Polynomial Predictor Research Articles

Alternative predictors in chaotic time series

In the scheme of reconstruction, non-polynomial predictors improve the forecast from chaotic time series. The algebraic manipulation in the Maple environment is the basis for obtaining of accurate predictors. Beyond the different times of prediction, the optional arguments of the computational routines optimize the running and the analysis of global mappings.

An enhanced dead reckoning algorithm with hybrid extrapolation models (AisaSim 2016)

The traditional Dead Reckoning algorithm predicts the future motion state based on a determined polynomial predictor, and the forecasting performance would vary with different types of motion entities. This paper proposes an enhanced dead reckoning algorithm based on hybrid extrapolation models, which can be used to reduce the communication in a distributed interactive simulation. The proposed algorithm perform extrapolation using a number of candidate predictors. Its idea is based on the assumption that a complex trajectory can be decomposed into several simple trajectories. The experimental evaluations show that the enhanced Dead Reckoning algorithm provides better performance in correction data reduction and accurate estimation.

Locally p-optimal designs for generalized linear models with a single-variable quadratic polynomial predictor

Finding optimal designs for generalized linear models is a challenging problem. Recent research has identified the structure of optimal designs for generalized linear models with single or multiple unrelated explanatory variables that appear as first-order terms in the predictor. We consider generalized linear models with a single-variable quadratic polynomial as the predictor under a popular family of optimality criteria. When the design region is unrestricted, our results establish that optimal designs can be found within a subclass of designs based on a small support with symmetric structure. We show that the same conclusion holds with certain restrictions on the design region, but in other cases a larger subclass may have to be considered. In addition, we derive explicit expressions for some D-optimal designs.

An Adaptive Prediction-Based Approach to Lossless Compression of Floating-Point Volume Data.

In this work, we address the problem of lossless compression of scientific and medical floating-point volume data. We propose two prediction-based compression methods that share a common framework, which consists of a switched prediction scheme wherein the best predictor out of a preset group of linear predictors is selected. Such a scheme is able to adapt to different datasets as well as to varying statistics within the data. The first method, called APE (Adaptive Polynomial Encoder), uses a family of structured interpolating polynomials for prediction, while the second method, which we refer to as ACE (Adaptive Combined Encoder), combines predictors from previous work with the polynomial predictors to yield a more flexible, powerful encoder that is able to effectively decorrelate a wide range of data. In addition, in order to facilitate efficient visualization of compressed data, our scheme provides an option to partition floating-point values in such a way as to provide a progressive representation. We compare our two compressors to existing state-of-the-art lossless floating-point compressors for scientific data, with our data suite including both computer simulations and observational measurements. The results demonstrate that our polynomial predictor, APE, is comparable to previous approaches in terms of speed but achieves better compression rates on average. ACE, our combined predictor, while somewhat slower, is able to achieve the best compression rate on all datasets, with significantly better rates on most of the datasets.

Flexible Quantitative Risk Assessment for Developmental Toxicity Based on Fractional Polynomial Predictors

Risk assessment for developmental toxicity studies in rodents is faced with the fairly involved data structure of clustered multivariate binary outcomes. While likelihood methods for this setting do not abound, we show that a conditional model, combined with pseudo-likelihood inference and fractional polynomial predictor functions, as proposed by Royston and Altman (1994), are a promising way forward. The methods are illustrated using teratology data collected under the National Toxicology Program.

Predictive head movement tracking using a Kalman filter

The use of head movements in control applications leaves the hands free for other tasks and utilizes the mobility of the head to acquire and track targets over a wide field of view. We present the results of applying a Kalman filter to generate prediction estimates for tracking head positions. A simple kinematics approach based on the assumption of a piecewise constant acceleration process is suggested and is shown to track head positions with an rms error under 2 degrees for head movements with accelerations smaller than 3000 degrees /s. To account for the wide range of head dynamic characteristics, an adaptive approach with input estimation is developed. The performance of the Kalman filter is compared to that based on a simple polynomial predictor.

Latency Compensation for Differential GPS

Differential GPS (DGPS) has the potential to reduce spherical position error standard deviation to approximately 1 m. However, two practical issues affect the accuracy that can be achieved in real-time applications: long sampling periods and data latency. Low-bandwidth communications channels can result in differential corrections with sampling periods greater than 5 s. A time delay (latency) is inherent between the generation of pseudorange corrections and their application by the user. For real-time applications (e.g., autonomous vehicle navigation), low DGPS correction update rates and data latency are a fundamental performance limitation. This paper analyzes the modeling of differential corrections, uses the resulting optimal models for differential correction latency compensation, and analyzes the resulting accuracy by comparison with the first-order polynomial predictors recommended in the RTCM-104 standard. The comparison shows that, as long as the base station produces appropriate coefficients for the polynomial predictor, there is no significant accuracy improvement achieved by an optimal (i.e., Kalman filter-based) predictor over the RTCM-recommended polynomial predictor.

