Receding Horizon Estimation Research Articles

Receding horizon estimation for multi‐rate sampled data systems under component‐based event‐triggered mechanisms: Handling delayed and degraded measurements

AbstractThe purpose of this article is to develop the receding horizon (RH) estimation for multi‐rate sampled systems with measurement delays and packet losses in the measurements. An event‐triggered transmission scheme is introduced to remove measurements that are unnecessary for the design of the estimator. The stochastic diagonal matrixes are introduced to represent the phenomenon of packet losses, where each component is subject to an individual Bernoulli process. The original system is firstly transformed into a delay‐free one by using the reorganized observation method. Further, a batch form and an iterative form of RH estimation are proposed by minimizing a given cost function that includes some terminal weighting terms based on the new system. The stability of the proposed RH estimation is guaranteed by the natural assumptions and a simulation instance is given to verify the effectiveness of the proposed method.

Analytical Co-Design of Receding Horizon Estimation and Control for Power Converters

Analytical Co-Design of Receding Horizon Estimation and Control for Power Converters

Concurrent Receding Horizon Control and Estimation Against Stealthy Attacks

In this work, we consider a game-theoretic framework for cyber-physical systems, where a defender develops a mitigation strategy against an intelligent attacker who exploits the system's uncertainty to remain undetected. The goal of the defender is to optimize a performance cost constructed specifically to account for robustness against stealthy attacks, so that the system is regulated. Conversely, the goal of the attacker is to disrupt the system's performance by leveraging its significant information advantage against the defender. Both players implement their policies in a moving horizon fashion, according to the principles of receding horizon control. However, because the defender has no access to the full state of the system, it concurrently employs receding horizon estimation to overcome this limitation. A rigorous theoretical analysis shows that such a concurrent policy can guarantee closed-loop boundedness, despite the stealthy attacks and the information disadvantage. Simulations verify and clarify these findings.

Continuous-Time Receding-Horizon Estimation via Primal-Dual Dynamics on Vehicle Path-Following Control

In vehicle control, state estimation is essential even as the sensor accuracy improves with technological development. One of the vehicle estimation methods is receding-horizon estimation (RHE), which uses a past series of the measured state and input of the plant, and determines the estimated states based on linear or quadratic programming. It is known that RHE can estimate the vehicular state to which the extended Kalman filter cannot be applied owing to modeling errors. This study proposes a new computational form of the RHE based on primal-dual dynamics. The proposed form is expressed by a dynamic system; therefore, we can consider the computational stability based on the dynamic system theory. In this study, we propose a continuous-time representation of the RHE algorithm and redundant filters to improve the convergence performance of the estimation and demonstrate its effectiveness through a vehicle path-following control problem.

Continuous-Time Receding-Horizon Estimation via Primal-Dual Dynamics and Stability Analysis

Receding-Horizon Estimation (RHE) is an optimal filterling approach which uses past series of the plant's measured output and input and finds estimated states based on linear programming or quadratic programming. It is known that RHE can estimate the plant state to which the Kalman filter cannot be applied due to modeling errors. This paper considers the new computational form of RHE based on the principal dual gradient algorithm. The proposed form is expressed by the dynamical system, so we can consider the computational stability based on the dynamical system theory. This paper discusses the continuous-time representation of the RHE algorithm (continuous-time RHE) and filter characteristics to improve the convergence performance of the estimation. On the basis of the small gain theorem, the dynamics of RHE is analyzed. Also, the characteristics of continuous-time RHE is demonstrated via a vehicle path tracking control problem.

