Joint State Estimation Research Articles

Spatiotemporal System Identification With Continuous Spatial Maps and Sparse Estimation.

We present a framework for the identification of spatiotemporal linear dynamical systems. We use a state-space model representation that has the following attributes: 1) the number of spatial observation locations are decoupled from the model order; 2) the model allows for spatial heterogeneity; 3) the model representation is continuous over space; and 4) the model parameters can be identified in a simple and sparse estimation procedure. The model identification procedure we propose has four steps: 1) decomposition of the continuous spatial field using a finite set of basis functions where spatial frequency analysis is used to determine basis function width and spacing, such that the main spatial frequency contents of the underlying field can be captured; 2) initialization of states in closed form; 3) initialization of state-transition and input matrix model parameters using sparse regression-the least absolute shrinkage and selection operator method; and 4) joint state and parameter estimation using an iterative Kalman-filter/sparse-regression algorithm. To investigate the performance of the proposed algorithm we use data generated by the Kuramoto model of spatiotemporal cortical dynamics. The identification algorithm performs successfully, predicting the spatiotemporal field with high accuracy, whilst the sparse regression leads to a compact model.

Continuous Cardiac Output Estimation Under Left Ventricular Assistance

Sufficient cardiac output is the main goal of ventricular assist device therapy. To date, there is no adequate method to estimate the combined amount of blood the heart and an continuous-flow assist device pump through the circulatory system. This paper presents an approach to estimate the cardiac output based on the signals provided by optical pressure sensors mounted on the inlet and outlet of an Impella CP pump. An extended Kalman filter for joint estimation of the aortic flow rate and the hydraulic resistance of the aortic valve is introduced. It uses a third order nonlinear state-space model of the aortic valve, aortic arch and systemic circulation with six parameters. The accuracy of the estimated cardiac output is investigated in an animal study with two sheep suffering from acute ischemic heart disease supported by a left ventricular assist device. The extended Kalman filter with joint parameter and state estimation yields an error of 0.47 ± 0.32 L · min−1. It is compared to an extended Kalman filter without parameter identification which achieves a comparable error of 0.49 ± 0.26 L · min−1. The errors are in the same order of magnitude as the accuracy of the clinical gold standard for invasive blood flow diagnostics. The introduced method enables cardiac output to be used as the control variable of a physiological control strategy for closed-loop ventricular assist device therapy.

Recursive Maximum Likelihood Identification of Jump Markov Nonlinear Systems

We present an online method for joint state and parameter estimation in jump Markov non-linear systems (JMNLS). State inference is enabled via the use of particle filters which makes the method applicable to a wide range of non-linear models. To exploit the inherent structure of JMNLS, we design a Rao-Blackwellized particle filter (RBPF) where the discrete mode is marginalized out analytically. This results in an efficient implementation of the algorithm and reduces the estimation error variance. The proposed RBPF is then used to compute, recursively in time, smoothed estimates of complete data sufficient statistics. Together with the online expectation maximization algorithm, this enables recursive identification of unknown model parameters including the transition probability matrix. The method is also applicable to online identification of jump Markov linear systems(JMLS). The performance of the method is illustrated in simulations and on a localization problem in wireless networks using real data.

An Integrated Approach to Prognosis of Hybrid Systems With Unknown Mode Changes

A new framework to design model-based prognosis for hybrid systems with unknown mode changes is proposed in this paper. The key step is the construction of an interacting diagnostic hybrid bond graph-particle filter (IDHBG-PF) module in the framework. In the module, the diagnostic hybrid bond graph (DHBG) part is employed for mode tracking after fault occurrence and fault isolation, and the particle filter (PF) part is used for joint state and parameter estimation as well as remaining useful life prediction. The DHBG part provides the set of suspected faults (SSF) to augment the dynamic model for the PF part, whereas the PF part outputs true faults for SSF refinement to facilitate prognosis and further fault isolation. During the prognosis, the probability density function (pdf) of the predicted remaining useful life under different operating modes can be calculated using the estimated mode-dependent degradation rate (MD-DR) and the user-selected failure threshold. The key concepts of the developed prognosis framework are validated by experimental results.

Parameter Estimation of MEMS Gyroscope Using Local State Estimation Methods

The topic of unknown parameters estimation of a MEMS gyroscope system in real-time is proposed and discussed. The problem is tackled using state estimation methodology. It is formulated as joint state and parameter estimation where three local estimators are utilized. The estimates are used to control the proof mass trajectory adaptively where the system is enforced to operate at the resonant frequency of the system without damping coefficients. The estimate quality of the considered estimators is compared. Numerical simulation results indicate that the proposed approach provides a better estimate quality in comparison with the extended Kalman filter both in terms of convergence speed and quality of estimates.

