Statistical geodesy—An engineering perspective

Motivated largely by the needs of the navigation community, engineers have become increasingly involved in understanding and modeling the fine structure of the earth's gravity field. In this endeavor, the engineer has augmented the applied mathematical tools of the "geodesist-scientist" with those of modern estimation and control theory, state-space mathematics, and random process theory. One of the outputs of this involvement has been the development of "statistical geodesy." In this paper, the mathematical structure and applications of statistical geodesy are reviewed, with an emphasis on the engineer's contribution. Geodetic terminology, geopotential theory, and estimation theory are briefly reviewed, and models with a random-process-theory structure are presented for uncertainties in the earth's gravity field. These models are then utilized in a variety of applications: estimation of gravimetric uncertainties, error analysis of inertial navigation systems, gravity gradiometry, satellite altimetry, etc. Finally, a new algorithm is presented-frequency-domain collocation-suitable for the efficient processing of large amounts of gravimetric data.

[1]  P. Whittle.  ON STATIONARY PROCESSES IN THE PLANE , 1954 .

[2]  R. A. Hirvonen.  On the precision of the gravimetric determination of the geoid , 1956 .

[3]  W. M. Kaula.  Accuracy of gravimetrically computed deflections of the vertical , 1957 .

[4]  W. M. Kaula,et al.  Statistical and harmonic analysis of gravity , 1959 .

[5]  R. A. Hirvonen.  STATISTICAL ANALYSIS OF GRAVITY ANOMALIES , 1962 .

[6]  Cornelius T. Leondes,et al.  Guidance and control of aerospace vehicles , 1963 .

[7]  Charles Broxmeyer,et al.  Inertial navigation systems , 1964 .

[8]  Raymond A. Nash.  Effect of Vertical Deflections and Ocean Currents on a Maneuvering Ship , 1968, IEEE Transactions on Aerospace and Electronic Systems.

[9]  J. R. Nash,et al.  The estimation and control of terrestrial inertial navigation system errors due to vertical deflections , 1968 .

[10]  A. Gelb,et al.  Effect of deflections of the vertical on the performance of a terrestrial inertial navigation system. , 1969 .

[11]  Shipboard or aircraft gravity vector determination by means of a three-channel inertial navigator , 1969 .

[12]  L. Shaw,et al.  Statistical models for the vertical deflection from Gravity-Anomaly Models , 1969 .

[13]  E. J. Hannan,et al.  Multiple time series , 1970 .

[14]  Raymond A. Nash,et al.  A statistical analysis of errors in gravimetrically computed vertical deflections , 1970 .

[15]  H. Moritz.  A general theory of gravity processing , 1970 .

[16]  Joseph F. Kasper,et al.  A second‐order Markov Gravity Anomaly Model , 1971 .

[17]  Raymond A. Nash,et al.  Direct Recovery of Deflections of the Vertical Using an Inertial Navigator , 1972 .

[18]  R. Nash,et al.  A statistical algorithm for computing vertical deflections gravimetrically , 1972 .

[19]  Stanley K. Jordan,et al.  Self‐consistent statistical models for the gravity anomaly, vertical deflections, and undulation of the geoid , 1972 .

[20]  T. W. Anderson,et al.  Statistical analysis of time series , 1972 .

[21]  Helmut Moritz,et al.  Advanced Least-Squares Methods, , 1972 .

[22]  K. Roy,et al.  Error analysis of hybrid aircraft inertial navigation systems , 1972 .

[23]  Stanley K. Jordan,et al.  Effects of Geodetic Uncertainties on a Damped Inertial Navigation System , 1973, IEEE Transactions on Aerospace and Electronic Systems.

[24]  R. Mehra,et al.  Computational aspects of maximum likelihood estimation and reduction in sensitivity function calculations , 1974 .

[25]  Comparison of Upward Continued Anomalies Computed by the Poisson Integral and by Collocation. , 1975 .

[26]  C. Tscherning.  Covariance expressions for second and lower order derivatives of the anomalous potential , 1976 .

[27]  Albert Jircitano,et al.  Inertial Navigation Performance Improvement Using Gravity Gradient Matching Techniques , 1976 .

[28]  S. W. Thomas,et al.  Efficient Estimation Techniques for Integrated Gravity Data Processing. , 1976 .

[29]  David E. Smith,et al.  Contributions to the National Geodetic Satellite Program by Goddard Space Flight Center , 1976 .

[30]  K. Lambeck.  Lateral density anomalies in the upper mantle , 1976 .

[31]  E. Wong.  Detection and filtering for two-dimensional random fields , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[32]  M. Ekstrom,et al.  Two-dimensional spectral factorization with applications in recursive digital filtering , 1976 .

[33]  Warren G. Heller,et al.  Error Analysis of Two New Gradiometer-Aided Inertial Navigation Systems , 1976 .

[34]  M. B. Dobrin.  Introduction to Geophysical Prospecting , 1976 .

[35]  U. Bernstein,et al.  The Effects of Vertical Deflections on Aircraft Inertial Navigation Systems , 1976 .

[36]  W. Larimore,et al.  Statistical inference on stationary random fields , 1977, Proceedings of the IEEE.

[37]  GEOFAST - A fast Gravimetric Estimation Algorithm. , 1977 .

[38]  S. Jordan.  Statistical model for gravity, topography, and density contrasts in the Earth , 1978 .

[39]  S. Jordan,et al.  Upward continuation of gravity disturbance covariance functions , 1978 .

[40]  Moving-Base Gravity Gradiometer Surveys and Interpretation , 1978 .