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Showing papers on "Invariant extended Kalman filter published in 1995"


BookDOI
29 Nov 1995
TL;DR: The discrete Kalman filter as mentioned in this paper is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error.
Abstract: In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation. The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error. The filter is very powerful in several aspects: it supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modeled system is unknown. The purpose of this paper is to provide a practical introduction to the discrete Kalman filter. This introduction includes a description and some discussion of the basic discrete Kalman filter, a derivation, description and some discussion of the extended Kalman filter, and a relatively simple (tangible) example with real numbers & results.

2,811 citations


Journal ArticleDOI
TL;DR: A Monte Carlo simulation example of a bearings-only tracking problem is presented, and the performance of the bootstrap filter is compared with a standard Cartesian extended Kalman filter (EKF), a modified gain EKF, and a hybrid filter.
Abstract: The bootstrap filter is an algorithm for implementing recursive Bayesian filters. The required density of the state vector is represented as a set of random samples that are updated and propagated by the algorithm. The method is not restricted by assumptions of linearity or Gaussian noise: It may be applied to any state transition or measurement model. A Monte Carlo simulation example of a bearings-only tracking problem is presented, and the performance of the bootstrap filter is compared with a standard Cartesian extended Kalman filter (EKF), a modified gain EKF, and a hybrid filter. A preliminary investigation of an application of the bootstrap filter to an exoatmospheric engagement with non-Gaussian measurement errors is also given.

168 citations


Patent
01 Nov 1995
TL;DR: In this paper, a system and method for fusing independent measures of the physiological parameter uses a Kalman filter for each possible combination of sensor measurements, and a confidence calculator uses Bayesian statistical analysis to determine a confidence level for each of the KF outputs, and selects a fused estimate for the physiological parameters based on the confidence level.
Abstract: A system and method for fusing independent measures of the physiological parameter uses a Kalman filter for each possible combination of sensor measurements. The Kalman filter utilize probability density functions of a nominal error contamination model and a prediction error model as well as past estimates of the physiological parameter to produce the Kalman filter outputs. A confidence calculator uses Bayesian statistical analysis to determine a confidence level for each of the Kalman filter outputs, and selects a fused estimate for the physiological parameter based on the confidence level. The fused estimate and the confidence level are used to dynamically update the nominal error contamination model and prediction error model to create an adaptive measurement system. The confidence calculator also takes into account the probability of artifactual error contamination in any or all of the sensor measurements. The system assumes a worst case analysis of the artifactual error contamination, thus producing a robust model able to adapt to any probability density function of the artifactual error and a priori probability of artifact.

163 citations


Journal ArticleDOI
TL;DR: The error dynamics of the extended Kalman filter (EKF), employed as an observer for a general nonlinear, stochastic discrete time system, are analyzed and an expression for the bound on the errors is given in terms of the size of the nonlinearities of the system and the error covariance matrices used in the design of the EKF.
Abstract: The error dynamics of the extended Kalman filter (EKF), employed as an observer for a general nonlinear, stochastic discrete time system, are analyzed. Sufficient conditions for the boundedness of the errors of the EKF are determined. An expression for the bound on the errors is given in terms of the size of the nonlinearities of the system and the error covariance matrices used in the design of the EKF. The results are applied to the design of a stable EKF frequency tracker for a signal with time-varying frequency.

111 citations


Journal ArticleDOI
01 May 1995
TL;DR: In this article, two algorithms are proposed for dynamic state estimation which incorporate the measurement function nonlinearities in the extended Kalman filter (EKF) scheme, and the performance of the schemes are compared with the standard linear EKF scheme under various conditions.
Abstract: Dynamic state estimation in power systems is based on the extended Kalman filter (EKF) scheme The EKF system uses a linearised measurement equation, neglecting the nonlinearities of the measurement function Under certain circumstances (eg large load changes) this leads to degradation in the filter performance Two algorithms are proposed for dynamic state estimation which incorporate the measurement function nonlinearities in the EKF scheme The performance of the schemes are compared with the standard linear EKF scheme under various conditions and comparative results are presented

