МОДЕЛЮВАННЯ ПРОЦЕСУ ВІДСТЕЖЕННЯ ЦІЛІ ЗА ДОПОМОГОЮ ФІЛЬТРІВ КАЛМАНА

Many technologies need to be established to realize autonomous ships. In particular, accurate state estimation in real time is one of the most important technologies. In the ship and ocean engineering fields, there have been many studies on state estimation using nonlinear Kalman filters. Several methods have been proposed for nonlinear Kalman filters. However, there is insufficient verification on the selection of which filter should be applied among them. Therefore, this study aims to validate the filter selection to provide a guideline for filter selection. The effects of modeling error, observation noise, and type of maneuvers on the estimation accuracy of the unscented Kalman filter (UKF) and ensemble Kalman filter (EnKF) used in this study were investigated. In addition, it was verified whether filtering could be performed in real time. The results show that modeling error significantly impacts the estimation accuracy of the UKF and EnKF. However, the observation noise and types of maneuvers did not have an impact like the modeling error. Thus, we obtained the guideline that UKF and EnKF should be used differently depending on the required computation time. We also obtained that keeping the modeling error sufficiently small is essential to improving the estimation accuracy.

The dynamic image reconstruction allows to combine the acquisition of projection data with the reconstruction task. The image is supposed to be a random field discrete in space. Taking into account the properties of the acquisition task, the data can be represented as a multi-dimensional discrete-time Markovian process. As a result the Kalman filter technique in the time domain is proposed for optimal linear dynamic reconstruction. The main restrictions for employing the Kalman filter approach consist in the huge dimension of the algorithm and the strong requirements to the introduced prior knowledge. The main goal of this paper is to investigate a pseudo Kalman filter algorithm that provides sufficient decrease of the dimension and reduction of the necessary amount of prior knowledge. The proposed approach is based on applying the regularization principle together with a recursive estimation procedure. The regularization principle allows to replace statistical prior by empirical prior. The appropriate co...

O RBIT determination algorithms are designed to estimate satellite position and inertial velocity from unbiased sensor measurements. Static and dynamic measurement biases, which are low-frequency systematic errors, cause biases in both position and velocity estimates that can significantly degrade track accuracy. As only the random error statistics are characterized, the filter covariance usually underestimates the biased track error statistics. Track biases and covariance fidelity are important issues for correlation and fusion of multiple sensor tracks [1,2]. Many algorithms have been developed [3–10] for estimation of bias parameters in the system dynamics, in the measurements, or in both. Generally, bias parameters are estimated jointly with the position and velocity states. Depending on the number of bias parameters, this approach can be computationally intensive, the system covariance matrix can become ill conditioned, and bias-state observability and separability can be problematic. Alternatively, two-step techniques extract bias parameters from the track measurement residuals. For current radar systems, measurement biases are calibrated by tracking one metric satellite having an accurate ephemeris, or by tracking many satellites with less accurate ephemerides [9]. Range and angle biases are calibrated after (not during) the data collection (s). A noteworthy exception is a real-time algorithm for angle bias estimation in wideband radars [10]. In this Note, an iterated 12-state extended Kalman filter EKF(12) is formulated for simultaneous (real-time) orbit determination and bias estimation. Orbit position and velocity states are augmented with six dynamic (rather than static) bias states that model radar orientation biases and radar range-angle measurement biases. Biasstate observability and separability are enhanced by physical models for the bias dynamics and by careful characterization of bias effects in the measurement residuals. For example, random and certain environmental (i.e., tropospheric) bias errors are intrinsic to the radar measurements, whereas radar orientation biases corrupt the transformation of the prior position estimate from inertial to radar coordinates. Performance evaluations will demonstrate accurate real-time state estimates and excellent covariance fidelity, which are essential for radar-to-radar track correlation and fusion. II. Sensor Models

A recursive state estimation procedure is derived for a linear time varying system with both parametric uncertainties and stochastic measurement droppings. This estimator has a similar form as that of the Kalman filter with intermittent observations, but its parameters should be adjusted when a plant output measurement arrives. A new recursive form is derived for the pseudo-covariance matrix of estimation errors, which plays important roles in analyzing its asymptotic properties. Based on a Riemannian metric for positive definite matrices, some necessary and sufficient conditions have been obtained for the strict contractiveness of an iteration of this recursion. It has also been proved that under some controllability and observability conditions, as well as some weak requirements on measurement arrival probability, the gain matrix of this recursive robust state estimator converges in probability one to a stationary distribution. Numerical simulation results show that estimation accuracy of the suggested procedure is more robust against parametric modelling errors than the Kalman filter.

