Showing papers on "Alpha beta filter published in 2007"

Nonlinear observers and applications

Abstract: An Overview on Observer Tools for Nonlinear Systems.- Uniform Observability and Observer Synthesis.- Adaptive-Gain Observers and Applications.- Immersion-Based Observer Design.- Nonlinear Moving Horizon Observers: Theory and Real-Time Implementation.- Asymptotic Analysis and Observer Design in the Theory of Nonlinear Output Regulation.- Parameter/Fault Estimation in Nonlinear Systems and Adaptive Observers.

An Iterative Ensemble Kalman Filter for Multiphase Fluid Flow Data Assimilation

Abstract: Summary The dynamical equations for multiphase flow in porous media are highly non-linear and the number of variables required to characterize the medium is usually large, often two or more variables per simulator gridblock. Neither the extended Kalman filter nor the ensemble Kalman filter is suitable for assimilating data or for characterizing uncertainty for this type of problem. Although the ensemble Kalman filter handles the nonlinear dynamics correctly during the forecast step, it sometimes fails badly in the analysis (or updating) of saturations. This paper focuses on the use of an iterative ensemble Kalman filter for data assimilation in nonlinear problems, especially of the type related to multiphase flow in porous media. Two issues are key: (1) iteration to enforce constraints and (2) ensuring that the resulting ensemble is representative of the conditional pdf (i.e. that the uncertainty quantification is correct). The new algorithm is compared to the ensemble Kalman filter on several highly nonlinear example problems, and shown to be superior in the prediction of uncertainty.

Optimal and Robust Estimation: With an Introduction to Stochastic Control Theory, Second Edition

Abstract: OPTIMAL ESTIMATION Classical Estimation Theory Mean-Square Estimation Maximum-Likelihood Estimation The Cramer-Rao Bound Recursive Estimation Wiener Filtering Problems Discrete-Time Kalman Filter Deterministic State Observer Linear Stochastic Systems The Discrete-Time Kalman Filter Discrete Measurements of Continuous-Time Systems Error Dynamics and Statistical Steady State Frequency Domain Results Correlated Noise and Shaping Filters Optimal Smoothing Problems Continuous-Time Kalman Filter Derivation from Discrete Kalman Filter Some Examples Derivation from Wiener-Hopf Equation Error Dynamics and Statistical Steady State Frequency Domain Results Correlated Noise and Shaping Filters Discrete Measurements of Continuous-Time Systems Optimal Smoothing Problems Kalman Filter Design and Implementation Modeling Errors, Divergence, and Exponential Data Weighting Reduced-Order Filters and Decoupling Using Suboptimal Gains Scalar Measurement Updating Problems Estimation for Nonlinear Systems Update of the Hyperstate General Update of Mean and Covariance Extended Kalman Filter Application to Robotics and Adaptive Sampling Problems ROBUST ESTIMATION Robust Kalman Filter Systems with Modeling Uncertainties Robust Finite Horizon Kalman A Priori Filter Robust Stationary Kalman A Priori Filter Convergence Analysis Linear Matrix Inequality Approach Robust Kalman Filtering for Continuous-Time Systems Problems H-Infinity Filtering of Continuous-Time Systems H-Infinity Filtering Problem Finite Horizon H-Infinity Linear Filter Characterization of All Finite Horizon H-Infinity Linear Filters Stationary H-Infinity Filter-Riccati Equation Approach Relationship with the Kalman Filter Convergence Analysis H-Infinity Filtering for a Special Class of Signal Models Stationary H-Infinity Filter-Linear Matrix Inequality Approach Problems H-Infinity Filtering of Discrete-Time Systems Discrete-Time H-Infinity Filtering Problem H-Infinity A Priori Filter H-Infinity A Posteriori Filter Polynomial Approach to H-Infinity Estimation J-Spectral Factorization Applications in Channel Equalization Problems OPTIMAL STOCHASTIC CONTROL Stochastic Control for State Variable Systems Dynamic Programming Approach Continuous-Time Linear Quadratic Gaussian Problem Discrete-Time Linear Quadratic Gaussian Problem Problems Stochastic Control for Polynomial Systems Polynomial Representation of Stochastic Systems Optimal Prediction Minimum Variance Control Polynomial Linear Quadratic Gaussian Regulator Problems Appendix A: Review of Matrix Algebra Basic Definitions and Facts Partitioned Matrices Quadratic Forms and Definiteness Matrix Calculus References Index

