Initial State Estimation Research Articles

An Initial Value Estimation Method for the Kalman and Extended Kalman Filters in Underground Metal Detection

As an underground metal detection technology, the electromagnetic induction (EMI) method is widely used in many cases. Therefore, the EMI detection algorithms with excellent performance are worth studying. One of the EMI detection methods in the underground metal detection is the filter method, which first obtains the secondary magnetic field data and then uses the Kalman filter (KF) and the extended Kalman filter (EKF) to estimate the parameters of metal targets. However, the traditional KF methods used in the underground metal detection have an unsatisfactory performance of the convergence as the algorithms are given a random or a fixed initial value. Here, an initial state estimation algorithm for the underground metal detection is proposed. The initial state of the target’s horizontal position is estimated by the first order central moments of the secondary field strength map. In addition, the initial state of the target’s depth is estimated by the full width at half maximum (FWHM) method. In addition, the initial state of the magnetic polarizability tensor is estimated by the least squares method. Then, these initial states are used as the initial values for KF and EKF. Finally, the position, posture and polarizability of the target are recursively calculated. A simulation platform for the underground metal detection is built in this paper. The simulation results show that the initial value estimation method proposed for the filtering algorithm has an excellent performance in the underground metal detection.

Optimal Maneuver Strategy of Observer for Bearing-Only Tracking in Threat Environment

The optimal maneuver of observer for bearing-only tracking (BOT) in a threat environment is a complex problem which involves nonlinear filtering, threat avoidance, and optimal maneuver strategy. Under comprehensive consideration, the reward function comprised of the lower bound on detFIM and threat cost was established; the finite-horizon MDP principle was applied to obtain the optimal strategy. The quantization method was used to discretize the BOT process and calculate the transition matrix of Markov chain; to achieve quantization in the beginning of each period, CKF was applied to provide the initial state estimate and the corresponding error covariance. The numerical simulations illustrated the applicability and superior performance for static and dynamic target tracking in several scenarios in the threat environment.

Accurate Initial State Estimation in a Monocular Visual-Inertial SLAM System.

The fusion of monocular visual and inertial cues has become popular in robotics, unmanned vehicles and augmented reality fields. Recent results have shown that optimization-based fusion strategies outperform filtering strategies. Robust state estimation is the core capability for optimization-based visual–inertial Simultaneous Localization and Mapping (SLAM) systems. As a result of the nonlinearity of visual–inertial systems, the performance heavily relies on the accuracy of initial values (visual scale, gravity, velocity and Inertial Measurement Unit (IMU) biases). Therefore, this paper aims to propose a more accurate initial state estimation method. On the basis of the known gravity magnitude, we propose an approach to refine the estimated gravity vector by optimizing the two-dimensional (2D) error state on its tangent space, then estimate the accelerometer bias separately, which is difficult to be distinguished under small rotation. Additionally, we propose an automatic termination criterion to determine when the initialization is successful. Once the initial state estimation converges, the initial estimated values are used to launch the nonlinear tightly coupled visual–inertial SLAM system. We have tested our approaches with the public EuRoC dataset. Experimental results show that the proposed methods can achieve good initial state estimation, the gravity refinement approach is able to efficiently speed up the convergence process of the estimated gravity vector, and the termination criterion performs well.

Iterative observer-based state and parameter estimation for linear systems

We propose an iterative method for joint state and parameter estimation using measurements on a time interval [0, T] for systems that are backward output stabilizable. Since this time interval is fixed, errors in initial state may have a big impact on the parameter estimate. We propose to use the back and forth nudging (BFN) method for estimating the system’s initial state and a Gauss–Newton step between BFN iterations for estimating the system parameters. Taking advantage of results on the optimality of the BFN method, we show that for systems with skew-adjoint generators, the initial state and parameter estimate minimizing an output error cost functional is an attractive fixed point for the proposed method. We treat both linear source estimation and bilinear parameter estimation problems.