Identification of Outages in Power Systems With Uncertain States and Optimal Sensor Locations

Joint outage identification and state estimation in power systems is studied. A Bayesian framework is employed, and a Gaussian prior distribution of the states is assumed. The joint posterior of the outage hypotheses and the network states is developed in closed form, which can be applied to obtain the optimal joint detector and estimator under any given performance criterion. Employing the minimum probability of error as the performance criterion in identifying outages with uncertain states, the optimal detector is obtained. Efficiently computable performance metrics that capture the probability of error of the optimal detector are developed. Under simplified model assumptions, closed-form expressions for these metrics are derived, and these lead to a mixed integer convex programming problem for optimizing sensor locations. Using convex relaxations, a branch and bound algorithm that finds the globally optimal sensor locations is developed. Significant performance gains from using the optimal detector with the optimal sensor locations are observed from simulations. Furthermore, performance with greedily selected sensor locations is shown to be very close to that with globally optimal sensor locations.

Sensor Fault Diagnosis for an UAV Control System Based on a Strong Tracking Kalman Filter

The fault diagnosis of unmanned aerial vehicle (UAV) flight control system is an important research of UAV in health management. The sensor is the link which easiest to have problems of the flight control system. Making timely and accurate prediction of its faults is particularly important. A strong tracking Kalman Filter method for the sensor fault diagnosis of UAV flight control system was presented in this paper. The parameters of the system were extended to the state variables, the sensor fault observer was constructed, and the joint estimation of states and parameters of flight control system were gotten. The method can be used to real-time estimate the unmeasured states and time-varying parameters. The results of simulation experiments show that the method has a good real-time and accuracy in the sensor fault diagnosis of flight control system.

A Smoothed GMS Friction Model Suited for Gradient-Based Friction State and Parameter Estimation

This paper presents a model that closely approximates the generalized Maxwell-Slip (GMS) model, a multistate friction model known to describe all essential friction characteristics in presliding and sliding motion. In contrast to the GMS model, which consists of a switching structure to accommodate for its hybrid nature, the new model, referred to as the smoothed GMS (S-GMS) model, consists of an analytic set of differential equations. Such a model is well suited for gradient-based state and parameter estimation, as in the extended Kalman filter (EKF) or in moving horizon estimation. Similar to the GMS model, the S-GMS model is a multistate model that also describes all essential friction characteristics. Moreover, the S-GMS model description includes the single-state LuGre model and Elastoplastic model as special cases. This paper also discusses the implementation of the EKF estimator for the S-GMS friction model and compares its performance to the LuGre model in joint state and parameter estimation.

Simultaneous State and Parameter Estimation Using Maximum Relative Entropy with Nonhomogenous Differential Equation Constraints

In this paper, we continue our efforts to show how maximum relative entropy (MrE) can be used as a universal updating algorithm. Here, our purpose is to tackle a joint state and parameter estimation problem where our system is nonlinear and in a non-equilibrium state, i.e., perturbed by varying external forces. Traditional parameter estimation can be performed by using filters, such as the extended Kalman filter (EKF). However, as shown with a toy example of a system with first order non-homogeneous ordinary differential equations, assumptions made by the EKF algorithm (such as the Markov assumption) may not be valid. The problem can be solved with exponential smoothing, e.g., exponentially weighted moving average (EWMA). Although this has been shown to produce acceptable filtering results in real exponential systems, it still cannot simultaneously estimate both the state and its parameters and has its own assumptions that are not always valid, for example when jump discontinuities exist. We show that by applying MrE as a filter, we can not only develop the closed form solutions, but we can also infer the parameters of the differential equation simultaneously with the means. This is useful in real, physical systems, where we want to not only filter the noise from our measurements, but we also want to simultaneously infer the parameters of the dynamics of a nonlinear and non-equilibrium system. Although there were many assumptions made throughout the paper to illustrate that EKF and exponential smoothing are special cases ofMrE, we are not “constrained”, by these assumptions. In other words, MrE is completely general and can be used in broader ways.