Short-Term Traffic Volume Forecasting Using Kalman Filter with Discrete Wavelet Decomposition

Abstract: : This article investigates the application of Kalman filter with discrete wavelet analysis in short-term traffic volume forecasting. Short-term traffic volume data are often corrupted by local noises, which may significantly affect the prediction accuracy of short-term traffic volumes. Discrete wavelet decomposition analysis is used to divide the original data into several approximate and detailed data such that the Kalman filter model can then be applied to the denoised data and the prediction accuracy can be improved. Two types of wavelet Kalman filter models based on Daubechies 4 and Haar mother wavelets are investigated. Traffic volume data collected from four different locations are used for comparison in this study. The test results show that both proposed wavelet Kalman filter models outperform the direct Kalman filter model in terms of mean absolute percentage error and root mean square error.

Feasibility studies of applying Kalman Filter techniques to power system dynamic state estimation

Abstract: The lack of dynamic information in the operation of power systems can be attributed to the use of steady state estimators, which generate the input values for many operational tools. This paper investigates the feasibility of applying Kalman Filtering techniques to include dynamic state variables in the state estimation process. The proposed Kalman Filter based dynamic state estimation is tested on a multi-machine system with both large and small disturbances. Sensitivity studies of the dynamic state estimation performance with respect to sampling rate and noise level are presented as well. The study results show that there is a promising path forward for the implementation of Kalman Filter based dynamic state estimation in conjunction with the emerging phasor measurement technologies.

Optimal fast tracking observer bandwidth of the linear extended state observer

Abstract: In current industrial control applications, the proportional + integral + derivative (PID) control is still used as the leading tool, but constructing controller requires precise mathematical model of plant, and tuning the parameters of controllers is not simple to implement. Motivated by the gap between theory and practice in control problems, linear active disturbance rejection control (LADRC) addresses a set of control problems in the absence of precise mathematical models. LADRC has two parameters to be tuned, namely, a closed-loop bandwidth and observer bandwidth. The performance of LADRC depends on the quick convergence of a unique state observer, known as the extended state observer, proposed by Jinqing Han (1994). Only one parameter, observer bandwidth, significantly affects the tracking speed of extended state observer. This paper studies numerically the optimal fast tracking observer bandwidth and the absolute tracking error estimation for a class of non-linear and uncertain motion control probl...

A Kalman filter for robust outlier detection

Abstract: In this paper, we introduce a modified Kalman filter that can perform robust, real-time outlier detection in the observations, without the need for manual parameter tuning by the user. Robotic systems that rely on high quality sensory data can be sensitive to data containing outliers. Since the standard Kalman filter is not robust to outliers, other variations of the Kalman filter have been proposed to overcome this issue, but these methods may require manual parameter tuning, use of heuristics or complicated parameter estimation. Our Kalman filter uses a weighted least squares-like approach by introducing weights for each data sample. A data sample with a smaller weight has a weaker contribution when estimating the current time step's state. We learn the weights and system dynamics using a variational Expectation-Maximization framework. We evaluate our Kalman filter algorithm on data from a robotic dog.

Unscented Kalman filtering for nonlinear structural dynamics

Abstract: Joint estimation of unknown model parameters and unobserved state components for stochastic, nonlinear dynamic systems is customarily pursued via the extended Kalman filter (EKF). However, in the presence of severe nonlinearities in the equations governing system evolution, the EKF can become unstable and accuracy of the estimates gets poor. To improve the results, in this paper we account for recent developments in the field of statistical linearization and propose an unscented Kalman filtering procedure. In the case of softening single degree-of-freedom structural systems, we show that the performance of the unscented Kalman filter (UKF), in terms of state tracking and model calibration, is significantly superior to that of the EKF.