Parallel List Decoding of Convolutional Codes: Algorithm and Implementation

List decoding is a promising technique for machine type communications (MTC) and other applications that pursue the high-coding gain of convolutional codes. However, there are obstacles that degrade the availability of list decoding. In specific, non-tail-biting list decoding involves high demands of data storage, while tail-biting list decoding requires substantial computational resources to preserve the optimal performance. In this paper, we rethink the parallel list decoder design from the aspects of algorithm and implementation to circumvent the foregoing obstacles. On the one hand, internal relations among the multiple decoding sequences are revealed and leveraged to redesign the non-tail-biting list decoding algorithm, which enables the design to extricate from the massive storage expense. On the other hand, a reliability-ordered initial-state estimator is designed for the tail-biting list decoder, which helps to alleviate the computational burden while retaining the optimal error-correction performance. In conjunction with the optimizations on underlying structures, the proposed list decoder achieves better energy efficiency than existing work under the same coding gain. In the MTC scenario, moreover, the proposed design will be less area consuming than existing schemes to fulfill coding gain enhancement.

Adaptive robust output‐feedback motion control of hydraulic actuators

SummaryMost previous advanced motion control of hydraulic actuators used full‐state feedback control techniques. However, in many cases, only position feedback is available, and thus, there are imperious demands for output‐feedback control for hydraulic systems. This paper firstly transforms a hydraulic model into an output feedback–dependent form. Thus, the K‐filter can be employed, which provides exponentially convergent estimates of the unmeasured states. Furthermore, this observer has an extended filter structure so that online parameter adaptation can be utilized. In addition, it is a well‐known fact that any realistic model of a hydraulic system suffers from significant extent of uncertain nonlinearities and parametric uncertainties. This paper constructs an adaptive robust controller with backstepping techniques, which is able to take into account not only the effect of parameter variations coming from various hydraulic parameters but also the effect of hard‐to‐model nonlinearities such as uncompensated friction forces, modeling errors, and external disturbances. Moreover, estimation errors that come from initial state estimates and uncompensated disturbances are dealt with via certain robust feedback at each step of the adaptive robust backstepping design. After that, a detailed stability analysis for the output‐feedback closed‐loop system is scrupulously checked, which shows that all states are bounded and that the controller achieves a guaranteed transient performance and final tracking accuracy in general and asymptotic output tracking in the presence of parametric uncertainties only. Extensive experimental results are obtained for a hydraulic actuator system and verify the high‐performance nature of the proposed output‐feedback control strategy.

Initial-state detectability of stochastic discrete-event systems with probabilistic sensor failures

Initial-state estimation is an important problem in discrete-event systems. In this problem, the initial-state of the system is unknown and one wants to determine the initial-state of the system based on its observation. In this paper, we investigate the problem of initial-state detection of partially-observed discrete-event systems in the stochastic setting. We consider two sources of randomness in this problem: stochastic dynamic of the system and probabilistic sensor failures. Specifically, we model a stochastic discrete-event system by a probabilistic finite-state automaton and we use a probabilistic projection function as the observation model. The notion of stochastic initial-state detectability (SI-detectability) is introduced in order to capture whether or not the probability of detecting the initial-state converges to one even in the presence of potential sensor failures. An approach for the verification of SI-detectability is proposed. We also investigate the complexity of the SI-detectability verification problem and we show that this problem is PSPACE-complete.

Low-cost adaptive square-root cubature Kalman filter for systems with process model uncertainty

A novel low-cost adaptive square-root cubature Kalman filter (LCASCKF) is proposed to enhance the robustness of process models while only increasing the computational load slightly. It is well-known that the Kalman filter cannot handle uncertainties in a process model, such as initial state estimation errors, parameter mismatch and abrupt state changes. These uncertainties severely affect filter performance and may even provoke divergence. A strong tracking filter (STF), which utilizes a suboptimal fading factor, is an adaptive approach that is commonly adopted to solve this problem. However, if the strong tracking SCKF (STSCKF) uses the same method as the extended Kalman filter (EKF) to introduce the suboptimal fading factor, it greatly increases the computational load. To avoid this problem, a low-cost introductory method is proposed and a hypothesis testing theory is applied to detect uncertainties. The computational load analysis is performed by counting the total number of floating-point operations and it is found that the computational load of LCASCKF is close to that of SCKF. Experimental results prove that the LCASCKF performs as well as STSCKF, while the increase in computational load is much lower than STSCKF.