78 citations


Journal ArticleDOI
TL;DR: In this paper, a time-domain method was proposed to identify a state space model of a linear system and its corresponding observer/Kalman filter from a given set of general input-output data.
Abstract: This paper presents a time-domain method to identify a state space model of a linear system and its corresponding observer/Kalman filter from a given set of general input-output data. The identified filter has the properties that its residual is minimized in the least squares sense, orthogonal to the time-shifted versions of itself, and to the given input-output data sequence. The connection between the state space model and a particular auto-regressive moving average description of a linear system is made in terms of the Kalman filter and a deadbeat gain matrix. The procedure first identifies the Markov parameters of an observer system, from which a state space model of the system and the filter gain are computed. The developed procedure is shown to improve results obtained by an existing observer/Kalman filter identification method, which is based on an auto-regressive model without the moving average terms. Numerical and experimental results are presented to illustrate the proposed method.

77 citations


Journal ArticleDOI
TL;DR: In this paper, a general formulation of least squares estimation is given, and an algorithm with a fixed-size moving estimation window and constraints on states, disturbances and measurement noise is developed through a probabilistic interpretation of least square estimation.

75 citations


Proceedings ArticleDOI
13 Dec 1995
TL;DR: Improvement in the system model provides for a more accurate state estimate in the feedback loop, thus enhancing the control signal so that the system behaves in a closer to optimal fashion.
Abstract: Develops an adaptive state-estimation technique using artificial neural networks, referred to as a neuro-observer. The neuro-observer is an extended Kalman filter structure that has its state-coupling function augmented by an artificial neural network that captures the unmodeled dynamics. The neural network of the neuro-observer trains on-line using an extended Kalman filter training paradigm. Improvement in the system model then provides for a more accurate state estimate in the feedback loop, thus enhancing the control signal so that the system behaves in a closer to optimal fashion.

75 citations


Proceedings ArticleDOI
13 Dec 1995
TL;DR: In this article, the optimal solution of estimating a set of dynamic state in the presence of a random bias employing a two-stage Kalman estimator is addressed, where the algebraic constraint is removed.
Abstract: The optimal solution of estimating a set of dynamic state in the presence of a random bias employing a two-stage Kalman estimator is addressed. It is well known that, under an algebraic constraint, the optimal estimate of the system state can be obtained from a two-stage Kalman estimator. Unfortunately, this algebraic constraint is seldom satisfied for practical systems. This paper proposes a general form of the optimal solution of the two-stage estimator, in which the algebraic constraint is removed. Furthermore, it is shown that, by applying the adaptive process noise covariance concept, the optimal solution of the two-stage Kalman estimator is composed of a modified bias-free filter and an bias-compensating filter, which can be viewed as a generalized form of the conventional two-stage Kalman estimator.

75 citations



Proceedings ArticleDOI
10 Jul 1995
TL;DR: In this article, a Kalman filter is proposed as a weight filter for the dynamic weighing system, which is based on the accurate model of the system in question, the exact model of load cell based dynamic weight system has been derived and presented.
Abstract: In the area of mass production, products are weighed using load cell based dynamic weighing systems. A load cell is an uncontrollable weighing device and the value of weight, for the passing product, is estimated by filtering the electrical signal from a load cell. Improvement in filtering increases the speed of weighing and enhances the measurement accuracy. In this paper a Kalman filter is proposed as a weight filter for the dynamic weighing system. Furthermore, the paper includes mathematical models of the load cell and forcing functions. These models are used to examine the suitability of the proposed Kalman filter approach. Since this approach is based on the accurate model of the system in question, the exact model of the load cell based dynamic weighing system has been derived and presented. For one particular value of the weight, the parameters of the model are time-varying due to the product coming onto the weigh-table and due to the product length. Changing the measurement from one value of the weight to another causes even greater changes in the values of the model parameters and introduces a nonlinearity in the system. Therefore an adaptivity approach has been considered and a solution proposed. The simulation and experimental results are presented and compared. The results achieved show that the Kalman filter may provide an effective alternative to the conventional method especially when the system is nonlinear and low frequency noise is incorporated in the bandwidth of the useful signal.

