Hybrid Estimation Algorithm Research Articles

Robust parameter estimation for hybrid dynamical systems with linear parametric uncertainty

We consider the problem of estimating a vector of unknown constant parameters for a class of hybrid dynamical systems – that is, systems whose state variables exhibit both continuous (flow) and discrete (jump) evolution – with dynamics that depend linearly on the unknown parameters. Using a hybrid systems framework, we propose a hybrid estimation algorithm that can operate during both flows and jumps that, under a notion of hybrid persistence of excitation, guarantees convergence of the parameter estimate to the true value. Furthermore, we show that the parameter estimate is input-to-state stable with respect to a class of hybrid disturbances. Simulation results including a spacecraft application show the merits of our proposed approach.

Refined Aircraft Positioning Based on Stochastic Hybrid Estimation with Adaptive Square-Root Unscented Particle Filtering

The positioning of civil aviation aircraft relative to a geographic reference point on Earth in a Cartesian frame is significant to detect the deviations from the desired path, especially for high-altitude airports or special airports based on performance-based navigation (PBN). To obtain these critical deviations during aircraft approach and landing, it is fundamental to estimate the continuous flight variables and discrete flight modes simultaneously with enough accuracy. With the coordinate conversion between the North, East, and Down (NED) frame and the geographic coordinate system based on World Geodetic System 1984 (WGS-84) considered, this study proposed a non-linear stochastic hybrid estimation algorithm with adaptive square-root unscented particle filtering (ASR-UPF) to estimate the true path. The probabilities of mode transition, represented by the normal cumulative density function of continuous states, determine whether to proceed with mode transitions. In addition, the adaptive update characterized by tracking variable noise and the importance sampling distributions based on the results of square-root unscented Kalman filtering (SR-UKF), as a comparative study of continuous system filtering, were used. The experiments illustrated the ASR-UPF is able to reduce the state estimation error more effectively, and more promptly track the error caused by incorrect mode estimation with adaptability compared to the SR-UKF. A further test with real flight data indicates that the proposed method gives the refined estimation of position and azimuth in NED frame.

State estimation of buses: A hybrid algorithm of deep neural network and unscented Kalman filter considering mass identification

Accurately obtaining vehicle state parameters is a crucial prerequisite for active safety control. However, key stability parameters of buses, such as sideslip angle and roll angle, are difficult to measure directly. Moreover, changes in the bus mass during the driving route can impact the vehicle state. To tackle these challenges, we identify the bus mass before state estimation, and propose a hybrid state estimation algorithm based on deep neural network (DNN) and unscented Kalman filter (UKF). First, the mass is identified using the recursive least squares (RLS) method based on longitudinal dynamics at each start of bus, and the yaw and roll moment of inertia are adaptively adjusted based on the identified mass. Second, a composite DNN combining the convolutional neural network (CNN), gated recurrent unit (GRU), and attention mechanism is designed to estimate sideslip and roll angles. As for the training dataset, it is acquired from different maneuvers simulated by TruckSim. Third, a UKF estimator is established based on 4-degree of freedom (DOF) vehicle dynamics model and magic tire formula, and the estimated values of DNN are inserted into UKF estimator as virtual observations. Finally, the proposed hybrid algorithm is validated through simulation maneuvers and real driving maneuvers based on MATLAB/Simulink and TruckSim software. The comparative results demonstrate that the proposed algorithm outperforms individual DNN estimation and UKF estimation, enhancing both estimation accuracy and reliability.

A Bad Data Resilient Multisensor Fusion Framework for Hybrid State Estimation

This paper proposes a novel estimation fusion approach for hybrid multi-stage power system state estimation. Hybrid estimation fusion architectures allow the incorporation of new classes of sensors without doing away with pre-existing estimators. The fusion module is responsible to produce final estimates based on the optimal merging of the individual estimators' outcomes. The proposed fusion formulation is based on the Maximum Correntropy Criterion (MCC), an optimization criterion borrowed from the information theoretic area that has been recently applied to conventional power system state estimation and enables the automatic suppression of bad data effects. In this paper, the correntropy-based formulation is used to replace the traditional minimum variance fusion methodology in the second stage of the hybrid estimation algorithm. To assess the applicability of the novel method, a three-sensor, MCC-based fusion architecture is evaluated through simulations conducted on the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">IEEE</i> 14-bus, 30-bus, 57-bus, and 118-bus test systems. In the absence of bad data, the results confirm the expected compatibility between the proposed MCC-based fusion and the conventional minimum variance formulation. In addition, extensive experiments considering distinct bad data scenarios under several operational conditions have been performed. They illustrate a novel functionality imparted by the proposed approach to the fusion module, namely, the ability to automatically reject discrepant data. Therefore, MCC fusion provides an extra layer of protection against the harming effects of individual estimates contaminated with gross errors.

