Showing papers on "Alpha beta filter published in 1991"

Identification of observer/Kalman filter Markov parameters: Theory and experiments

Abstract: An algorithm to compute Markov parameters of an observer or Kalman filter from experimental input and output data is discussed The Markov parameters can then be used for identification of a state space representation, with associated Kalman gain or observer gain, for the purpose of controller design The algorithm is a non-recursive matrix version of two recursive algorithms developed in previous works for different purposes The relationship between these other algorithms is developed The new matrix formulation here gives insight into the existence and uniqueness of solutions of certain equations and gives bounds on the proper choice of observer order It is shown that if one uses data containing noise, and seeks the fastest possible deterministic observer, the deadbeat observer, one instead obtains the Kalman filter, which is the fastest possible observer in the stochastic environment Results are demonstrated in numerical studies and in experiments on an ten-bay truss structure

Design and implementation of an extended Kalman filter for the state estimation of a permanent magnet synchronous motor

Abstract: Practical considerations for implementing the discrete extended Kalman filter in real time with a digital signal processor are discussed. The system considered is a permanent magnet synchronous motor (PMSM) without a position sensor, and the extended Kalman filter is designed for the online estimation of the speed and rotor position by only using measurements of the motor voltages and currents. The algorithms developed to allow efficient computation of the filter are presented. The computational techniques used to simplify the filter equations and their implementation in fixed-point arithmetic are discussed. Simulation and experimental results are presented to demonstrate the feasibility of this estimation process. >

The Diffuse Kalman Filter

Abstract: The Kalman recursion for state space models is extended to allow for likelihood evaluation and minimum mean square estimation given states with an arbitrarily large covariance matrix. The extension is computationally minor. Application is made to likelihood evaluation, state estimation, prediction and smoothing.

Observers for induction motor state and parameter estimation

Abstract: The Kalman filter in its basic form is a state estimator and can be applied to the problem of estimating induction motor rotor currents in a vector control scheme. This filter is shown to combine information from the plant model with output measurements to produce an optimal estimate of the unmeasured states. Also described is the application of the extended Kalman filter algorithm to the online estimation of rotor resistance in an induction motor drive. Significant savings in computing requirements are obtained with a reduced-order model of the motor, in which measured, rather than computed, values of stator currents are used. >

Simplification of the Kalman filter for meteorological data assimilation

Abstract: The paper proposes a new statistical method of data assimilation that is based on a simplification of the Kalman filter equations. The forecast error covariance evolution is approximated simply by advecting the mass-error covariance field, deriving the remaining covariances geostrophically, and accounting for external model-error forcing only at the end of each forecast cycle. This greatly reduces the cost of computation of the forecast error covariance. In simulations with a linear, one-dimensional shallow-water model and data generated artificially, the performance of the simplified filter is compared with that of the Kalman filter and the optimal interpolation (OI) method. The simplified filter produces analyses that are nearly optimal, and represents a significant improvement over OI.

Initializing the kalman filter for nonstationary time series models

Abstract: . The problem of initializing the Kalman filter for nonstationary time series models is considered. Ansley and Kohn have developed a ‘modified Kalman filter’ for use with nonstationary models to produce estimates from what they call a ‘transformation approach’. We show that the same results can be obtained with a suitable initialization of the ordinary Kalman filter. Assuming there are d starting values for the nonstationary series, we initialize the Kalman filter using data through time d with the transformation approach estimate of the state vector and its associated error covariance matrix at time d. We give details of the initialization for ARIMA models, ARIMA component models and dynamic linear models. We present an example to illustrate how the results may differ from results obtained under more naive initializations that have been suggested.

Adaptive Kalman filtering

Abstract: The increased power of small computers makes the use of parameter estimation methods attractive. Such methods have a number of uses in analytical chemistry. When valid models are available, many methods work well, but when models used in the estimation are in error, most methods fail. Methods based on the Kalman filter, a linear recursive estimator, may be modified to perform parameter estimation with erroneous models. Modifications to the filter involve allowing the filter to adapt the measurement model to theexperimental data through matching the theoretical and observed covoriance of the filter innovations sequence. The adaptive filtering methods that result have a number of applications in analytical chemistry.

Data processing system using a kalman filter

Abstract: For processing data relating to the performance of an apparatus, the data is analyzed using a Kalman Filter. After a first pass of data through the filter, the results are refined by discarding at least one less significant component performance change and/or sensor bias. The Kalman Filter is then re-run using the modified data. As further runs of the Kalman Filter are performed, as required, the input of each successive run is refined by discarding from the preceding run at least one further component performance change and/or sensor bias. For each run, an objective function is evaluated for the amount of unexplained measurement change and/or the amount of component performance change and sensor bias. The run whose results show an acceptable value for the objective function is selected as the best solution. In this way, the tendency of the Kalman Filter to distribute the cause of any sensed performance change over all the possible sources of that change is avoided. The sets of measurement data are then analyzed to determine levels and/or trends in component performance and sensor bias.