Proceedings ArticleDOI
16 May 1995
TL;DR: In this paper, a novel solution to the problem of applying kinematic inequality constraints to a Kalman filter based radar tracker using pseudo-measurements is presented, where height and speed constraints are applied to a Cartesian radar tracking filter.
Abstract: A novel solution to the problem of applying kinematic inequality constraints to a Kalman filter based radar tracker using pseudo-measurements is presented. The technique is demonstrated by applying height and speed constraints to a Cartesian radar tracking filter. (5 pages)

Proceedings ArticleDOI
26 Jun 1995
TL;DR: In this article, the authors propose to use neurofuzzy estimators to initialize the states of Kalman and extended Kalman filters, and they show that using these estimators can improve the performance of the filters.
Abstract: It is traditional to initialise Kalman filters and extended Kalman filters with estimates of the states calculated directly from the observed (raw) noisy inputs, but unfortunately their performance is extremely sensitive to state initialisation accuracy: good initial state estimates ensure fast convergence whereas poor estimates may give rise to slow convergence or even filter divergence. Divergence is generally due to excessive observation noise and leads to error magnitudes that quickly become unbounded (R.J. Fitzgerald, 1971). When a filter diverges, it must be re initialised but because the observations are extremely poor, re initialised states will have poor estimates. The paper proposes that if neurofuzzy estimators produce more accurate state estimates than those calculated from the observed noisy inputs (using the known state model), then neurofuzzy estimates can be used to initialise the states of Kalman and extended Kalman filters. Filters whose states have been initialised with neurofuzzy estimates should give improved performance by way of faster convergence when the filter is initialised, and when a filter is re started after divergence.

Proceedings ArticleDOI
21 Jun 1995
TL;DR: In this article, a new approach for detecting sensor failures which affect only subsets of system measurements is presented, where a bank of auxiliary Kalman filters are used to provide the state estimates which serve as failure detection references, and failure detection is undertaken by checking the consistency between the state estimate of the main Kalman filter and those of the auxiliary filters by means of the chi-square statistical hypothesis test.
Abstract: This investigation presents a new approach for detecting sensor failures which affect only subsets of system measurements. In addition to a main Kalman filter, which processes all the measurements to give the optimal state estimate, a bank of auxiliary Kalman filters is also used, which process subsets of the measurements to provide the state estimates which serve as failure detection references. After the statistical property of the difference between the state estimate of the main Kalman filter and those of the auxiliaries is derived with an application of the orthogonal projection theory, failure detection is undertaken by checking the consistency between the state estimate of the main Kalman filter and those of the auxiliaries by means of the chi-square statistical hypothesis test.

Journal ArticleDOI
TL;DR: In this article, the first and second-order moments of noise processes are estimated simultaneously with the system states, using the QQ-plot of the noise samples generated in the robustified Kalman filter algorithm.
Abstract: Noise distribution arising in certain applications frequently deviates from the assumed gaussian model, often being characterized by heavier tails generating the outliers. Since, in the presence of outliers, the performance of a Kalman filter can be very poor, a statistical approach-named QQ-plot—is suggested to make the Kalman filter more robust. In addition, the first and the second-order moments of noise processes are estimated simultaneously with the system states, using the QQ-plot of the noise samples generated in the ‘robustified’ Kalman filter algorithm. Results of simulation demonstrating the robustness of the proposed state estimators are also included.