State Estimation Using SCADA and PMU Measurements for Networks Containing Classic HVDC Links

• Hybrid state estimation (HSE) algorithm based on SCADA and PMUs measurements for AC power systems with embedded classic high voltage direct current (HVDC) links. • AC and DC measurements are modeled independently as functions of AC and DC states, respectively. • AC and DC measurements (states) are processed (estimated) simultaneously. • Coupling of AC and DC states is expressed by a set of three nonlinear equality constraints. This paper proposes a hybrid state estimation (HSE) algorithm which employs conventional measurements received from supervisory control and data acquisition (SCADA) system and synchrophasors measured from phasor measurement units (PMUs) for AC power systems with embedded classic high voltage direct current (HVDC) links. DC measurements obtained from the HVDC link are assumed to be sampled at the same rate as AC measurements. Zero injections and AC/DC coupling equations are modeled as equality constraints. By applying the nonlinear weighted least squares (WLS) algorithm with equality constraints, the HSE calculates both AC and DC states simultaneously. The effectiveness of the proposed algorithm is verified by simulations on the IEEE standard 14 and 30 bus test systems. The test results reveal the benefits of the proposed approach in terms of estimation accuracy and convergence speed.

A Two-Step Stochastic Hybrid Estimation for GNSS Carrier Phase Tracking in Urban Environments

This article presents a two-step stochastic hybrid estimation (TS-SHE) algorithm for robust and accurate carrier phase tracking of global navigation satellite system (GNSS) signals in urban environments with significant power degradation and fluctuation. The proposed algorithm adaptively combines a bank of parallel Kalman filters (KFs) with different dynamic state models to cope with the nonstationarity of GNSS signals. Different from conventional approaches, including the phase lock loop (PLL), the KF, and the interacting multiple-model (IMM) method, which strongly rely on the a priori fixed signal model to ensure good tracking performance, we develop a novel stochastic filter transition strategy utilizing the information from reliable signal condition evaluation to overcome the performance degradation caused by the model mismatch in urban environments. Therein, for the first time, we use the prior information of signal fading conditions for more accurate combined weighting of all component filters. Specifically, to obtain the prior information, GNSS data are sequentially buffered and analyzed in the first step. Then, in the second step, optimized filter weights are generated, and the overall combined carrier phase is estimated. We analyze the theoretical performance of the new algorithm and show the effects of different design parameters on the performance. The primary advantages of the proposed algorithm include: 1) the ability to rapidly recover carrier phase observation when blocked signals are reacquired and 2) high accuracy in carrier phase estimation of GNSS signals corrupted by strong multipath fading. Simulation and real data experiment results show the enhanced robustness and improved accuracy of the proposed TS-SHE algorithm compared with conventional carrier phase tracking methods.

Hybrid Fuzzy Regression Analysis Using the F-Transform

This paper proposes a hybrid estimation algorithm for independently estimating the response function for the center and the response function for the spread in fuzzy regression model. The proposed algorithm combines the least absolute deviations estimation with discriminant analysis. In addition, the F-transform is used to convert spreads of the dependent variable into several groups. Two examples show that our method is superior to the existing methods based on the fuzzy regression model that assumes the same function for spread and center.