Estimation of exact initial states of fractional order systems

The initial condition problem of fractional order systems is investigated in this paper. Firstly, a named aberration phenomenon is introduced, which reveals the nature of initial condition problem. And then, in order to interpret this odd phenomenon, definitions of the Riemann–Liouville derivative and Caputo derivative are revisited. As a result, the fractional order systems described by fractional differential equations and exact state-space models are linked much more closely, and it is found that relationship between these two kinds of models basically lies in the exact initial state distribution. The results also show the inborn defects of these two derivatives. Afterward, a practical method to estimate the exact initial states is studied naturally. At last, several simulation examples carefully illustrate the effectiveness of proposed method.

Output error minimizing back and forth nudging method for initial state recovery

We show that for linear dynamical systems with skew-adjoint generators, the initial state estimate given by the back and forth nudging method with colocated feedback, converges to the minimizer of the discrepancy between the measured and simulated outputs — given that the observer gains are chosen suitably and the system is exactly observable. If the system’s generator A is essentially skew-adjoint and dissipative (with not too much dissipation), the colocated feedback has to be corrected by the operator eAteA∗t in order to obtain such convergence. In some special cases, a feasible approximation for this operator can be found analytically. The case with wave equation with constant dissipation will be presented.

Comparison of a particle filter and other state estimation methods for prognostics of lithium-ion batteries

A particle filter (PF) is shown to be more accurate than non-linear least squares (NLLS) and an unscented Kalman filter (UKF) for predicting the remaining useful life (RUL) and time until end of discharge voltage (EODV) of a Lithium-ion battery. The three algorithms, i.e. PF, UKF, and NLLS track four states with correct initial estimates of the states and 5% variation on the initial state estimates. The four states are data-driven, equivalent circuit properties or Lithium concentrations and electroactive surface areas depending on the model. The more accurate prediction performance of PF over NLLS and UKF is reported for three Lithium-ion battery models: a data-driven empirical model, an equivalent circuit model, and a physics-based single particle model.

大規模線形ネットワークに対する平均値オブザーバ

In this paper, towards efficient state estimation for large-scale networked linear systems, we propose a method for designing observers to estimate the average behavior of systems, which we call average state observers. First, we give a mathematical formulation of the average state observer. Furthermore, we derive the error system clarifying that not only an initial state estimation error but also the initial value response of systems and the input signal are relevant to the observation error. On the basis of this error analysis, we devise a systematic design procedure for average state observers. The proposed method does not require the information on how to choose a set of average states of systems. The efficiency of the proposed method is shown through a numerical example for a diffusion system.

Influence of atmospheric turbulence on planetary transceiver laser ranging

In this paper we investigate the influence of atmospheric turbulence on the performance of the uplink of a planetary transceiver laser ranging system using a single photon detector. We numerically combine the influence of turbulence in the mean intensity profile variations, scintillation, beam-wander induced pointing errors and stochastic time-of-flight variations, using the Hufnagel–Valley turbulence profile to model the ground turbulence behavior. We map the intensity variations due to turbulence to variations in the probability distribution of the arrival time of the 1st photon in a laser pulse, which influences the range measurement error probability distribution. The turbulence models are applied to assess the influence on single-pass range accuracy and precision statistics, as well as the parameter estimation quality of a Phobos Laser Ranging (PLR) mission.The difference in range measurement error between weak and strong turbulence is 3–4mm in a PLR concept. This indicates that turbulence is a potentially important contributor to the error budget of interplanetary laser ranging missions, which aim at mm-level accuracy and precision. The single-shot precision is weakly influenced by turbulence, but strong turbulence is found to cause a strong decrease in detected pulse fraction, reducing normal point precision. We show that a trade-off between range accuracy and precision must be made when selecting laser system parameters, considerations for which are influenced by atmospheric turbulence effects. By consistently operating at the single-photon signal strength level, accuracy variations can be largely removed, at the expense of normal point precision, due to the reduced detection probability. We perform parameter estimation of Phobos initial state and observation biases using simulated measurements with and without turbulence, using a daily periodic turbulence strength model. We show that the parameter estimation quality is degraded significantly below that of the turbulence-free case only in the presence of strong turbulence. This shows the existence of a limit of ground turbulence strength below which its influence on parameter estimation becomes negligible.