Moving horizon estimation of vehicle state and parameters

For the active safety control of the vehicle, it is extremely important to estimate the vehicle state in real-time and accurately during the driving process. A joint state and parameter estimation method based on QR decomposition and receding horizon estimation (RHE) is proposed. Firstly, by introducing the receding horizon strategy, the authors optimized the state and parameter estimation with a fixed number of variables, which can better deal with the estimation problem of time-varying parameters. Then, based on the principle of forward dynamic programming, the calculation of arrival cost is transformed into a least square equation, which is solved by QR decomposition. At the same time, an update method of arrival cost based on QR decomposition is given. In this way, the whole receding horizon estimation method is based on the optimization, and the feedback mechanism is introduced to improve the estimation accuracy and speed. The simulation results show that the accuracy of receding horizon estimation is obviously better than that of unscented Kalman filter (UKF), and the arrival cost update method based on QR decomposition is more convenient than the traditional arrival cost update method based on error covariance estimation.

WayFAST: Navigation With Predictive Traversability in the Field

We present a self-supervised approach for learning to predict traversable paths for wheeled mobile robots that require good traction to navigate. Our algorithm, termed WayFAST (Waypoint Free Autonomous Systems for Traversability), uses RGB and depth data, along with navigation experience, to autonomously generate traversable paths in outdoor unstructured environments. Our key inspiration is that traction can be estimated for rolling robots using kinodynamic models. Using traction estimates provided by an online receding horizon estimator, we are able to train a traversability prediction neural network in a self-supervised manner, without requiring heuristics utilized by previous methods. We demonstrate the effectiveness of WayFAST through extensive field testing in varying environments, ranging from sandy dry beaches to forest canopies and snow covered grass fields. Our results clearly demonstrate that WayFAST can learn to avoid geometric obstacles as well as untraversable terrain, such as snow, which would be difficult to avoid with sensors that provide only geometric data, such as LiDAR. Furthermore, we show that our training pipeline based on online traction estimates is more data-efficient than other heuristic-based methods.

Incident indicators for freeway traffic flow models

Developed in this paper is a traffic flow model parametrised to describe abnormal traffic behaviour. In large traffic networks, the immediate detection and categorisation of traffic incidents/accidents is of capital importance to avoid breakdowns, further accidents. First, this claims for traffic flow models capable to capture abnormal traffic condition like accidents. Second, by means of proper real-time estimation technique, observing accident related parameters, one may even categorize the severity of accidents. Hence, in this paper, we suggest to modify the nominal Aw-Rascle (AR) traffic model by a proper incident related parametrisation. The proposed Incident Traffic Flow (ITF) model is defined by introducing the incident parameters modifying the anticipation and the dynamic speed relaxation terms in the speed equation of the AR model. These modifications are proven to have physical meaning. Furthermore, the characteristic properties of the ITF model is discussed in the paper. A multi stage numerical scheme is suggested to discretise in space and time the resulting non-homogeneous system of PDEs. The resulting systems of ODE is then combined with receding horizon estimation methods to reconstruct the incident parameters. Finally, the viability of the suggested incident parametrisation is validated in a simulation environment.

Consensus-based distributed receding horizon estimation

This paper studies the distributed state estimation over sensor networks based on receding horizon estimation (RHE). Firstly, a new scheme of centralized RHE is introduced, which gathers the decomposition terms instead of collecting the measurements of each node. Then, we present a distributed estimate algorithm based on the centralized RHE. To avoid the quadratic programming (QP) problem, the proposed algorithm takes advantage of the analytical solution of the centralized RHE and performs consensus steps to generalize the distributed estimation for each node, which greatly reduces each node’s computation. Under the assumption of collective observability over networks, the proposed algorithm can guarantee the stability of estimation error in the case of enough consensus steps. Finally, the simulation results verify the effectiveness of the proposed method.

Observer-Based Unknown Input Estimator of Wave Excitation Force for a Wave Energy Converter