Patent
30 Mar 1995
TL;DR: In this article, an antenna tracking controller for generating signals used to position an antenna for tracking a moving signal source includes a first Kalman filter (Figure 9) for estimating parameters of a first model of the motion of the moving source, and a second Kalman filtering (2KF) is used to estimate the parameters of the second model.
Abstract: An antenna tracking controller (102) for generating signals used to position an antenna for tracking a moving signal source includes a first Kalman filter (Figure 9) for estimating parameters of a first model of the motion of the moving signal source a second Kalman filter (Figure 9) for estimating parameters of a second model of the motion of the moving signal source. The second Kalman filter uses the parameters estimated by the first Kalman filter as initial values. A model quality charge/discharge is also provided to monitor the status of the data base.

Proceedings ArticleDOI
13 Dec 1995
TL;DR: A modified version of the extended Kalman filter (EKF), when used as an observer for nonlinear discrete-time systems, is presented, and efficiency of this approach is shown through a nonlinear identification problem.
Abstract: In the current paper, a modified version of the extended Kalman filter (EKF), when used as an observer for nonlinear discrete-time systems, is presented. The approach proposed consists in introducing time varying matrices to enhance convergence and stability of the obtained estimator. Based on a new formulation of the first order linearization technique, sufficient conditions to ensure local asymptotic convergence are established. Efficiency of this approach, compared to the classical version of the EKF, is shown through a nonlinear identification problem.

Proceedings ArticleDOI
Fred Daum1
01 Sep 1995
TL;DR: A new exact nonlinear filter which generalizes the Kalman filter is described, which will be explained using block diagrams, for maximal clarity, in addition to detailed equations.
Abstract: This paper describes a new exact nonlinear filter which generalizes the Kalman filter. The filter will be explained using block diagrams, for maximal clarity, in addition to detailed equations. A comparison with the Kalman filter will be given, highlighting the similar structure and low computational complexity. Using this block diagram comparison, engineers who are familiar with the Kalman filter will readily grasp the new nonlinear filter technique.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Journal ArticleDOI
TL;DR: A parallel algorithm for Kalman filtering with contaminated observations is developed, which represents a great improvement over serial implementations reducing drastically computational costs for each state update and avoiding numerical instability problems.
Abstract: A parallel algorithm for Kalman filtering with contaminated observations is developed. This algorithm is suitable for the parallel computer implementation allowing to treat dynamic linear systems with large number of state variables in a robust recursive way. The implementation is based on the square root version of the Kalman filter. It represents a great improvement over serial implementations reducing drastically computational costs for each state update and avoiding numerical instability problems.

Journal ArticleDOI
TL;DR: In this paper, a simplified Kalman filter (SKF) is proposed to reduce computational requirements and improve numerical stability of the steering algorithm based on a Kalman Filter. But the SKF does not require any a priori information about interference statistics and is totally numerically stable.
Abstract: Adaptive antenna arrays controlled by the Kalman filter excel in high rate of convergence, low misadjustment and independence on a priori information about interference statistics. High computational requirements and potential numerical non-stability are drawbacks of the Kalman's steering. The author describes a way of reducing computational requirements and improving numerical stability of the steering algorithm based on a Kalman filter. Rate of convergence and misadjustment of the resultant algorithm (simplified Kalman filter, (SKF)) are better in comparison with the optimal LMS and worse than the pure Kalman filter. Computational requirements of the SKF are approximately three times higher in comparison with the LMS. SKF does not require any a priori information about interference statistics and is totally numerically stable. >

Journal ArticleDOI
TL;DR: In this paper, the Kalman filter equations were derived when the system state and the observation error of a state-space model are correlated, and they were extended to nonnegative definite variance-covariance matrices and disturbance probability distributions that are conditional on some information related to the observation process.

