is iterated from the previous measurement value through least squares iteration to update the state parameters. Finally, the effectiveness of the algorithm was verified by shaking the magnetometer in a “figure-eight” pattern. Experiments have shown that compared with the traditional least squares algorithm, the recursive least squares algorithm requires less data processing and offers faster calculation speed. Compared to LS calibration, the standard deviation of the magnetic vector modulus obtained from RLS calibration decreased by 24.4%, 17.4%, and 23.2% in three different environments, respectively. Additionally, by performing real-time detection and analysis of the state covariance matrix, it was determined that the calibration process is essentially complete after 3500 iterations.

Maximum Correntropy Extended Kalman Filtering with Nonlinear Regression Technique for GPS Navigation

One technique that is widely used in various fields, including nonlinear target tracking, is the extended Kalman filter (EKF). The well-known minimum mean square error (MMSE) criterion, which performs magnificently under the assumption of Gaussian noise, is the optimization criterion that is frequently employed in EKF. Further, if the noises are loud (or heavy-tailed), its performance can drastically suffer. To overcome the problem, this paper suggests a new technique for maximum correntropy EKF with nonlinear regression (MCCEKF-NR) by using the maximum correntropy criterion (MCC) instead of the MMSE criterion to calculate the effectiveness and vitality. The preliminary estimates of the state and covariance matrix in MCKF are provided via the state mean vector and covariance matrix propagation equations, just like in the conventional Kalman filter. In addition, a newly designed fixed-point technique is used to update the posterior estimates of each filter in a regression model. To show the practicality of the proposed strategy, we propose an effective implementation for positioning enhancement in GPS navigation and radar measurement systems.

Synthetic orbit uncertainty generation through regression analysis of historical Conjunction Data Messages

Synthetic orbit uncertainty generation through regression analysis of historical Conjunction Data Messages

Artificial neural network based on strong track and square root UKF for INS/GNSS intelligence integrated system during GPS outage

When INS/GNSS (inertial navigation system/global navigation satellite system) integrated system is applied, it will be affected by the insufficient number of visible satellites, and even the satellite signal will be lost completely. At this time, the positioning error of INS accumulates with time, and the navigation accuracy decreases rapidly. Therefore, in order to improve the performance of INS/GNSS integration during the satellite signals interruption, a novel learning algorithm for neural network has been presented and used for intelligence integrated system in this article. First of all, determine the input and output of neural network for intelligent integrated system and a nonlinear model for weighs updating during neural network learning has been established. Then, the neural network learning based on strong tracking and square root UKF (unscented Kalman filter) is proposed for iterations of the nonlinear model. In this algorithm, the square root of the state covariance matrix is used to replace the covariance matrix in the classical UKF to avoid the filter divergence caused by the negative definite state covariance matrix. Meanwhile, the strong tracking coefficient is introduced to adjust the filter gain in real-time and improve the tracking capability to mutation state. Finally, an improved calculation method of strong tracking coefficient is presented to reduce the computational complexity in this algorithm. The results of the simulation test and the field-positioning data show that the proposed learning algorithm could improve the calculation stability and robustness of neural network. Therefore, the error accumulation of INS/GNSS integration is effectively compensated, and then the positioning accuracy of INS/GNSS intelligence integrated system has been improved.

Constrained minimum variance and covariance steering based on affine disturbance feedback control parameterization

AbstractThis paper deals with finite‐horizon minimum‐variance and covariance steering problems subject to constraints. The goal of the minimum variance problem is to steer the state mean of an uncertain system to a prescribed vector while minimizing the trace of its terminal state covariance whereas the goal in the covariance steering problem is to steer the covariance matrix of the terminal state to a prescribed positive definite matrix. The paper proposes a solution approach that relies on a stochastic version of the affine disturbance feedback control parametrization. In this control policy parametrization, the control input at each stage is expressed as an affine function of the history of disturbances that have acted upon the system. It is shown that this particular parametrization reduces the stochastic optimal control problems considered in this paper into tractable convex programs or difference of convex functions programs with essentially the same decision variables. In addition, the paper proposes a variation of this control parametrization that relies on truncated histories of past disturbances, which allows for sub‐optimal controllers to be designed that strike a balance between performance and computational cost. The suboptimality of the truncated policies is formally analyzed and closed form expressions are provided for the performance loss due to the use of the truncation scheme. Finally, the paper concludes with a comparative analysis of the truncated versions of the proposed policy parametrization and other standard policy parametrizations through numerical simulations.

On the update of algebraic states during state estimation of differential–algebraic equation (DAE) systems

On the update of algebraic states during state estimation of differential–algebraic equation (DAE) systems

Stabilizing preparation of quantum Gaussian states via continuous measurement

Stabilizing preparation of quantum Gaussian states via continuous measurement

Maneuverability indices estimation of nonlinear response model based on full-scale trial data and square root unscented Kalman filter

Maneuverability indices estimation of nonlinear response model based on full-scale trial data and square root unscented Kalman filter

Tire-road friction coefficient estimation for automatic guided vehicle under multiple road conditions