Target tracking algorithms for phased array radar

Abstract: Phased array radar have an additional degree of freedom compared with track-while-scan radar, in that a variable update time may be used in the former. On detection of a manoeuvre, the update time may be reduced leading to an improved tracking accuracy. It has been shown how a variable update time may be incorporated into the alpha beta filter, the value of this update time being dependent on the magnitude of the residual. The algorithm of Cohen (1986) is tested by application of Monte-Carlo simulations to a wide variety of target tracks. Additional strategies in choosing the update time are also examined. The dependence of the mean square estimation errors and the mean update times are investigated for a range of parameters of the algorithm. It is concluded that in choosing the parameters of the algorithm, there is a trade-off between keeping the estimation errors low and restricting the mean update time from becoming excessively small. >

Square root parallel Kalman filtering using reduced-order local filters

Abstract: The basic parallel Kalman filtering algorithms derived by H.R. Hashemipour et al. (IEEE Trans. Autom. Control. vol.33, p.88-94, 1988) are summarized and generalized to the case of reduced-order local filters. Measurement-update and time-update equations are provided for four implementations: the conventional covariance filter, the conventional information filter, the square-foot covariance filter, and the square-foot information filter. A special feature of the suggested architecture is the ability to accommodate parallel local filters that have a smaller state dimension than the global filter. The estimates and covariance or information matrices (or their square roots) from these reduced-order filters are collated at a central filter at each step to generate the full-size, globally optimal estimates and their associated error covariance or information matrices (or their square roots). Aspects of computational complexity and the ensuing tradeoff with communication are discussed. >

Maneuvering target tracking using extended Kalman filter

Abstract: A numerically well-conditioned, quasi-extended Kalman filter is proposed. The filter is numerically described. The simulation results presented show that the estimation performance of the quasi-extended filter is superior, for short distances, compared with the widely used linear tracking filters. In addition, the simplicity of the quasi-extended filter makes it very easy to implement. >

The response of the transfer function of an alpha-beta filter to various measurement models

Abstract: The response characteristics of the alpha-beta filter are used to quantify the filter's performance against different measurement models representing a target's trajectory. The transfer functions for an alpha-beta filter are used to derive closed form (solutions) expressions for smoothed position and velocity outputs for various measurement models. The filter's response to constant velocity targets is found to be the input plus a sinusoidal transient. Constant acceleration measurement models, in addition, yield a steady state bias that is a function of the filter parameters alpha and beta . Finally, the filter's response to a sinusoidal input is determined. >

Extended Kalman Filter and System Identification

Abstract: The Kalman filtering process has been designed to estimate the state vector in a linear model. If the model turns out to be nonlinear, a linearization procedure is usually performed in deriving the filtering equations. We will consider a real-time linear Taylor approximation of the system function at the previous state estimate and that of the observation function at the corresponding predicted position. The Kalman filter so obtained will be called the extended Kalman filter. This idea to handle a nonlinear model is quite natural, and the filtering procedure is fairly simple and efficient. Furthermore, it has found many important real-time applications. One such application is adaptive system identification which we will also discuss briefly in this chapter. Finally, by improving the linearization procedure of the extended Kalman filtering algorithm, we will introduce a modified extended Kalman filtering scheme which has a parallel computational structure. We then give two numerical examples to demonstrate the advantage of the modified Kalman filter over the standard one in both state estimation and system parameter identification.

Parallel and sequential block Kalman filtering and their implementations using systolic arrays

Abstract: Two sets of block Kalman filtering equations that differ in the manner of generating the initial and updated estimates are derived. Parallel and sequential schemes for generating these estimates are adopted. It is shown that the parallel implementation inherently leads to a block Kalman estimator which provides filtered estimates at the vector (block) level and fixed-lag smoother estimates at the sample level. The sequential implementation scheme, on the other hand, generates the estimates of each sample recursively, leading naturally to a scalar (filter) estimator. These scalar estimates are arranged in a vector form, resulting in a block estimator which solely generates filtered estimates both at the vector and sample levels. Simulation results on a speech signal are presented which indicate the advantages of the sequential block Kalman filter. An algorithm for iterative calculation of Kalman gain and error covariance matrices is given which does not require any matrix inversion operation. The implementation of this algorithm using available systolic array processors is presented. A ring systolic array which can be used to implement the state update part of the block Kalman filter is suggested. >

A synopsis of the smoothing formulae associated with the Kalman Filter

Abstract: This paper provides straightforward derivations of a wide variety of smoothing formulae which are associated with the Kalman filter. The smoothing operations are of perennial interest in the fields of communications engineering and signal processing. Recently they have begun to interest statisticians and economists. It is often asserted that it is tedious and difficult to derive the formulae. We show that this need not be so. Citation Copyright 1993 by Kluwer Academic Publishers. (This abstract was borrowed from another version of this item.)