The Effect of Initial State Estimates on Just-in-Time Adaptive Disturbanc Estimation

Run-to-Run control algorithms for high-mix semiconductor processes typically require that the initial product state estimates have sufficient accuracy for satisfactory control. In this paper, we use historical process data and apply single observation just-in-time adaptive disturbance estimation (JADE) to find the initial product state estimates. Single observation JADE with random selection, high-frequency sampling, and exclusion of the earliest data from the average is shown to provide satisfactory initial product state estimates. The effect of initial state estimate accuracy is demonstrated by several simulation and industrial data examples. We also provide a method to estimate relative confidence between individual product state estimates, information that may be used to determine assignment of process error between the tool and product state.

Magnetometer-only attitude and angular velocity filtering estimation for attitude changing spacecraft

This paper presents an improved real-time sequential filter (IRTSF) for magnetometer-only attitude and angular velocity estimation of spacecraft during its attitude changing (including fast and large angular attitude maneuver, rapidly spinning or uncontrolled tumble). In this new magnetometer-only attitude determination technique, both attitude dynamics equation and first time derivative of measured magnetic field vector are directly leaded into filtering equations based on the traditional single vector attitude determination method of gyroless and real-time sequential filter (RTSF) of magnetometer-only attitude estimation. The process noise model of IRTSF includes attitude kinematics and dynamics equations, and its measurement model consists of magnetic field vector and its first time derivative. The observability of IRTSF for small or large angular velocity changing spacecraft is evaluated by an improved Lie-Differentiation, and the degrees of observability of IRTSF for different initial estimation errors are analyzed by the condition number and a solved covariance matrix. Numerical simulation results indicate that: (1) the attitude and angular velocity of spacecraft can be estimated with sufficient accuracy using IRTSF from magnetometer-only data; (2) compared with that of RTSF, the estimation accuracies and observability degrees of attitude and angular velocity using IRTSF from magnetometer-only data are both improved; and (3) universality: the IRTSF of magnetometer-only attitude and angular velocity estimation is observable for any different initial state estimation error vector.

Adaptive Finite-time Observer for a Nonlinear and Flexible Space Launch Vehicle

In this paper we propose a new finite-time state observer for a nonlinear space launch vehicle with flexible dynamics and uncertain parameters. Indeed, flexible states are required to ensure nonlinear control objectives of both reference path tracking and bending mode damping. Our main contribution is to show that it is enough to observe a sublinear uncertain system to ensure a finite-time convergence of the whole state. For that purpose, a Luenberger observer is mixed with a parameter and initial state estimator, based on algebraic estimation tools. Closed loop simulations show the effectiveness of the observer in combination with a backstepping control design (extended to flexible systems).

Modified Unscented Kalman Filter for a Multirate INS/GPS Integrated Navigation System

Instead of the extended Kalman filter, the unscented Kalman filter (UKF) has been used in nonlinear systems without initial accurate state estimates over the last decade because the UKF is robust against large initial estimation errors. However, in a multirate integrated system, such as an inertial navigation system (INS)/Global Positioning System (GPS) integrated navigation system, it is difficult to implement a UKF-based navigation algorithm in a low-grade or mid-grade microcontroller, owing to a large computational burden. To overcome this problem, this letter proposes a modified UKF that has a reduced computational burden based on the basic idea that the change of probability distribution for the state variables between measurement updates is small in a multirate INS/GPS integrated navigation filter. The performance of the modified UKF is verified through numerical simulations.