Journal ArticleDOI
TL;DR: In this article, the performance robustness of a prediction-type Kalman filter for linear discrete-time systems with structured plant uncertainty and noise uncertainty was investigated, and two methods were proposed to achieve upper and lower bounds on the mean square of the estimation error, measuring the effect of the uncertainty on the performance of the filter.
Abstract: The performance robustness of a prediction-type Kalman filter is considered for linear discrete-time systems with structured plant uncertainty and noise uncertainty. Two methods are proposed to achieve upper and lower bounds on the mean square of the estimation error, measuring the effect of the uncertainty on the performance of the filter. An illustrative example is given

Journal ArticleDOI
TL;DR: The EKf matrices are analyzed in detail, exploiting the sparsity and structure of the EKF matrices to reduce the number of computations, leading to difficulties in broadband real-time applications.
Abstract: GPS is capable of providing 100 m level accuracy for a great number of users worldwide. In GPS, range and range-rate data can be used with satellite position and velocity to compute user position and velocity using an extended Kalman filter (EKF). However, the EKF is computationally intensive, leading to difficulties in broadband real-time applications. Hence, it is necessary to resort to techniques to improve EKF speed. Therefore, in this paper, the EKF matrices are analyzed in detail, exploiting the sparsity and structure of the EKF matrices to reduce the number of computations. A typical trajectory is simulated, and a comparison of the computation speed of sequential implementations of EKF, both with and without the proposed reduction of computations, is reported. Further, an algorithm is developed to obtain an initial estimate of user position and velocity which is used to initialize the state vector of the EKF algorithm.

Proceedings ArticleDOI
Samer S. Saab1
21 Jun 1995
TL;DR: In this article, the sensitivity due to class of errors in the statistical modeling employing a Kalman filter is discussed, and it is shown that Kalman filters can be insensitive to scaling of covariance matrices.
Abstract: The optimum filtering results of Kalman filtering for linear dynamic systems require an exact knowledge of the process noise covariance matrix Q, the measurement noise covariance matrix R and the initial error covariance matrix P/sub 0/. In a number of practical solutions, Q, R and P/sub 0/, are either unknown or are known only approximately. In this paper the sensitivity due to class of errors in the statistical modeling employing a Kalman filter is discussed. In particular, we present a special case where it is shown that Kalman filter gains can be insensitive to scaling of covariance matrices. Some basic results are derived to describe the mutual relations among the three covariance matrices (actual and perturbed covariance matrices), their respective Kalman gain K/sub k/ and the error covariance matrices P/sub k/. Experimental results using a tactical grade inertial measurement unit are presented to illustrate the theoretical results.

Journal ArticleDOI
TL;DR: Simulation results indicate that the multirate Kalman reconstruction filters possess better estimation/interpolation performances than a Wiener reconstruction filter under adequate numerical complexity.
Abstract: The use of the Kalman filter is investigated in this work for interpolating and estimating values of an AR or MA stochastic signal when only a noisy, down-sampled version of the signal can be measured. A multirate modeling theory of the AR/MA stochastic signals is first derived from a block state-space viewpoint. The missing samples are embedded in the state vector so that missing signal reconstruction problem becomes a state estimation scheme. Next, Kalman state estimation theory is introduced to treat the combined estimation-interpolation problem. Some extensions are also discussed for variations of the original basic problem. The proposed Kalman reconstruction filter can be also applied toward recovering missing speech packets in a packet switching network with packet interleaving configuration. By analysis of state estimation theory, the proposed Kalman reconstruction filters produce minimum-variance estimates of the original signals. Simulation results indicate that the multirate Kalman reconstruction filters possess better estimation/interpolation performances than a Wiener reconstruction filter under adequate numerical complexity. >

Journal ArticleDOI
TL;DR: In this paper, the authors derived equations for optimum and near-optimum Kalman filters for the filtration problem with a singular covariance matrix for the noise in the observations in the case when the processes under consideration are described by Ito's stochastic differential equations with measure.