The traditional unscented Kalman filter (UKF) will have the problem of reduced accuracy or even divergence in the estimation process due to state model perturbation, unknown noise of the system, and other factors, which in turn affect the estimation results of the tire-road friction coefficient. By this problem, the paper investigates the tire-road friction coefficient estimation by taking an automatic guided vehicle (AGV) as the research object and proposes an adaptive singular value decomposition unscented Kalman filter (ASVD-UKF) with a noise estimator. Singular value decomposition (SVD) is introduced into the unscented Kalman filter (UKF) for Sigma sampling to suppress the negative definiteness of the state covariance matrix in UFK. The paper considered estimation schemes for joint road, μ-split road, and μ-different road and constructed corresponding ASVD-UKF observers to reduce the dimension of the road estimation model and real-time observation of four tire-road friction coefficients. Results show that the average absolute error of the μ-split road, joint road, and μ-different road proposed in this paper is significantly smaller than that of UFK, and the estimation accuracy is improved by 13.39%, 6.74%, and 5.71%, respectively. A Distributed Drive AGV prototype was developed for a real vehicle verification experiment, with only a 1.14% error between simulation and experiment. It is further proved that the designed observers are practical. The research can provide a theoretical basis and experimental foundation for the tire-road friction coefficient estimation.

An Adaptive Federated Filter Based on Variational Bayes With Application to Multisource Navigation

Information fusion is one of the key technologies in airborne multi-source navigation, where federated filter is widely used due to its simple structure. However, the sensor measurement of multi-source navigation system will become unreliable in some interferential environment, which leads to the state and measurement noise covariance matrix change over time and estimate difficultly. Inaccurate covariance matrice cause the loss of positioning accuracy in traditional federated filter. To address the problems, this paper puts forward an adaptive federal Kalman filtering algorithm based on Variational Bayesian and applies it to the INS/GPS/Terrain/Geomagnetic multi-source navigation system. Simulation and experiment results show that the proposed filter outperforms the traditional federated filter at improving the positioning accuracy under the condition of time-varying or even unknown state and measurement noise covariance matrix, which plays a positive role in UAV multi-source navigation.

Generalized deep thermalization for free fermions

In noninteracting isolated quantum systems out of equilibrium, local subsystems typically relax to nonthermal stationary states. In the standard framework, information on the rest of the system is discarded, and such states are described by a generalized Gibbs ensemble (GGE), maximizing the entropy while respecting the constraints imposed by the local conservation laws. Here we show that the latter also completely characterize a recently introduced projected ensemble (PE), constructed by performing projective measurements on the rest of the system and recording the outcomes. By focusing on the time evolution of fermionic Gaussian states in a tight-binding chain, we put forward a random ensemble constructed out of the local conservation laws, which we call deep GGE (dGGE). For infinite-temperature initial states, we show that the dGGE coincides with a universal Haar random ensemble on the manifold of Gaussian states. For both infinite and finite temperatures, we use a Monte Carlo approach to test numerically the predictions of the dGGE against the PE. We study, in particular, the $k$ moments of the state covariance matrix and the entanglement entropy, finding excellent agreement. Our work provides a first step towards a systematic characterization of projected ensembles beyond the case of chaotic systems and infinite temperatures.

An integrated adaptive Kalman filter for improving the reliability of navigation systems

Abstract Integrated GPS/INS using Kalman filter is the best technique for improving navigation accuracy. Assuming that the covariance matrices are known and constant, a conventional Kalman filter (CKF) is usually used, however, when they are unknown and time-varying, several adaptive estimation approaches have to be developed to estimate the statistical information of the measurement (R), process (Q), and state (P) covariance matrices. In many situations, blunders/faults in the measurement model and/or sudden changes in the dynamic model may occur during the navigation period. Therefore, the CKF, as well as the adaptive Kalman filter (AKF) will exhibit abnormal behavior and may lead the filter to be suboptimal or even diverge. In this study, the Sage-Husa adaptive Kalman filter (SHAKF) and innovation-based adaptive Kalman filter (IAKF) approaches are employed for adapting the measurement covariance matrix(R). In the case of abrupt changes in the dynamic model, the state covariance matrix (P) is adapted using the strong tracking filter (STF). The performance of these adaptive approaches is evaluated before and after simulating a fault of different sizes in the measurement and dynamic models. The results show that with a large window width, the SHAKF outperforms the CKF and IAKF. However, when the system encounters any fault either in the measurement or dynamic model, the SHAKF loses its optimality and diverges. The sensitivity of the SHAKF to the fault is because the R matrix accumulates with the propagation of the recursive noise estimator. On the other hand, the IAKF and STF provide better performance than both the CKF and SHAKF because the gain matrix is adaptively adjusted to mitigate the influence of the fault, and therefore, they behave normally when a fault of any size occurs in the measurement and/or dynamic model.

Distributed Moving Horizon Fusion Estimation for Nonlinear Constrained Uncertain Systems

This paper studies the state estimation of a class of distributed nonlinear systems. A new robust distributed moving horizon fusion estimation (DMHFE) method is proposed to deal with the norm-bounded uncertainties and guarantee the estimation performance. Based on the given relationship between a state covariance matrix and an error covariance matrix, estimated values of the unknown parameters in the system model can be obtained. Then, a local moving horizon estimation optimization algorithm is constructed by using the measured values of sensor nodes themselves, the measured information of adjacent nodes and the prior state estimates. By solving the above nonlinear optimization problem, a local optimal state estimation is obtained. Next, based on covariance intersection (CI) fusion strategy, the local optimal state estimates sent to the fusion center are fused to derive optimal state estimates. Furthermore, the sufficient conditions for the square convergence of the fusion estimation error norm are given. Finally, a simulation example is employed to demonstrate the effectiveness of the proposed algorithm.