A hierarchical Bayesian model for forecasting state-level corn yield

Historically, the National Agricultural Statistics Service crop forecasts and estimates have been determined by a group of commodity experts called the Agricultural Statistics Board (ASB). The corn yield forecasts for the “speculative region,” ten states that account for approximately 85 % of corn production, are based on two sets of monthly surveys, a farmer interview survey and a field measurement survey. The members of the ASB subjectively determine a forecast on the basis of a discussion of the survey data and auxiliary information about weather, average planting dates, and crop maturity. The ASB uses an iterative procedure, where initial state estimates are adjusted so that the weighted sum of the final state estimates is equal to a previously-determined estimate for the speculative region. Deficiencies of the highly subjective ASB process are lack of reproducibility and a measure of uncertainty. This paper describes the use of Bayesian methods to model the ASB process in a way that leads to objective forecasts and estimates of the corn yield. First, we use small area estimation techniques to obtain state-level forecasts. Second, we describe a way to adjust the state forecasts so that the weighted sum of the state forecasts is equal to a previously-determined regional forecast. We use several diagnostic techniques to assess the goodness of fit of various models and their competitors. We use Markov chain Monte Carlo methods to fit the models to both historic and current data from the two monthly surveys. Our results show that our methodology can provide reasonable and objective forecasts of corn yields for states in the speculative region.

Skill of a global seasonal streamflow forecasting system, relative roles of initial conditions and meteorological forcing

We investigate the relative contributions of initial conditions (ICs) and meteorological forcing (MF) to the skill of the global seasonal streamflow forecasting system FEWS‐World, using the global hydrological model PCRaster Global Water Balance. Potential improvement in forecasting skill through better climate prediction or by better estimation of ICs through data assimilation depends on the relative importance of these sources of uncertainty. We use the Ensemble Streamflow Prediction (ESP) and reverse ESP (revESP) procedure to explore the impact of both sources of uncertainty at 78 stations on large global basins for lead times upto 6 months. We compare the ESP and revESP forecast ensembles with retrospective model simulations driven by meteorological observations. For each location, we determine the critical lead time after which the importance of ICs is surpassed by that of MF. We analyze these results in the context of prevailing hydroclimatic conditions for larger basins. This analysis suggests that in some basins forecast skill may be improved by better estimation of initial hydrologic states through data assimilation; whereas in others skill improvement depends on better climate prediction. For arctic and snowfed rivers, forecasts of high flows may benefit from assimilation of snow and ice data. In some snowfed basins where the onset of melting is highly sensitive to temperature changes, forecast skill depends on better climate prediction. In monsoonal basins, the variability of the monsoon dominates forecasting skill, except for those where snow and ice contribute to streamflow. In large basins, initial surface water and groundwater states are important sources of skill.

Verification of initial-state opacity in security applications of discrete event systems

In this paper, we formulate and analyze methodologies for verifying the notion of initial-state opacity in discrete event systems that are modeled as non-deterministic finite automata with partial observation on their transitions. A system is initial-state opaque if the membership of its true initial state to a set of secret states remains opaque (i.e., uncertain) to an intruder who observes system activity through some projection map. Initial-state opacity can be used to characterize security requirements in a variety of applications, including tracking problems in sensor networks. In order to model and analyze the intruder capabilities regarding initial-state opacity, we first address the initial-state estimation problem in a non-deterministic finite automaton via the construction of an initial-state estimator. We analyze the properties and complexity of the initial-state estimator, and show how the complexity of the verification method can be greatly reduced in the special case when the set of secret states is invariant. We also establish that the verification of initial-state opacity is a PSPACE-complete problem.