Principles of accuracy and predicted accuracy in photogrammetric-based geopositioning
Presenters: John Dolloff & Hank Theiss
This webinar addresses the importance and use of both accuracy and predicted accuracy in a Geolocation System. Accuracy is typically represented as a LE90, CE90, and/or SE90 corresponding to 90% probable vertical, horizontal, and 3d spherical radial error, respectively, of an arbitrary geolocation or geolocation product generated by or using data from the Geolocation System. Order statistics are recommended for their computation based on a recommended minimum number of independent and identically distributed (iid) samples of error, or approximately iid samples of error if certain constraints are met. The underlying probability distribution of errors is neither required nor used. Based on these samples, a best estimate of LE90, CE90, and/or SE90 are computed, as well as corresponding least-upper-bounds computed at a 90% confidence level, in order to assess the accuracy of the Geolocation System and/or determine if corresponding specified requirements are met.
Predicted accuracy is associated with an arbitrary but specific geolocation associated with the Geolocation System. It is a “current” geolocation, either already extracted using the Geolocation System’s data, typically via a Weighted Least Squares (WLS) Solution using multiple images, or contained in one of the Geolocation System’s products, such as a Digital Surface Model (DSM). The WLS provides both a best estimate of the geolocation as well as its specific error covariance matrix.
Predicted Accuracy is based on predictive statistics, the key statistic is the error covariance matrix uniquely associated with each geolocation, and an assumed type of probability distribution of geolocation errors, typically, either multivariate Gaussian or Laplacian. Using this data, either a 90% probability error ellipsoid (or ellipse) can be computed, and scalar accuracy metrics (LE90, CE90, and SE90) can also be computed that contain less information than the ellipsoid but are convenient summaries.
Predicted accuracy is assessed using (approximately) iid samples of geolocation error normalized by their corresponding error covariance matrices. Results are quantified based on how reliably the error covariance and corresponding probability distribution represent actual geolocation errors. The assessment can also be used to determine if corresponding predicted accuracy requirements for the Geolocation System are met. Reliable predicted accuracy enables informed use of geolocations and/or corresponding products as well as optimal fusion with other geolocation products.
This Webinar also presented recommended processing associated with geolocations and their accuracy and/or predicted accuracy, including: (1) specification, assessment, and validation of requirements, (2) computation of error ellipsoids and scalar accuracy metrics, (3) representation of geolocation errors as random vectors, stochastic processes, or random fields, (4) Estimators and their Quality Control, such as WLS batch solutions and Kalman Filter sequential solutions, and (5) Monte-Carlo simulation or errors. Corresponding details are also provided in publicly available and referenced NGA-authored Technical Guidance Documents.
John Dolloff, a senior scientist at KBR, has been involved in various aspects of geopositioning for over 40 years supporting the NGA and related organizations as a Subject Matter Expect (SME) specializing in applying advanced linear algebra, estimation theory, probability, and statistics; particularly, as related to photogrammetric principles.
Hank Theiss, a senior scientist who works part-time at KBR, is a Research Associate Professor at the University of Arkansas in the Center for Advanced Spatial Technologies (CAST) with over 25 years of experience supporting NGA and related organizations as a photogrammetry SME.
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