Left-invariant extended Kalman filter and attitude estimation

Abstract: We consider a left-invariant dynamics on a Lie group. One way to define driving and observation noises is to make them preserve the symmetries. We propose a left- invariant (i.e, intrinsic and thus symmetry-preserving) extended Kalman filter such that the left-invariant estimation error obeys a stochastic differential equation independent of the system trajectory. The theory is illustrated by an attitude estimation example.

Combined Design of Disturbance Model and Observer for Offset-Free Model Predictive Control

Abstract: This note presents a method for the combined design of an integrating disturbance model and of the observer (for the augmented system) to be used in offset-free model predictive controllers. A dynamic observer is designed for the original (nonaugmented) system by solving an Hprop control problem aimed at minimizing the effect of unmeasured disturbances and plant/model mismatch on the output prediction error. It is shown that, when offset-free control is sought, the dynamic observer is equivalent to choosing an integrating disturbance model and an observer for the augmented system. An example of a chemical reactor shows the main features and benefits of the proposed method.

Robust Nonlinear Observer for Lipschitz Nonlinear Systems Subject to Disturbances

Abstract: This note proposes a robust nonlinear observer for systems with Lipschitz nonlinearity. The proposed nonlinear observer, whose linear part adopts the linear LTR observer design technique, has two important advantages over previous designs. First, the new observer does not impose the small-Lipschitz-constant condition on the system nonlinearity, nor other structural conditions on the system dynamics as in the existing observer designs. Second, it is robust in the sense that its state estimation error decays to almost zero even in the face of large external disturbances.

Robust Nonlinear Fusion of Inertial and Visual Data for position, velocity and attitude estimation of UAV

Abstract: This paper presents a coupled observer that uses accelerometer, gyrometer and vision sensors to provide estimates of pose and linear velocity for an aerial robotic vehicle. The observer is based on a non-linear complimentary filter framework and incorporates adaptive estimates of measurement bias in gyrometers and accelerometers commonly encountered in low-cost inertial measurement systems. Asymptotic stability of the observer estimates is proved as well as bounded energy of the observer error signals. Experimental data is provided for the proposed filter run on data obtained from an experiment involving a remotely controlled helicopter.

History Matching and Production Forecast Uncertainty by Means of the Ensemble Kalman Filter: A Real Field Application