Speech enhancement based on Kalman filtering and EM algorithm

Abstract: Speech enhancement via Kalman filtering is considered. It is generally agreed that the quality of the estimate of speech production model parameters is crucial to the performance of the Kalman filter. The Kalman filter with a more accurate estimate of the LPC parameters will generally achieve better noise cancellation results. In practice only the noisy speech is available for the LPC analysis. Then the estimate of the LPC parameters is usually inaccurate, which in turn degrades the performance of the Kalman filter. In order to overcome the problem, a Kalman filtering scheme applied in conjunction with the EM algorithm is proposed. Simulation results demonstrate the expected performance improvement in terms of signal-to-noise ratio (SNR) gains by the new method. >

Lp‐stability of estimation errors of kalman filter for tracking time‐varying parameters

Abstract: One presents a detailed analysis for the L p -stability of tracking errors when the Kalman filter is used for tracking undknown time-varying parameters. The results of this paper differ from the previous ones in that the regression vector (in a linear regression model) or the output matrix (in state space terminology) is random rather than deterministic. The context is kept general so that, in particular, the time-varying parameter is allowed to be unbounded, and no assumption of stationarity or independence for signals is made

A kalman filter in the presence of outliers

Abstract: A Kalman Filtering algorithm which is robust to observational outliers is developed by assuming that the measurement error may come from either one of two Normal distributions, and that the transition between these distributions is governed by a Markov Chain. The resulting algorithm is very simple, and consists of two parallel Kalman Filters having different gains. The state estimate is obtained as a weighted average of the estimates from the two parallel filters, where the weights are the posterior probabilities that the current observation comes from either of the two distributions. The large improvements obtained by this Robust Kalman Filter in the presence of outliers is demonstrated with examples.

Observer control system

Abstract: An observer control system which monitors a machine system, estimates state variables and controls the machine system. The system comprises a main observer (7) for estimating the state variables relating to linear elements of the machine system (4a), a disturbance estimation observer (8) for estimating the state variables relating to non-linear elements of the machine system, and an adder (6) for removing the non-linear elements from the input of the main observer (7). The disturbance estimation observer (8) estimates the non-linear state variables and deletes the non-linear terms from the main observer (8). Since the main observer (7) can estimate the state variables by only the linear term, the estimated state variables free from the influences of the non-linear term can be obtained. When the machine system is controlled by this estimated state variable, the state feedback gain of the machine system can be increased.

Kalman Filter: An Elementary Approach

Abstract: This chapter is devoted to a most elementary introduction to the Kalman filtering algorithm. By assuming invertibility of certain matrices, the Kalman filtering “prediction-correction” algorithm will be derived based on the optimality criterion of least-squares unbiased estimation of the state vector with the optimal weight, using all available data information. The filtering algorithm is first obtained for a system with no deterministic (control) input. By superimposing the deterministic solution, we then arrive at the general Kalman filtering algorithm.

The Kalman-Bucy filter accuracy in the guaranteed estimation problem

Abstract: The optimal guaranteed a priori estimation problem is considered. The Kalman-Bucy filter is used for the approximate solution of this problem. An analytical estimate for the nonoptimality degree of the Kalman-Bucy filter is obtained. This estimate is determined solely by the Kalman-Bucy filter characteristics. Thus the Kalman-Bucy filter efficiency can be established without accurate solution of the difficult optimal guaranteed estimation problem. >

Mass property identification - A comparison study between extended Kalman filter and neuro-filter approaches

Abstract: Two algorithms, extended Kalman filter and neuro-filter, are formulated to perform mass property identification for the Space Station Freedom. Control moment gyros that are part of the Station's basic momentum management system are chosen to provide input excitation in the form of applied torques. These torques together with the measured angular body rate responses are supplied to the filters. From these data, both algorithms are shown to accurately identify the station mass properties when excitation levels are high and balanced between axes. The neuro-filter, however, is shown to be more robust and to perform well even with weakly persistent, unbalanced signals contaminated with noise.

Parallel Computation of the Modified Extended Kalman Filter.

Abstract: In this paper, we describe certain techniques for mapping the modified extended Kalman filter (MEKF) onto systolic array processors. First, we introduce a square-root algorithm based on the singular value decomposition (SVD) for the Kalman filter. Then, we develop a VLSI architecture of the systolic array type for its implementation. Compared with other existing square-root Kalman filtering algorithms, our new design is numerically more stable and has nicer parallel and pipelining characteristics when it is applied to the MEKF. Moreover, it achieves higher efficiency. For n-dimensional state vector estimations, the proposed architecture consists of O(3/2n 2) processing elements and completes an iteration in time O((s + 8)n), in contrast to the time complexity of O((s + 3)n 3) for a sequential implementation, where s ≈ log n.

Optimal observer solution for predictive and LQG optimal control

Abstract: Considers the formulation of linear quadratic Gaussian (LQG) feedback optimal control and optimal generalised predictive control (GPC). It has previously been shown that GPC design can be improved if the future output predictions are based on a Kalman filter state estimate, in a similar fashion to LQG design. Optimality conditions on the Kalman filter can then be investigated and a suitable state-space formulation is considered. An incremental CARMA model of the process under control is employed in a reconstructible canonical form in order to simplify the Kalman filter representation. >