Recursive Kalman Filter Research Articles

A three-step cloud clearing procedure for infrared sounder measurements

Abstract A new cloud clearing procedure applied to High-resolution Infrared Radiation Sounder (HIRS/2) radiance measurements is presented, based on knowledge of the typical statistical features of both clear and cloud contaminated radiance fields and on the application of some well known techniques for the statistical handling of data. The procedure consists of three sequential steps. In the first, the clear sky latitudinal gradient is restored using statistical correlation among HIRS/2 and MSU measurements. In the second step the scene variability (i.e. the dynamics along the longitudinal gradient) is retrieved by a discrete Fourier developments and a recursive Kalman filter. Finally, the characteristic smoothness of clear fields is introduced using a low-pass filter (third step). Applications of the whole filtering technique to measured HIRS/2 channel 5, 6 and 7 brightness temperatures are discussed and its performance is checked by comparing sets of filtered and stimulated data.

Rates of convergence to steady state for the linear growth version of a dynamic linear model (DLM)

The use of dynamic linear models and structural models for time series analysis and forecasting requires some form of initial conditions to commence the Kalman filter recursions. It is known that eventually a steady state is reached which is independent of prior knowledge. This paper is concerned with the rate of approach to steady state for the practically important ‘linear growth model’. Aspects of forecasting in the transient period are also included. Numerical results suggest that there is significant influence of the start on rates of convergence to steady state particularly for (i) high signal-to-noise variance ratios of the trend component, and (ii) the presence of initial covariance between the level and trend components.

Robust adaptive flight-path reconstruction technique for nonsteady longitudinal flight test maneuvers

Computational schemes are presented that allow accurate reconstruction of the flight path of the longitudinal aircraft motion in real time. The reconstruction of the flight path is formulated as a discrete, linear, time-variant state reconstruction problem that can be solved via Kalman filtering techniques. This imposes some conditions upon the flight test equipment. A reliable square-root covariance filter implementation is chosen and further developed in a fully adaptive flight-path reconstruction scheme. Therefore, the chosen Kalman filter implementation is modified to cope with several practical problems such as the automatic control of the convergence of the Kalman filter recursions, time-varying bias errors on the input signal of the system model used in the Kalman filter, variations in the wind, and the changing aircraft dynamics owing to a change in nominal flight condition. The developed solutions for these problems are all implemented in a numerically stable way, which guarantees the overall flight-path reconstruction scheme to be robust. Furthermore, some special features of the system model are exploited to make the algorithmic implementation very efficient. These different capabilities are highlighted in an experimental analysis using simulated flight test data.

An extension of the SRIF Kalman filter

We consider the problem of implementing the Kalman filter recursions in square root information filter form. We suggest a general linear, dynamical model which directly incorporates the fact that many of the unknowns are not time varying. The resulting implementation is widely applicable, numerically sound, and extends easily to smoothing problems.

Discrete Algorithms for Residential Heating Strategies an Application of Optimal Control Theory

The recent significant expansion of electric space heating calls for proper load management strategies for a northern climate. In this paper, a multimode system including heat pump technology with storage is developed. The variations of the room temperature setpoint are studied in relation to heating power and the setback pattern. A discrete-time solution to the problem of determining the optimal amount of energy required from an electrical source in order to minimize consumption and temperature droop has been obtained. The present solution is suboptimal in the sense that it is a linear approximation of a non-linear plant. The recursive Kalman filter was employed for the linear regulator solution. Pontryagin's minimum principle was used to express the singular algorithm. The implementation problems of the above feedback controllers are discussed. Numerical results from computer simulations are compared with the bang-bang regulator performances. A real-time adaptive control application using hourly predictions of climatic conditions is foreseen.

An Edge-Preserving Recursive Noise-Smoothing Algorithm for Image Data

Recursive Kalman filters are often used for noise reduction in image data. These linear filters are based on the second-order statistics of image and noise. The noise is effectively reduced by the filtering operation, but the edges in the image are blurred and image contrast is reduced as well. These effects decrease the subjective quality of the image. A simple and computationally fast scan-ordered one-dimensional Kalman filter is derived, which is then provided with additional structural information about the edges in the noisy image. This filter behaves like the original noise-smoothing Kalman filter if no edges are present but has a greatly improved step response. In this way the edge-blurring phenomenon is effectively reduced. Results of several experiments are presented to demonstrate the feasibility of our approach.

Linear digital filtering for laboratory automation

The design of nonrecursive and recursive digital filters using linear least squares or linear minimum variance is described. This method of design requires a model, and since polynomial approximations are widely used in laboratory automation, a polynomial state model is first utilized. Then an exact scalar signal model is employed that results in a completely time-varying filter. For both models, the design leads to the recursive Kalman filter. The operation of the filters for noise reduction is first demonstrated for simulated data, and design forms are compared. For the exact scalar signal model, noise reduction and peak separation are demonstrated using simulated data and data obtained from a mass spectrometer. By using the correct model, excellent peak separation and noise reduction can be obtained.

Alternate methods of harmonic analysis

A modification of the traditional least square estimate is introduced and applied to the harmonic analysis of noisy periodic waveforms. The recursive Kalman filter approach is reviewed and the two methods are compared. The modified least square estimate is found to be a more efficient computational technique when the form of the signal allows its use.

Nonlinear extensions of the fading memory filter

The equations for a recursive extended Kalman filter with exponential age-weighting of data and dynamics are derived. A similar result is given for a second-order filter. It is seen that the filter equations are essentially of the same form as their unfaded counterparts. This technique offers promise in controlling the divergence problem that recursive filtering often encounters.