Several energy maximization control approaches for point-absorber wave-energy converter (PAWEC) systems require knowledge of the wave excitation force (WEF) that is not measurable during the PAWEC operation. Many WEF estimators have been proposed based on stochastic PAWEC modeling using the Kalman filter (KF), extended KF (EKF), or receding-horizon estimation. Alternatively, a deterministic WEF estimator is proposed here based on the fast unknown input estimation (FUIE) concept. The WEF is estimated as an unknown input obviating the requirement to represent its dynamics. The proposed observer-based unknown input estimator (OBUIE) inherits the capability of estimating fast-changing signals from the FUIE, which is important when considering irregular wave conditions. Unlike preceding methods, the OBUIE is designed based on a PAWEC model, including the nonlinear viscous drag force. It has been shown that the nonlinear viscous drag force is essential for accurate PAWEC model description, within the energy maximization control role. The performance of the proposed estimator is evaluated in terms of PAWEC conversion efficiency in a single degree-of-freedom PAWEC device operating in regular and irregular waves. Simulation results are obtained using MATLAB to evaluate the estimator under different control methods and subject to parametric uncertainty.

Receding horizon estimation for linear discrete-time systems with multi-channel observation delays

This paper investigates the receding horizon state estimation for the linear discrete-time system with multi-channel observation delays. The receding horizon estimation is designed by the reorganized observation technique and the linear unbiased estimation method. The estimation gains are developed by solving a set of Riccati equations, and a stability result about the state estimation is shown. Finally, an example is given to illustrate the efficiency of the receding horizon state estimation.

A New Approach to Receding Horizon State Estimation for LTI Systems in the Presence of Non-uniform Sampled Measurements

This paper proposes a recursive solution as an estimation strategy that incorporates non-uniform sampled measurements for a Linear Time-Invariant (LTI) Systems. The estimator is based on a modified Receding Horizon Estimator. The proposed approach allows system states to be recursively estimated, reducing estimation error by including measurements available at different sampling times, using a well-known structure. A discussion of the observability of the system in the presence of non-uniform measurements and the convergence conditions of the proposed estimator are also presented. Finally, numerical simulation demonstrates the effectiveness of the proposed estimator in comparison with a method using a Kalman filter with augmented state widely reported in the literature.

Suboptimal receding horizon estimation via noise blocking

For discrete-time linear systems, we propose a suboptimal approach to constrained estimation so that the associated computation burden is reduced. This is achieved by enforcing a move blocking (MB) structure in the estimated process noise sequence (PNS). We show that full information estimation (FIE) and receding horizon estimation (RHE) with MB are both stable in the sense of an observer. The techniques in proving stability are inspired by those that have been proposed for standard RHE. To be specific, stability results are mainly achieved by (i) carefully embellishing the general assumptions for standard RHE to accommodate the MB requirement; (ii) exploiting the principle of optimality, as well as convexity of the quadratic programs (QPs) associated with FIE and RHE; (iii) relying on the fact that the Kalman filter is the best linear estimator in the least-squares sense. A crucial requirement in achieving stability for MB RHE is that the segment structure (SS) of the PNS of MB FIE for the optimization steps within the receding horizon (i.e., steps between T−N and T−1) has to be enforced in the MB RHE optimization. As a result, the MB RHE strategy becomes a dynamic estimator with a periodically varying computational complexity. The theoretical results have been illustrated with examples.

High‐precision control of tracked field robots in the presence of unknown traction coefficients

AbstractAccurate steering through crop rows that avoids crop damage is one of the most important tasks for agricultural robots utilized in various field operations, such as monitoring, mechanical weeding, or spraying. In practice, varying soil conditions can result in off‐track navigation due to unknown traction coefficients so that it can cause crop damage. To address this problem, this paper presents the development, application, and experimental results of a real‐time receding horizon estimation and control (RHEC) framework applied to a fully autonomous mobile robotic platform to increase its steering accuracy. Recent advances in cheap and fast microprocessors, as well as advances in solution methods for nonlinear optimization problems, have made nonlinear receding horizon control (RHC) and receding horizon estimation (RHE) methods suitable for field robots that require high‐frequency (milliseconds) updates. A real‐time RHEC framework is developed and applied to a fully autonomous mobile robotic platform designed by the authors for in‐field phenotyping applications in sorghum fields. Nonlinear RHE is used to estimate constrained states and parameters, and nonlinear RHC is designed based on an adaptive system model that contains time‐varying parameters. The capabilities of the real‐time RHEC framework are verified experimentally, and the results show an accurate tracking performance on a bumpy and wet soil field. The mean values of the Euclidean error and required computation time of the RHEC framework are equal to 0.0423 m and 0.88 ms, respectively.

