An Application of Error-Covariance Analysis to Inertial Platform Errors

1986 ◽  
Author(s):  
Shirley J. Tucker ◽  
Henry E. Stern
Keyword(s):  
Covariance Analysis ◽  
Error Covariance

scholarly journals Comparison of Probabilistic Statistical Forecast and Trend Adjustment Methods for North American Seasonal Temperatures

2014 ◽  
Vol 53 (4) ◽  
pp. 935-949 ◽  
Author(s):  
Daniel S. Wilks
Keyword(s):  
North American ◽  
Forecast Error ◽  
Forecast Accuracy ◽  
Covariance Analysis ◽  
Cold Bias ◽  
Seasonal Forecasts ◽  
Multivariate Statistical ◽  
Maximum Covariance Analysis ◽  
Error Covariance ◽  
Alternative Approaches

AbstractThe three multivariate statistical methods of canonical correlation analysis, maximum covariance analysis, and redundancy analysis are compared with respect to their probabilistic accuracy for seasonal forecasts of gridded North American temperatures. Derivation of forecast error covariance matrices for the methods allows a probabilistic formulation for the forecasts, assuming Gaussian predictive distributions. The three methods perform similarly with respect to probabilistic forecast accuracy as reflected by the ranked probability score, although maximum covariance analysis may be preferred because of its slightly better forecast skill and calibration. In each case the forecast accuracy for North American seasonal temperatures compares favorably to results from previously published studies. In addition, two alternative approaches are compared for alleviating the cold biases in the forecasts that derive from ongoing climate warming. Adding lagging 15-yr means to forecast temperature anomalies improved forecast accuracy and reduced the cold bias in the forecasts, relative to using the more conventional lagging 30-yr mean.

Steady-State Covariance Analysis for a Forward-Pass Fixed-Interval Smoother

1986 ◽  
Vol 108 (2) ◽  
pp. 136-140
Author(s):  
Keigo Watanabe
Keyword(s):  
Steady State ◽  
Simple Algorithm ◽  
Lyapunov Equation ◽  
Fixed Interval ◽  
Covariance Analysis ◽  
Algebraic Riccati Equation ◽  
Stabilizing Solution ◽  
Error Covariance ◽  
Forward Pass ◽  
Necessary And Sufficient

This paper studies the solution of the steady-state error covariance equation (which is represented by the algebraic Lyapunov equation) associated with a forward-pass fixed-interval smoother for discrete-time linear systems. A necessary and sufficient condition is given to assure the existence of a unique stabilizing solution. A simple algorithm for solving such an equation is also proposed by using four eigenvector matrices, which are generated by a symplectic matrix, corresponding to the algebraic Riccati equation of a backward-pass information filter. Thus the results have application to the important problem of the limiting covariance analysis of smoothing prior to practically dealing with a finite interval of data.

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