Book ChapterDOI
04 Dec 1995
TL;DR: This work proposes the use of a Recursive Total Least Squares Filter, which is easily updated to incorporate new sensor data, and in the authors' experiments converged faster and to greater accuracy than the Kalman filter.
Abstract: In the robot navigation problem, noisy sensor data must be filtered to obtain the best estimate of the robot position. The discrete Kalman filter, commonly used for prediction and detection of signals in communication and control problems, has become a popular method to reduce the effect of uncertainty from the sensor data. However, in the domain of robot navigation, sensor readings are not only uncertain, but can also be relatively infrequent compared to traditional signal processing applications. In addition, a good initial estimate of location, critical for Kalman convergence, is often not available. Hence, there is a need for a filter that is capable of converging with a poor initial estimate and many fewer readings than the Kalman filter. To this end, we propose the use of a Recursive Total Least Squares Filter. This filter is easily updated to incorporate new sensor data, and in our experiments converged faster and to greater accuracy than the Kalman filter.

Journal ArticleDOI
TL;DR: A novel Kalman filtering approach to the suppression of narrowband interference from direct sequence spread spectrum communications systems based on the digital phase-locked loop Kalman filter, characterized as a function of theKalman filter parameters through computer simulation for narrowband Gaussian noise interference.
Abstract: This paper presents a novel Kalman filtering approach to the suppression of narrowband interference from direct sequence spread spectrum communications systems. The approach is based on the digital phase-locked loop Kalman filter. Because the interference is assumed to be much stronger than either the signal or noise, the Kalman filter locks onto a function related to the interference. The net result is an estimate of the phase of the interference and its envelope. Though more optimum for interferer's of constant envelope, the algorithm is characterized as a function of the Kalman filter parameters through computer simulation for narrowband Gaussian noise interference. Examples of the phase- and envelope-tracking capabilities of the algorithm are presented, followed by bit error rate curves for interference bandwidths ranging from 0.5% to 5.0% of the chip rate of the spread spectrum signal. >

01 Nov 1995
TL;DR: In this paper, three state estimation algorithms are applied to the hourly traffic volume system using the observation data obtained from 7 a.m. to 7 p.m in Fukuyama, Japan.
Abstract: This paper applies three state estimation algorithms to an hourly traffic volume system. The observation values of traffic volume by detectors are contaminated by errors depending on type, setting, sensitivity, and so on. From the statistical analysis of hourly traffic volume data, it is assumed that hourly traffic volumes vary depending on the day of the week and time. The hourly traffic volume system is described by a linear time-varying discrete dynamic system. State and observation equations are described in such linear equations that the state variables are additively affected by the state and observation noises respectively. In order to remove errors caused by type, setting, and sensitivity of a detector, the authors apply such state estimation algorithms as the Kalman filter, the fixed-interval smoother, and the MIPA Kalman filter to the hourly traffic volume system. The Kalman filter and the fixed-interval smoother are optimal for the linear dynamic system with Gaussian noises. The MIPA Kalman filter, based on the M-interval polynomial approximation method, is a robust Kalman filter for the linear dynamic system with non-Gaussian noise. Three state estimation algorithms are applied to the hourly traffic volume system using the observation data obtained from 7 a.m. to 7 p.m. in Fukuyama, Japan. Estimates of the Kalman filter are fairly improved compared with the observation values, and estimates of the fixed-interval smoother are more accurate than the Kalman filter estimates. Estimates of the MIPA Kalman filter are the most accurate and robust as compared with other estimates.

Proceedings ArticleDOI
05 Mar 1995
TL;DR: In this paper, a reduced-order extended Kalman filter (EKF) was proposed to estimate rotor speed and flux estimation only by measuring stator currents, which has some advantages of saving computation time in comparison with the full-order EKF.
Abstract: The extended Kalman filter (EKF) has been known to be correctly capable of estimating system parameters and state variables by eliminating virtually all influences of structural noise in the field-oriented control scheme for induction motors. This paper presents a design method of a reduced-order extended Kalman filter which consists of rotor speed and flux estimation only by measuring stator currents. The proposed method has some advantages of saving computation time in comparison with the full-order extended Kalman filter. For the noise reduction, robust speed sensorless vector control is realized in the thesis. Experimental results show the effectiveness of the control strategy proposed here for induction motor drives. >