Abstract: During history match reservoir models are calibrated against production data to improve forecasts reliability. Often, the calibration ends up with a handful of matched models, sometime achieved without preserving the prior geological interpretation. This makes the outcome of many history matching projects unsuitable for a probabilistic approach to production forecast, then motivating the quest of methodologies casting history match in a stochastic framework. The Ensemble Kalman Filter (EnKF) has gained popularity as Monte-Carlo based methodology for history matching and real time updates of reservoir models. With EnKF an ensemble of models is updated whenever production data are available. The initial ensemble is generated according to the prior model, while the sequential updates lead to a sampling of the posterior probability function. This work is one of the first to successfully use EnKF to history match a real field reservoir model. It is, to our knowledge, the first paper showing how the EnKF can be used to evaluate the uncertainty in the production forecast for a given development plan for a real field model. The field at hand was an on-shore saturated oil reservoir. Porosity distribution was one of the main uncertainties in the model, while permeability was considered a porosity function. According to the geological knowledge, the prior uncertainty was modeled using Sequential Gaussian Simulation and ensembles of porosity realizations were generated. Initial sensitivities indicated that conditioning porosity to available well data gives superior results in the history matching phase. Next, to achieve a compromise between accuracy and computational efficiency, the impact of the size of the ensemble on history matching, porosity distribution and uncertainty assessment was investigated. In the different ensembles the reduction of porosity uncertainty due to production data was noticed. Moreover, EnKF narrowed the production forecast confidence intervals with respect to estimate based on prior distribution. Introduction Reservoir management of modern oil and gas fields requires periodic updates of the simulation models to integrate in the geological parameterization production data collected over time. In these processes the challenges nowadays are many. First, a coherent view of the geomodel requires updating the simulation decks in ways consistent with geological assumptions. Second, the management is requiring more and more often a probabilistic assessment of the different development scenarios. This means that cumulative distribution functions, reflecting the underlying uncertainty in the knowledge of the reservoir, for key production indicators, e.g. cumulative oil production at Stock Tank condition (STC), along the entire time-life of the field, are expected outcomes of a reservoir modeling project. Moreover, production data are nowadays collected with increasing frequencies, especially for wells equipped with permanent down-hole sensors. Decision making, based on most current information, requires frequent and rapid updates of the reservoir models. The Ensemble Kalman Filter (EnKF) is a Monte-Carlo based method developed by Evensen to calibrate oceanographic models by sequential data assimilation. Since the pioneering application on near-well modeling problems by Naevdal et al., EnKF has become in the reservoir simulation community a popular approach for history matching and uncertainty assessment. This popularity is motivated by key inherent features of the method. EnKF is a sequential data assimilation methodology, and then production data can be integrated in the simulation model as they are available. This makes EnKF well suited for realtime application, where data continuously collected have to be used to improve the reliability of predictive models. EnKF maintains a Gaussian ensemble of models aligned with the most current production data by linear updates of the model parameters. In that way the statistical properties of the Gaussian ensemble, that is to say mean, variance and twopoint correlations are preserved. Because EnKF does not need either history matching gradients or sensitivity coefficients, any reservoir simulator with restarting capabilities can be used in an EnKF workflow, without modifying simulator source code. This represents an obvious advantage with respect to methods like the Randomized Maximum Likelihood (RML) method, which requires a simulator with adjoint gradient capabilities. These reasons motivate the interest on EnKF in the Upstream Industry. Nonetheless, only a few real applications were published before this work. Skjervheim et. al. compared results on using EnKF to assimilate 4D seismic data and production data, and obtained results that slightly improved the base case used for comparison. Haugen et al., see Ref. 13, report that the EnKF was used to successfully history match the simulation model of a Northern sea field, with substantial improvement compared to the reference case. In this paper we applied EnKF to history match the Zagor simulation model, quantifying also the reduction of uncertainty due to the assimilation of the production data. Different ensembles were used to investigate the connection between the effectiveness of EnKF and the size of the statistical samples. Next, we used one of the ensembles updated with EnKF to assess the uncertainty in the production forecasts. To our knowledge, this is the first paper where EnKF was used on a real reservoir from history match to uncertainty analysis of production forecasts. The paper proceeds as follows. The next section is dedicated to the discussion of the EnKF methodology, including its mathematical background and some remarks on the current limitations. Then the Zagor reservoir model is described. That includes the geological parameterization used in this work and the presentation of the different ensembles utilized in the application. The results of the application are presented in two subsequent sections. The first is dedicated to history matching and the second dedicated to the assessment of the uncertainty in the production forecasts. Finally, conclusions based on our results are drawn and some perspectives for future works are given. The Ensemble Kalman Filter The EnKF is a statistical methodology suitable to solve inverse problem, especially in cases where observed data are available sequentially in time. Assuming that the evolution of a physical system can be approximated by a numerical model, typically by the discretisation of a partial differential equation, a state vector can be used to represent the model parameters and observations. Using multiple realizations of the state vector one is able to explicitly express the model uncertainty. The EnKF can describe the evolution of the system by updating the ensemble of state vectors whenever an observation is available. In reservoir simulation, EnKF can be applied to integrate production data by updating sequentially an ensemble of reservoir models during the simulation. Each reservoir model in the ensemble is kept up-to-date as production data are assimilated sequentially. In this context every reservoir state vector comprises three types of parameters: static parameters, dynamic parameters and production data. The static parameters are the parameters that in traditional history matching do not vary with time during a simulation, such as permeability (K) and porosity (φ). The dynamic parameters include the fundamental variables of the flow simulation. These are, for black oil models, the cell pressure (p), water saturation (Sw), gas saturation (Sg) and solution gas-oil ratio (RS). In addition to the variables for each cells one add observations of the production data in each well. Production data usually include simulated data corresponding to observations such as well production rates, bottom-hole pressure values, water cut (WCT) and gas oil ratio (GOR) values. Thus, using the notation by X. H. Wen and W. H. Chen, the ensemble of state variables is modelled by multiple realizations:

Robust Extended Kalman Filtering in Hybrid Positioning Applications

Abstract: The Kalman filter and its extensions has been widely studied and applied in positioning, in part because its low computational complexity is well suited to small mobile devices. While these filters are accurate for problems with small nonlinearities and nearly Gaussian noise statistics, they can perform very badly when these conditions do not prevail. In hybrid positioning, large nonlinearities can be caused by the geometry and large outliers (blunder measurements) can arise due to multipath and non line-of-sight signals. It is therefore of interest to find ways to make positioning algorithms based on Kalman-type filters more robust. In this paper two methods to robustify the Kalman filter are presented. In the first method the variances of the measurements are scaled according to weights that are calculated for each innovation, thus giving less influence to measurements that are regarded as blunder. The second method is a Bayesian filter that approximates the density of the innovation with a non-Gaussian density. Weighting functions and innovation densities are chosen using Hubers min-max approach for the epsilon contaminated normal neighborhood, the p-point family, and a heuristic approach. Six robust extended Kalman filters together with the classical extended Kalman filter (EKF) and the second order extended Kalman filter (EKF2) are tested in numerical simulations. The results show that the proposed methods outperform EKF and EKF2 in cases where there is blunder measurement or considerable linearization errors present.

Non-fragile observer-based controls of linear system via LMI approach

Abstract: This paper investigates the non-fragile observer-based controls for continuous systems. Exponential stabilization for the systems is studied and the convergence rate is given. Two types of uncertainties which perturb the gains of control and observer are considered. Linear matrix inequality (LMI) approach is used to design the non-fragile observer-based control. The control and observer gains are given from LMI feasible solution. A numerical example is given to illustrate our method.

Learning an Outlier-Robust Kalman Filter

Abstract: We introduce a modified Kalman filter that performs robust, real-time outlier detection, without the need for manual parameter tuning by the user Systems that rely on high quality sensory data (for instance, robotic systems) can be sensitive to data containing outliers The standard Kalman filter is not robust to outliers, and other variations of the Kalman filter have been proposed to overcome this issue However, these methods may require manual parameter tuning, use of heuristics or complicated parameter estimation procedures Our Kalman filter uses a weighted least squares-like approach by introducing weights for each data sample A data sample with a smaller weight has a weaker contribution when estimating the current time step's state Using an incremental variational Expectation-Maximization framework, we learn the weights and system dynamics We evaluate our Kalman filter algorithm on data from a robotic dog

Noise robust voice activity detection based on switching Kalman filter

Abstract: This paper addresses the problem of voice activity detection (VAD) in noisy environments. The VAD method proposed in this paper is based on a statistical model approach, and estimates statistical models sequentially without a priori knowledge of noise. Namely, the proposed method constructs a clean speech / silence state transition model beforehand, and sequentially adapts the model to the noisy environment by using a switching Kalman filter when a signal is observed. In this paper, we carried out two evaluations. In the first, we observed that the proposed method significantly outperforms conventional methods as regards voice activity detection accuracy in simulated noise environments. Second, we evaluated the proposed method on a VAD evaluation framework, CENSREC-1-C. The evaluation results revealed that the proposed method significantly outperforms the baseline results of CENSREC-1-C as regards VAD accuracy in real environments. In addition, we confirmed that the proposed method helps to improve the accuracy of concatenated speech recognition in real environments.