Polynomial prediction using incomplete data

We derive an FIR polynomial predictor for data in which some samples are missing. The method is compared with a computationally lighter algorithm that is based on decision-driven recursion. Both schemes are found to perform almost identically well on predicting a sinusoidal signal corrupted by both impulsive and Gaussian noise.

Polynomial predictors for complex-valued vector signals

Polynomial FIR predictors for complex-valued vector signals are derived. It is shown that the generalisation of the polynomial predictor for complex-valued signals results in the same filter as that for real-valued signals. The application of complex-valued vector polynomial prediction is illustrated by prediction of the components of a signal transmitted through a multipath Rayleigh fading channel.

Imbalance Response and Stability of Eccentric Squeeze-Film-Damped Nonlinear Rotor Bearing Systems.

Solutions for the imbalance response and stability of squeeze-film-damped nonlinear rotor bearing systems are presented. The rotor imbalance response is approximated by a trigonometric series whose coefficients are determined using a collocation method together with a nonlinear least squares regression. To improve numerical efficiency, the number of nonlinear equations for iterative solution is reduced to that corresponding to the number of nonlinear supports. A linear polynomial predictor is used to provide initial values for the iteration and, to ensure continuity through critical points, an arc-length continuation algorithm is used. To investigate the stability of the solution, the Floquet transition matrix method is used with an approximate transition matrix computed using a rectangular ripple method. Numerical examples are given for an eccentric squeeze-film-damper-mounted rigid rotor.

The Mean-Square Error for a Recursive Moving Polynomial Predictor

The Mean-Square Error for a Recursive Moving Polynomial Predictor

Computer Optimization of Pharmaceutical Formulations I: General procedure

A technique was developed whereby a formulation with optimum properties, according to predetermined criteria, can be selected via computer analysis. The results of a statistically designed set of experiments based on five independent variables were used as the data input to the computer. Regression analysis of these data resulted in a set of second-order polynomial predictor equations. Restrictions placed by the pharmacist on the characteristics of interest serve to eliminate undesirable formulations. Ultimately, the formulator can trade off properties to obtain an optimum formulation. Computer-generated graphs further aid the formulator in the understanding of the particular system. An example is presented of the selection of an optimum formulation by this procedure and of its preparation in the laboratory. Predictions and experimental results show excellent agreement.

Performance of Predictors with Non-Gaussian Inputs

The trajectory of a maneuvering aircraft can be described by piecewise-constant-coefficient second-order polynomials which constitute a non-Gaussian process at the input of a linear fire control predictor. Consequently, the ?on- target? probability which is determined by the predictor output cannot be analytically evaluated. Using this a priori assumption for this type of target trajectory, the structure of a finite-time polynomial filter is determined. By using the ?go-no-go? characteristic of the loss function, the smoothing time of the predictor can be optimized to yield the highest possible ?on-target? probability. The results obtained constitute lower bounds whose validity is verified by digital simulation of the system. This shows that, on the average, they are 15 percent below the exact values. The simulation program is also used in a comparative study, with a conventional predictor and a Wiener-type predictor. The results demonstrate that the finite time polynomial predictor is markedly superior to both systems for a wide range of parameters and their combinations.

Exponential Smoothing and Short-Term Sales Forecasting

Non-seasonal forecasting methods are examined by considering demand generating processes which are reasonable and general descriptions of customer demand and for which the popular predictors are shown to be optimal. Tests of the adequacy of the generating processes are described. The way in which the forecasting errors vary with the forecasting period is examined, and it is shown that this is dependent not only on the length of the period but also on the values of the forecasting parameters. The sensitivity of the predictors to departures from the optimal parameters is investigated, and the long debated comparison of Holt's linear growth predictor (1957) and Brown's linear growth predictor (1959) is examined. It is shown for the assumed generating model and for forecasting parameters lying within the usual limits, that even if there is an infinite amount of data available to establish the optimum forecasting parameters, the standard error of the one step ahead predictor exceeds that of the Holt predictor by no more than 1.6 percent. The generalized polynomial generating process is shown to have as its optimal least squares predictor the corresponding Box-Jenkins polynomial predictor (1962).