Joint estimation of state and noise parameters in a linear dynamic system with impulsive measurement noise: Application to OFDM systems

Interference mitigation is one of the main challenges in wireless communication, especially in ad hoc networks. In such context, the Multiple Access Interference (MAI) is known to be of an impulsive nature. Therefore, the conventional Gaussian assumption is inadequate to model this type of interference. Nevertheless, it can be accurately modeled by stable distributions. In fact, it was shown in literature that the α-stable distribution is a useful tool to model impulsive data. In this paper, we tackle the problem of noise compensation in ad hoc networks. More precisely, this issue is addressed within an Orthogonal Frequency Division Multiplexing (OFDM) transmission link assuming a symmetric α-stable model for the signal distortion due to MAI. Based on Bayesian estimation, the proposed approach estimates the transmitted OFDM symbols in the time domain using the Sequential Monte Carlo (SMC) methods. Unlike existing schemes, we consider the more realistic case where the impulsive noise parameters are assumed to be unknown at the receiver. Consequently, our approach deals also with the difficult task of noise parameters estimation which can be very useful for other purposes such as target tracking in wireless sensor networks or channel estimation. Simulations results, provided in terms of Mean Square Error (MSE) and Bit Error Rate (BER), illustrate the efficiency and the robustness of this scheme.

Linear minimum‐mean‐square error estimation of Markovian jump linear systems with Stochastic coefficient matrices

This study presents the state estimation problem of discrete-time Markovian jump linear systems with stochastic coefficient matrices which is motivated by the idea of establishing the general filter framework of the joint state estimation and data association in clutters for tracking the manoeuvering target. According to the orthogonality principle, the linear minimum-mean-square error estimator for this system (abbreviated as LMSCE estimator) is derived recursively and sufficient conditions are given for the stability of the LMSCE estimator. The simulation about tracking the manoeuvering target in clutters shows that the LMSCE estimator obtains much more accurate estimate than the well-known interacting multiple model probabilistic data association filter.

Soil moisture and soil properties estimation in the Community Land Model with synthetic brightness temperature observations

AbstractThe Community Land Model (CLM) includes a large variety of parameterizations, also for flow in the unsaturated zone and soil properties. Soil properties introduce uncertainties into land surface model predictions. In this paper, soil moisture and soil properties are updated for the coupled CLM and Community Microwave Emission Model (CMEM) by the Local Ensemble Transform Kalman Filter (LETKF) and the state augmentation method. Soil properties are estimated through the update of soil textural properties and soil organic matter density. These variables are used in CLM for predicting the soil moisture retention characteristic and the unsaturated hydraulic conductivity, and the soil texture is used in CMEM to calculate the soil dielectric constant. The following scenarios were evaluated for the joint state and parameter estimation with help of synthetic L‐band brightness temperature data assimilation: (i) the impact of joint state and parameter estimation; (ii) updating of soil properties in CLM alone, CMEM alone or both CLM and CMEM; (iii) updating of soil properties without soil moisture update; (iv) the observation localization of LETKF. The results show that the characterization of soil properties through the update of textural properties and soil organic matter density can strongly improve with assimilation of brightness temperature data. The optimized soil properties also improve the characterization of soil moisture, soil temperature, actual evapotranspiration, sensible heat flux, and soil heat flux. The best results are obtained if the soil properties are updated only. The coupled CLM and CMEM model is helpful for the parameter estimation. If soil properties are biased, assimilation of soil moisture data with only state updates increases the root mean square error for evapotranspiration, sensible heat flux, and soil heat flux.

Adaptive filter of non‐linear systems with generalised unknown disturbances

This study presents the state estimation problem of discrete-time non-linear stochastic system with generalised unknown disturbance (GUD) in the measurements. To the best of our knowledge, there is no research result on the filter design dealing with such estimation problem. Here, an upper-bound filter is designed for the linear time-varying system with the GUD existing in the measurement equation, and optimal parameters are derived so that the minimum upper-bounds filter is obtained. The result is further extended to the non-linear case via the iterative optimisation of joint state estimation and parameter identification (the linearised measurement matrix). The simulation about tracking a target via one biased radar and one biased electronic support measure (ESM) shows the effectiveness and robustness of the proposed filter.

Sequential Monte Carlo Methods for State and Parameter Estimation in Abruptly Changing Environments

This paper develops a novel sequential Monte Carlo (SMC) approach for joint state and parameter estimation that can deal efficiently with abruptly changing parameters which is a common case when tracking maneuvering targets. The approach combines Bayesian methods for dealing with change-points with methods for estimating static parameters within the SMC framework. The result is an approach that adaptively estimates the model parameters in accordance with changes to the target's trajectory. The developed approach is compared against the Interacting Multiple Model (IMM) filter for tracking a maneuvering target over a complex maneuvering scenario with nonlinear observations. In the IMM filter a large combination of models is required to account for unknown parameters. In contrast, the proposed approach circumvents the combinatorial complexity of applying multiple models in the IMM filter through Bayesian parameter estimation techniques. The developed approach is validated over complex maneuvering scenarios where both the system parameters and measurement noise parameters are unknown. Accurate estimation results are presented.