Decentralized State Estimation for Networked Navigation Systems with Communication Delay and Packet Loss: The Receding Horizon Case

The paper deals with the problem of state estimation for a class of navigation-oriented carriers within navigation carrier ad-hoc networks (NC-NET): the state evolves according to a linear discretetime model subject to communication delay and packet loss. A decentralized estimation scheme is designed mainly based on the receding horizon estimation concept. Hereinto, the communication delay and packet loss are modeled in a uniform Markov process. Also, the approach through the reorganization of measurements is comprised to preprocess the delay-affect observations. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed scheme.

Estimation of the Blood Velocity for Nanorobotics

This paper aims to estimate the blood velocity to enhance the navigation of an aggregate in the human vasculature. The considered system is a polymer-binded aggregate of ferromagnetic nanorobots immersed in a blood vessel. The drag force depends on the blood velocity and especially acts on the aggregate dynamics. In the design of advanced control laws, the blood velocity is usually assumed to be known or set to a constant mean value to achieve the control objectives. We provide theoretical tools to online estimate the blood velocity from the sole measurement of the aggregate position and combine the state estimator with a backstepping control law. Two state estimation approaches are addressed and compared through simulations: a high-gain observer and a receding horizon estimator. Simulations illustrate the efficiency of the proposed approach combining online estimation and control for the navigation of an aggregate of nanorobots.

Receding Horizon Estimation of Arbitrarily Changing Unknown Inputs

In this paper we present a receding horizon estimation method for linear time invariant systems, subject to unknown inputs. The proposed approach is based on the idea of asymptotically decoupling the state estimation problem from the unknown input estimation problem. Consequently, the latter is formulated as a weighted least squares problem in a receding horizon manner. The proposed method does not assume a dynamic model for the unknown input, but it allows to incorporate prior knowledge about its abrupt nature by adding ℓ1-regularization terms to the cost function of the weighted least squares problem. The receding horizon input estimation method and the necessary conditions for it to hold are outlined. The proposed method is illustrated in simulation for the case of abruptly changing piece-wise constant unknown inputs.

State estimation and detection of changes in time interval models

This paper presents an estimation approach for Time Event Graphs such as P-Time Event Graphs and Time Stream Event Graphs. It is assumed that the nominal behavior is known and that transitions are partitioned as observable and unobservable transitions. The technique is applied to the detection of changes which are (possibly small) finite variations of dynamic models compared to this nominal behavior. The detected changes provide indications that can be used in future maintenance operations. Using the algebra of dioids, the approach uses a receding-horizon estimation of the greatest state and analyzes the consistency of the data.

Receding horizon estimation to networked control systems with multirate scheme

This paper investigates the problem of receding horizon state estimation for networked control systems (NCSs) with random network-induced delays less than one sample period, which are formulated as multirate control systems. Based on a batch of recent past slow rate measurements in a finite horizon window, the initial state estimation in this window is solved by minimizing a receding-horizon objective function, and then the fast rate state estimations are calculated by the prediction of dynamic equation to compensate for the network-induced time delays. Furthermore, convergence results and unbiasedness properties are analyzed. An upper bound of estimation error is presented under the assumption of bounded disturbances acting on the system and measurement equations. A simulation example shows the effectiveness of the proposed method.

Nonlinear predictive control in the LHC accelerator

This paper describes the application of a nonlinear model-based control strategy in a real challenging process. A predictive controller based on a nonlinear model derived from physical relationships, mainly heat and mass balances, has been developed and commissioned in the inner triplet heat exchanger unit (IT-HXTU) of the large hadron collider (LHC) particle accelerator at European Center for Nuclear Research (CERN). The advanced regulation maintains the magnets temperature at about 1.9 K. The development includes a constrained nonlinear state estimator with a receding horizon estimation procedure to improve the regulator predictions.