The presence of fixed and stochastic parameters in a mixed linear regression model has been dealt with for the case where the stochastic parameters follow a stationary process. The solution is given either by Generalized Least Squares (e.g. Rao, 1965, p. 192) or by a recursive state space estimation procedure such as the Kalman filter and smoother (e.g. Sallas and Harville 1981). The estimation of non-stationary stochastic parameters has been mainly approached in the state space framework, either as an initial condition problem (see among others, Ansley and Kohn, 1985, 1989; Kohn and Ansley, 1986; Bell and Hillmer, 1991 and De Jong, 1989, 1991); or as a hierarchical model with “fixed” effects in the hierarchy given a flat prior distribution (see Sallas and Harville, 1981, 1988; Tsimikas and Ledolter, 1994).KeywordsKalman FilterTime Series AnalysisAmerican Statistical AssociationARIMA ModelGeneralize Little SquareThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The performance of a Kalman filter that estimates core power in a pressurized water reactor was evaluated using data from the Loss of Fluid Test (LOFT) Reactor and linear error analysis techniques. The Kalman filter provides a more accurate core power estimate in real time than does the conventional method of power estimation. Accuracies of better than 0.75% of rated power are obtained with the Kalman filter. If this accuracy improvement can be translated into higher levels of power operation, then more revenue can be generated by a commercial power plant. Scaling the LOFT 150-MW(thermal) l accuracy improvement up to a 1000-MW(electric) commercial power plant size, assuming that average power production is increased by the amount of the accuracy improvement, results in more than $800 000 of extra revenue per year ($0.06/kW·h).

BART is a state-of-the-art active end-to-end bandwidth measurement method that estimates not only the available bandwidth but also the link capacity of the bottleneck link. It uses a Kalman filter to give estimates in real time during a measurement session. In this paper, we have studied the impact of 802.11 networks on the bandwidth estimates produced by BART. The Kalman filter used by BART is tunable, and one of the contributions of this paper is to show how the Kalman filter should be adjusted to improve real-time tracking and estimation accuracy when the bottleneck is an 802.11 link. Further, the paper contributes by discussing how to interpret the estimates produced by BART and similar bandwidth estimation tools relying on self-induced congestion when used in wireless scenarios. An analysis show that the BART estimates produced are correct - but corresponds to a fair share of the wireless link rather than to the unused capacity. However, the estimates do indicate how much bandwidth an application or device in the wireless network can expect when sending and/or receiving network traffic.

This study addresses the development of probability distributions of travel times for one‐dimensional (vertical) solute transport in soils. The field‐scale soils are considered heterogeneous, with stationary fluctuations of soil hydraulic properties in the horizontal direction but nonstationary fluctuations of these properties in the vertical direction due to layering of the soil, which induces nonstationary heterogeneity. Approximate ensemble probability distribution functions of conservative solute travel time for vertical convective solute transport were derived directly from the convective transport stochastic partial differential equation, under both deterministic and stochastic soil surface water flux (infiltration rate) and under unsteady and nonuniform soil water flows. General depth‐varying initial and time‐varying boundary conditions were used in these derivations. The magnitude of the approximation in the theoretical probability distribution functions of travel time is quantified mathematically. Utilizing the soil water content data from a University of California, Davis, field site, it is shown that the mathematical condition for this approximation is satisfied for this field. The spatial heterogeneity is represented through a nonstationary soil water content random field which covaries both in time and in space. Dispersion emerges naturally in the derived ensemble probability distribution functions of solute travel time, owing to the stochasticity of soil water content at field scale. Then the theoretical expression for mean solute concentration over a field is derived, by means of the theoretical solute travel time distribution, as a function of time and soil depth, under vertical transport with rectangular pulse solute loading for the upper boundary condition. Comparisons of theoretical probability density functions of solute travel time against their empirical counterparts, obtained from field experimental observations under steady but nonuniform soil water flow, show good agreement. Comparisons of theoretical mean solute concentrations, as they evolve with time and soil depth, against field experimental observations also show good agreement. However, further field experiments under unsteady flow conditions are required for the comprehensive validation of the developed theory.