Intent Inference Based Trajectory Prediction and Smooth for UAS in Low-altitude Airspace with Geofence

In order to meet the higher accuracy requirement of trajectory prediction for Unmanned Aircraft System (UAS) in Unmanned Aircraft System Traffic Management (UTM), an Intent Based Trajectory Prediction and Smooth Based on Constrained State-dependent-transition Hybrid Estimation (CSDTHE-IBTPS) algorithm is proposed. Firstly, an intent inference method of UAS is constructed based on the information of ADS-B and geofence system. Moreover, a geofence layering algorithm is proposed. Secondly, the Flight Mode Change Points (FMCP) are used to define the relevant mode transition parameters and design the guard conditions, so as to generate the mode transition probability matrix and establish the continuous state-dependent-transition model. After that, the constrained Kalman filter (CKF) is applied to improve State-dependent-transition Hybrid Estimation (SDTHE) algorithm by applying equality constraint to the velocity of UAS in the straight phase and turning phase, respectively, and thus the constrained state-dependent-transition hybrid estimation (CSDTHE) algorithm is constructed. Finally, the results of intent inference and hybrid estimation are used to make trajectory prediction. Furthermore, each flight segment of trajectory is smoothed respectively by Rauch-Tung-Striebel (RTS) backward smooth method using the proposed CSDTHE-RTS algorithm, so as to obtain more accurate trajectory prediction results. The simulation shows that the proposed algorithm can reduce the errors of trajectory prediction and the time delay of intent inference.

Hybrid Estimation Algorithm for Lithium-ion Battery based on PI Observer

In view of poor adaptive ability and accuracy when estimating SOC with a single algorithm, a hybrid estimation algorithm with PI observer and Coulomb counting method is proposed in this paper. The algorithm firstly uses the RLS (Recursive Least Squares) method to identify parameters of the battery. Secondly, the open circuit voltage is calculated by the PI observer. Based on the difference between the calculated value and the estimated value, a PI dynamic adjustment is performed. Thus the integration coefficient of the Coulomb integration is optimized in real time. The research shows that, the method can dynamically correct the cumulative deviation of the Coulomb method.

Intent-Based Detection and Characterization of Aircraft Maneuvers in En Route Airspace

To improve the safety and efficiency of air traffic control, it is important to detect any deviations (or maneuvers) of an aircraft from its planned route. In addition to the detection of maneuvers, the characterization of maneuvers can enhance the situational awareness of air traffic controllers. In this paper, an algorithm for the inference of aircraft maneuvers from flight plans and flight tracks is proposed that identifies when the maneuver starts and ends, what type of maneuver is taken, and how an aircraft takes the maneuver. The aircraft maneuvers in current operations are modeled as a sequence of simple or elementary motions, called intents, and the intents are inferred based on the continuous and discrete states of an aircraft obtained from a hybrid estimation algorithm. The proposed algorithm is demonstrated with flight data from the Airspace Concept Evaluation System, which is a multifidelity modeling and simulation system with full gate-to-gate representation of all the major components of the National Airspace System.

Aircraft parameter estimation using Hybrid Neuro Fuzzy and Artificial Bee Colony optimization (HNFABC) algorithm

In this paper, method of aerodynamic parameter estimation of aircraft, in the presence of process and measurement noise, have been introduced with the help of relevant experiments carried out on simulated as well as real aircraft data. A merger between two recently proposed artificial intelligence based techniques one of which simulates the intelligent foraging behavior of honey bee swarm viz. Artificial Bee Colony (ABC) optimization along with well-known Adaptive Neuro-Fuzzy System (ANFIS) that simulates the working of a unit of brain viz. neuron combined with the knowledge-based decision making capability of fuzzy system have been shown to be a promisingly new approach to the problem of aerodynamic modeling and parameter estimation for both aerodynamically stable aircraft in the presence of measurement error (sensor noise). Obtained results have been compared with benchmark estimation methods viz. Least Square, Filter Error Method. Corroborating results and comparisons have been furnished highlighting the efficacy of proposed algorithm. Furthermore, it has been shown that the proposed hybrid estimation algorithm can have realizable application in extracting stability and control variables utilizing kinematics of stable aircraft even in absence of adequate information content in the data history.

State of charge estimation of power Li-ion batteries using a hybrid estimation algorithm based on UKF

Based on the analysis of the existing State of charge (SOC) Estimation Algorithms of batteries, this paper proposes a hybrid estimation algorithm according to the UKF method, the Ah method and the open circuit method in SOC estimation of battery pack which consists of 320 batteries. The “buckets effect” exists between series batteries and the differences between each cell were also been taken into consideration during estimating the SOC of power batteries. Finally, the hybrid estimation algorithm was applied to estimate SOC of battery pack under ECE driving cycles. The result shows that the error of the hybrid estimation algorithm is less than 5%.