State of charge estimation for lithium-ion batteries: An adaptive approach

State of charge (SoC) estimation is of key importance in the design of battery management systems. An adaptive SoC estimator, which is named AdaptSoC, is developed in this paper. It is able to estimate the SoC in real time when the model parameters are unknown, via joint state (SoC) and parameter estimation. The AdaptSoC algorithm is designed on the basis of three procedures. First, a reduced-complexity battery model in state-space form is developed from the well-known single particle model (SPM). Then a joint local observability/identifiability analysis of the SoC and the unknown model parameters is performed. Finally, the SoC is estimated simultaneously with the parameters using the iterated extended Kalman filter (IEKF). Simulation and experimental results exhibit the effectiveness of the AdaptSoC.

Multiple Vehicle Cooperative Localization with Spatial Registration Based on a Probability Hypothesis Density Filter

This paper studies the problem of multiple vehicle cooperative localization with spatial registration in the formulation of the probability hypothesis density (PHD) filter. Assuming vehicles are equipped with proprioceptive and exteroceptive sensors (with biases) to cooperatively localize positions, a simultaneous solution for joint spatial registration and state estimation is proposed. For this, we rely on the sequential Monte Carlo implementation of the PHD filtering. Compared to other methods, the concept of multiple vehicle cooperative localization with spatial registration is first proposed under Random Finite Set Theory. In addition, the proposed solution also addresses the challenges for multiple vehicle cooperative localization, e.g., the communication bandwidth issue and data association uncertainty. The simulation result demonstrates its reliability and feasibility in large-scale environments.

Adaptive High-Gain observer for joint state and parameter estimation: A comparison to Extended and Unscented Kalman filter

An adaptive High-Gain observer (AHG) as well as an Extended (EKF) and Unscented Kalman filter (UKF) are implemented for joint state and parameter estimation of a novel multi-axial electromagnetically actuated punch. These observers are compared in terms of convergence and response time to erroneous parameter and state initialization, as well as parameter modifications during operation. The AHG is further analyzed proposing an adaptive gain, which reduces the observer's high sensibility with respect to noise. Simulation results show that AHG is more suitable compared to state-of-the-art EKF and UKF.

Tire Radii Estimation Using a Marginalized Particle Filter

In this paper, the measurements of individual wheel speeds and the absolute position from a global positioning system are used for high-precision estimation of vehicle tire radii. The radii deviation from its nominal value is modeled as a Gaussian random variable and included as noise components in a simple vehicle motion model. The novelty lies in a Bayesian approach to estimate online both the state vector and the parameters representing the process noise statistics using a marginalized particle filter (MPF). Field tests show that the absolute radius can be estimated with submillimeter accuracy. The approach is tested in accordance with regulation 64 of the United Nations Economic Commission for Europe on a large data set (22 tests, using two vehicles and 12 different tire sets), where tire deflations are successfully detected, with high robustness, i.e., no false alarms. The proposed MPF approach outperforms common Kalman-filter-based methods used for joint state and parameter estimation when compared with respect to accuracy and robustness.

Adaptive Observer for Switching Linear Parameter-Varying (LPV) Systems

In this paper, the problem of joint state and parameter estimation in switching Linear Parameter-Varying (LPV) systems is considered. The proposed solution relies on an adaptive observer, which is designed finding a solution to a system of Trilinear Matrix Inequalities (TMIs). It is shown that, under certain assumptions, the TMIs can be reduced to Linear Matrix Inequalities (LMIs) that can be solved using available software. An example of a four wheeled omnidirectional mobile robot subject to unknown offsets in the motor voltages is used to illustrate the efficiency of the proposed approach.

Set Adaptive Observers for Linear Parameter-Varying Systems: Application to Fault Detection

This paper deals with the problem of joint state and parameter estimation based on a set adaptive observer design. The problem is formulated and solved for an LPV (linear parameter-varying) system. The resolution methodology avoids the exponential complexity obstruction usually encountered in the set-membership parameter estimation. A simulation example is presented to illustrate the efficiency of the proposed approach.