Real-time inverse estimation of multi-directional random waves from vessel-motion sensors using Kalman filter

Zero velocity update (ZUPT) is an inexpensive and effective method for error control of inertial navigation system (INS). Detecting the stopping time interval is important for ZUPT methods. The ZUPT method based on Kalman filter has a higher degree of precision compared with the ZUPT method based on curve fitting and the ZUPT method based on maximum likelihood estimation, but the modeling of Kalman filter is critical for the performance of INS. In this paper, three kinds of zero-velocity detectors and a linear discrete Kalman filter model are applied in ZUPT for INS. Simulation results show that the three kinds of zero-velocity detectors are effective, and the ZUPT method based on the linear discrete Kalman filter model makes the positioning accuracy of INS significantly improved.

We provide algorithms for inferring GPS (Global Positioning System) location and for quantifying the uncertainty of this estimate in real time. The algorithms are tested on GPS data from locations in the Southern Hemisphere at four significantly different latitudes. In order to rank the algorithms, we use the so-called log-score rule. The best algorithm uses an Ornstein–Uhlenbeck (OU) noise model and is built on an enhanced Kalman Filter (KF). The noise model is capable of capturing the observed autocorrelated process noise in the altitude, latitude and longitude recordings. This model outperforms a KF that assumes a Gaussian noise model, which under-reports the position uncertainties. We also found that the dilution-of-precision parameters, automatically reported by the GPS receiver at no additional cost, do not help significantly in the uncertainty quantification of the GPS positioning. A non-learning method using the actual position measurements and employing a constant uncertainty does not even converge to the correct position. Inference with the enhanced noise model is suitable for embedded computing and capable of achieving real-time position inference, can quantify uncertainty and be extended to incorporate complementary sensor recordings, e.g., from an accelerometer or from a magnetometer, in order to improve accuracy. The algorithm corresponding to the augmented-state unscented KF method suggests a computational cost of , where is the dimension of the augmented state-vector and is an adjustable, design-dependent parameter corresponding to the length of “past values” one wishes to keep for re-evaluation of the model from time to time. The provided algorithm assumes . Hence, the algorithm is likely to be suitable for sensor fusion applications.

Monitoring Daily Milk Yields with a Recursive Test Day Repeatability Model (Kalman Filter)

The Kalman filter is a recursive estimator and plays a fundamental role in statistics for filtering, prediction and smoothing. The key element in any recursive estimator is the estimate of the current state, xk, at time k, based on observations up to and including observation k and the Kalman filter enables the estimate of the state to be updated as new observations become available. In this paper we have tried to derive the Kalman filter as simple as possible.

A novel rotor velocity estimation scheme applicable to vector controlled induction motors has been described. The proposed method evaluates rotor velocity, /spl omega//sub r/, online, does not require any extra transducers or injection of any signals, nor does it employ complicated algorithms such as MRACS or Kalman filters. Furthermore, the new scheme operates at all velocities including zero with very little error. The procedure employs motor model equations; however all differential and integral terms have been eliminated giving a very fast, low-cost, and practical alternative to methods currently available. Furthermore, the resistance estimation technique is also implemented. Not only does this ensure the tuned operation of the vector controller, but also results in the aforementioned velocity estimator being completely parameter insensitive. A detailed and thorough explanation of the underlying theory of both velocity and parameter estimation techniques is given. These are supported by various simulation tests, taking into consideration the PWM inverter, and practical results.

Response latency in spiking activity is frequently investigated and often defined in different ways. In this study it is the time period from the stimulus application to the change in the neural firing rate evoked by the stimulation. While methods of latency estimation were proposed mostly for excitatory response (e.g. in [1], [2], [3]), the opposite kind of reaction has not been investigated. Therefore, we focus on the estimation of the latency in the case of inhibitory response. The approach is based on observations of the time from the stimulus onset to the occurrence of the first spike after the stimulus (forward recurrence time) in n independent trials (the same approach as in [3]). Two types of models of a spike train are introduced. The characteristic feature of the first type is the assumption of a constant latency across trials. On the contrary, in models of the second type, the latency is a random variable; hence it can vary across trials. The statistical properties of the latency are estimated in the second case. Either the probability density function of the forward recurrence time or its Laplace transform is derived for a given model and is then employed in several methods of latency estimation. Moment estimators and maximum-likelihood estimators are applications of generally known estimation methods. Another method uses the Laplace transform of the probability density function of the forward recurrence time. And the last proposed method is semiparametric and its idea is to compare the theoretical cumulative distribution function of the forward recurrence time derived for the model in absence of stimulation to the empirical distribution function obtained from data.