Partially‐observable stochastic hybrid systems (poshss) state estimation and optimal control

AbstractThis paper discusses the state estimation and optimal control problem of a class of partially‐observable stochastic hybrid systems (POSHS). The POSHS has interacting continuous and discrete dynamics with uncertainties. The continuous dynamics are given by a Markov‐jump linear system and the discrete dynamics are defined by a Markov chain whose transition probabilities are dependent on the continuous state via guard conditions. The only information available to the controller are noisy measurements of the continuous state. To solve the optimal control problem, a separable control scheme is applied: the controller estimates the continuous and discrete states of the POSHS using noisy measurements and computes the optimal control input from the state estimates. Since computing both optimal state estimates and optimal control inputs are intractable, this paper proposes computationally efficient algorithms to solve this problem numerically. The proposed hybrid estimation algorithm is able to handle state‐dependent Markov transitions and compute Gaussian‐ mixture distributions as the state estimates. With the computed state estimates, a reinforcement learning algorithm defined on a function space is proposed. This approach is based on Monte Carlo sampling and integration on a function space containing all the probability distributions of the hybrid state estimates. Finally, the proposed algorithm is tested via numerical simulations.

Neuro-evolutionary approaches to power system harmonics estimation

This paper focuses on exploiting two computational intelligence techniques such as artificial neural network and evolutionary computation techniques in estimation of harmonics in power system. Accurate estimation of harmonics in distorted power system current/voltage signal is essential to effectively design filters for eliminating harmonics. No standard design is available for handling of local minima and training of NN but Evolutionary Computation (EC) techniques are capable of resolving local minima. Neural Network and Evolutionary Computing (Bacterial Foraging Optimization (BFO)) are combined to achieve accurate estimation of different harmonics components of a distorted power system signal. First estimation of unknown parameters are carried out using BFO, then optimized output of BFO are taken as initial values of the unknown parameters for Adaline. Amplitude and phase of fundamental and harmonics components are determined from final updated values of unknown parameters using Adaline. This Adaline based Bacterial Foraging Optimization (Adaline-BFO) hybrid estimation algorithm addresses the problems of slow convergence and reduction of time generation of off-springs happening in Genetic Algorithm (GA), and to avoid local minima in Particle Swarm Optimization (PSO). The proposed Adaline-BFO algorithm has been applied for estimation of harmonics of the voltage obtained across the inverter terminals of a prototype Photovoltaic (PV) system. From the obtained results, it is confirmed that the proposed Adaline-BFO algorithm provides superior estimation performance in terms of improvement in % error in estimation, processing time in computation and performance in presence of inter and sub-harmonic components when compared with the Discrete Fourier Transform (DFT), Kalman Filter (KF) and BFO algorithms.

Multi-Sensor Fusion and Fault Detection using Hybrid Estimation for Air Traffic Surveillance

Data fusion for multiple surveillance sensors in air traffic control (ATC) is studied. The goal is to build up software redundancy for better target tracking accuracy and robustness against sensor faults. A set of hybrid estimation algorithms for different sensors is designed to run in parallel for tracking aircraft with changing flight modes. The proposed sensor fusion algorithm combines the estimates from each hybrid estimation algorithm and identifies potential sensor faults.

Optimal sensor scheduling for hybrid estimation

A sensor scheduling problem was considered for a class of hybrid systems named as the stochastic linear hybrid system (SLHS). An algorithm was proposed to select one (or a group of) sensor at each time from a set of sensors. Then, a hybrid estimation algorithm was designed to compute the estimates of the continuous and discrete states of the SLHS based on the observations from the selected sensors. As the sensor scheduling algorithm is designed such that the Bayesian decision risk is minimized, the true discrete state can be better identified. Moreover, the continuous state estimation performance of the proposed algorithm is better than that of hybrid estimation algorithms using only predetermined sensors. Finally, the algorithms are validated through an illustrative target tracking example.