Exploring scalar fields using multiple sensor platforms: Tracking level curves

Abstract: Autonomous mobile sensor networks are employed to measure large scale environmental scalar fields. Yet an optimal strategy for mission design addressing both the cooperative motion control and the collaborative sensing is still under investigation. We develop one strategy which uses four moving sensor platforms to explore a noisy scalar field defined in the plane; each platform can only take one measurement at a time. We derive a Kalman filter in conjunction with a nonlinear filter to produce estimates for the field value, the gradient and the Hessian along the averaged trajectories of the moving platforms. The shape of the platform formation is designed to minimize error in the estimates, and a cooperative control law is designed to asymptotically achieve the optimal formation. We develop a motion control law to allow the center of the platform formation to move along level curves of the averaged field. Convergence of the control laws are proved, and performance of both the filters and the control laws are demonstrated in simulated ocean fields.

Nonlinear Observer for Vehicle Velocity with Friction and Road Bank Angle Adaptation - Validation and Comparison with an Extended Kalman Filter

Abstract: Many active safety systems in automotive vehicles, for instance yaw stability systems such as ESC/ESP, depend on information about vehicle velocity, in particular lateral velocity or side-slip angle, to be able to function properly. However, the vehicle velocity is rarely measured directly due to issues of cost and reliability, and must therefore in general be inferred from other measurements, such as wheel speed, steering angle, yaw rate, and acceleration measurements.

Design of sliding mode unknown input observer for uncertain Takagi-Sugeno model

Abstract: This paper addresses the analysis and design of a sliding mode observer on the basis of a Takagi-Sugeno (T-S) model subject both to unknown inputs and uncertainties. The main contribution of the paper is the development of a robust observer with respect to the uncertainties as well as the synthesis of sufficient stability conditions of this observer. The stabilization of the observer is performed by the search of suitable Lyapunov matrices. It is shown how to determine the gains of the local observers, these gains being solutions of a set of linear matrix inequalities (LMI). The validity of the proposed methodology is illustrated by an academic example.

An impulsive observer that estimates the exact state of a linear continuous-time system in predetermined finite time

Abstract: This paper presents a new observer for the class of linear continuous-time systems. In contrast to many well-established observers, which normally estimate the system state in an asymptotic fashion, the proposed observer estimates the exact system state in predetermined finite time. The finite convergence time of the proposed observer is achieved by updating the observer state based on current observer data at a definite time instant. Simulation results are presented to illustrate the convergence behavior of the proposed observer.

On Kalman Active Observers

Abstract: The paper introduces the Active Observer (AOB) algorithm in the framework of Kalman filters. The AOB reformulates the Kalman filter to accomplish model-reference adaptive control based on: (1) A desired closed loop system. (2) An extra equation to estimate an equivalent disturbance referred to the system input. An active state is introduced to compensate unmodeled terms, providing a feedforward compensation action. (3) Stochastic design of the Kalman matrices. Stability analysis with model errors is discussed. An example of robot force control with an external and unknown nonlinear disturbance is presented (SISO system). Another example of model-matching control for steer-by-wire (SBW) vehicles with underactuated structure is discussed (MIMO system).

Some Practical Issues on Real-Time Reservoir Model Updating Using Ensemble Kalman Filter