Robust estimation and fault detection and isolation algorithms for stochastic linear hybrid systems with unknown fault input

In this study, we develop algorithms for robust estimation and fault detection and identification for a class of hybrid systems called the stochastic linear hybrid system (SLHS). The authors propose a robust hybrid estimation algorithm that estimates the continuous state and the discrete state of an SLHS with unknown fault inputs. The algorithm decouples the unknown fault input from the estimation error dynamics for each discrete state of the hybrid system to guarantee the convergence of the estimation error. The robust hybrid estimation algorithm is designed for two kinds of discrete state transition models: the Markov-jump transition model whose discrete transition probabilities are constant (i.e. independent of the continuous state) and the state-dependent transition model whose discrete state transitions are determined by some guard conditions (i.e. dependent on the continuous state). The proposed residual generation algorithm computes residuals to facilitate fault detection and isolation. The residuals have the properties that they can reconstruct (in the mean sense) the unknown fault input vector. The authors also demonstrate the performance of the proposed algorithm with a vertical take-off and landing aircraft example.

Algorithm for Conformance Monitoring in Air Traffic Control

Conformance monitoring in air traffic control is an approach that is used to detect any deviations of the aircraft from its cleared (or planned) flight path that might compromise safety and efficiency. This task is made difficult by the fact that some deviations are normally expected of a conforming aircraft due to uncertainties. In this paper, a conformance monitoring algorithm that uses a stochastic linear hybrid system model is proposed. The stochastic linear hybrid system model divides the aircraft dynamics into a number of flight modes and is able to describe the random deviations in (conforming) aircraft trajectories. The detection of any nonconforming trajectories is determined by a fault detection technique. First, a hybrid estimation algorithm is used to estimate the hybrid state of the stochastic linear hybrid system and generate a residual vector based on the measurements. The statistical characteristics of the residual expected of a conforming aircraft are derived. Then, a statistical decision test is used to detect any deviation of the observed residual from the expected residual. Two illustrative examples are presented to demonstrate the performance of the proposed algorithm.

Terminal-Area Aircraft Tracking Using Hybrid Estimation

A bottleneck to the flow of air traffic is in the traffic around airports. Accurate tracking of aircraft movements around airports is important to improve traffic capacity and safety. We propose a hybrid estimation algorithm that uses the knowledge of departure or arrival aircraft flight plans and nominal flight profiles to improve tracking of aircraft movements around airports. The algorithm also provides an accurate estimation of aircraft flight modes that is often used in conflict detection, intent inference, and trajectory prediction algorithms. In the algorithm, we first develop a methodology to model flight mode transitions based on typical aircraft landing profiles, takeoff profiles, and standard flight routes around airports. Based on the model, we derive a conditional mode transition matrix that is dependent (or conditioned) on the continuous state of the aircraft. The aircraft-tracking problem is then solved using a hybrid estimation algorithm. We also present an analytical result that reduces the dimension, and hence the computational cost, of a multivariate integral that arises due to the continuous-state-dependent mode transition matrix. We present two simulation examples to illustrate the performance of our aircraft-tracking algorithm.

Stochastic Linear Hybrid Systems: Modeling, Estimation, and Application in Air Traffic Control

We propose a discrete-time model for a stochastic hybrid system (SHS) in which the continuous state evolution is described by stochastic difference equations and the discrete state evolution is governed by stochastic guards (or conditions that contain random parameters). The stochastic guards model system's uncertainties that directly affect the discrete state evolution and thus incorporate uncertainties that are different from those due to the stochastic evolution of the continuous state. A special class of the SHS family, called stochastic linear hybrid system (SLHS), is then presented. In the SLHS, the continuous state evolution is described by a set of stochastic linear difference equations, and the stochastic guards are a set of polyhedral partitions of a real vector space (which is a union of the continuous state space and the random parameter space). Some examples of practical systems that can be modeled as the SLHS are presented. Utilizing the properties of the SLHS, we propose a corresponding hybrid estimation algorithm. The algorithm approximates the conditional probability density functions (pdfs) of the continuous state by Gaussian pdfs. Both the conditional continuous state pdf and the discrete state pdf are then propagated analytically using a Bayesian approach. The SLHS model and the proposed hybrid estimation algorithm are used in an aircraft tracking application in air traffic control. It is illustrated that, in this application, a more accurate modeling of the discrete state transitions with the stochastic guards results in better hybrid estimation accuracy compared with other models/algorithms that assume deterministic guards or constant transition probabilities.