Abstract: The concept of “closed-loop” reservoir management is currently receiving considerable attention in the petroleum industry. A “realtime” or “continuous” reservoir model updating technique is a critical component for the feasible application of any closed-loop, model-based reservoir management process. This technique should be able to rapidly and continuously update reservoir models assimilating the up-to-date observations of production data so that the performance predictions and the associated uncertainty are up-to-date for optimization of future development/operations. The ensemble Kalman filter (EnKF) method has been shown to be quite efficient for this purpose in large-scale nonlinear systems. Previous studies show that a relatively large ensemble size is required for EnKF to reliably assess the uncertainty, and a confirming step is recommended to ensure the consistency of the updated static and dynamic variables with the flow equations. In this paper, we further explore the capability of EnKF, focusing on some practical issues including the correction of the linear and Gaussian assumptions during filter updating with iteration, the reduction of ensemble size with a resampling scheme, and the impact of data assimilation time interval. Results from the example in this paper demonstrate that the proposed iterative EnKF performs better with more accurate predictions and less uncertainty than the traditional noniterative EnKF. The use of iteration reduces the impact of nonlinearity and non-Gaussianity. Results also show that iteration may only be required when predictions are considerably deviated from the observations. The proposed resampling scheme can significantly reduce the ensemble size necessary for reliable assessment of uncertainty with improved accuracy. Finally, we show that the noniterative EnKF is sensitive to the size of time interval between the assimilation steps. Using the proposed iterative EnKF, results are more stable, more accurate reservoir models and predictions can be obtained even when a large time interval is used. This also indicates that iteration within the EnKF updating serves as a process that corrects the stronger nonlinear and non-Gaussian behaviors when larger time interval is used.

A Simple Nonlinear Observer for a Class of Uncertain Mechanical Systems

Abstract: A simple nonlinear observer is proposed for a class of uncertain nonlinear multiple-input-multiple-output (MIMO) mechanical systems whose dynamics are first-order differentiable. The global asymptotic observation of the proposed observer is proved. Thus, the observer can be designed independently of the controller. Furthermore, the proposed observer is formulated without any detailed model knowledge of the system. These advantages make it easy to implement. Numerical simulations are included to illustrate the effectiveness of the proposed observer.

Gaussian Particle Implementations of Probability Hypothesis Density Filters

Abstract: The probability hypothesis density (PHD) filter is a multiple-target filter for recursively estimating the number of targets and their state vectors from sets of observations. The filter is able to operate in environments with false alarms and missed detections. Two distinct algorithmic implementations of this technique have been developed. The first of which, called the Particle PHD filter, requires clustering techniques to provide target state estimates which can lead to inaccurate estimates and is computationally expensive. The second algorithm, called the Gaussian Mixture PHD (GM-PHD) filter does not require clustering algorithms but is restricted to linear-Gaussian target dynamics, since it uses the Kalman filter to estimate the means and covariances of the Gaussians. Extensions for the GM-PHD filter allow for mildly non-linear dynamics using extended and Unscented Kalman filters. A new particle implementation of the PHD filter which does not require clustering to determine target states is presented here. The PHD is approximated by a mixture of Gaussians, as in the GM-PHD filter but the transition density and likelihood function can be non-linear. The resulting filter no longer has a closed form solution so Monte Carlo integration is applied for approximating the prediction and update distributions. This is calculated using a bank of Gaussian particle filters, similar to the procedure used with the Gaussian sum particle filter. The new algorithm is derived here and presented with simulated results.

Development of a Tiny Orientation Estimation Device to Operate under Motion and Magnetic Disturbance

Abstract: A tiny absolute orientation estimating device equipped with a network function has been developed using accelerometers and magnetometers to estimate gravity and the geomagnetic field, respectively. Because accelerometers measure motion other than gravity, a method has been proposed to eliminate the effect of motion. An estimation method is proposed that excludes the effect of magnetic disturbances. An advantage of this estimation method is that models can be switched according to the environment. Sigma Points Kalman Filters (SPKFs) were evaluated to determine the proper filter for the proposed algorithm. A Square-Root Central Difference Kalman Filter (SR-CDKF) was the best method considering stability, accuracy, and calculation cost. Using simulations and the realized device, the proposed algorithm stably estimated the orientation in the presence of motion and magnetic disturbances.

A tool for kalman filter tuning

Abstract: The Kalman filter requires knowledge about the noise statistics. In practical applications, however, the noise covariances are generally not known. In this paper, a method for estimating noise covariances from process data has been investigated. This method yields least-squares estimates of the noise covariances, which can be used to compute the Kalman filter gain.