We can use 3 dimensional base functions to model any function of the gravity filed (potential anomaly, gravity anomaly, height anomaly) using iterative method like least square, levenberg marquardt and etc, from which aspect we can compare these methods and choose the best algorithm? With the number of base functions that we have used? With the final value of STD? With the number of iteration?
Conference Paper Regional gravity field modeling by the free-positioned point...
Radial base functions are used in Least-squares collocation and are denoted covariance functions or reproducing kernels (supposing a rotational invariant inner product is used in the RKH). The base functions are by definition then the Riez-representer associated with the observation. No iteration is needed, but then as many base functions as observations have to be used in the modelling. That this procedure is the "best" is due to the fact that it is optimal in a Hilbert space of harmonic functions, and it can be seen also by comparing observed values with computed values and then comparing with the error-estimate. In the IAG JSG0.3 group comparisons are to be made and have been made, see e.g. http://cct.gfy.ku.dk/ jsg03.htm
Thank you so much for your response,
Exactly you right, but you know we can use iterative least square method such as Gauss Newton, Levenberg Marquardt and etc to find optimal RBF solution, then when i want to compare these methods with each other to choose the best one, my main question is about the comparison criteria, you know we can use different RBF networks (different RBF centers) to find optimal solution, now which of them is the best? absolutely we cant believe that the best STD values show the best method, because there are different networks in each method
But this criteria is not meaningful for LSC, because this method has the property that the model reproduces the observations exactly for noise free data. So, other methods should be based on how well they agree with the LSC solution. Alternatively comparisons can be made using the test data of IAG JSG 0.1. In my opinion you should drop using other radial basis function methods, since theory proves that LSC gives the optimal/best results.
Thank you,
So based on your answer, we should use only LSC, but i was looking for another methods that may give better result in comparison to LSC.
LSC will by definition give the best answer if you can find a reproducing kernel
which model the empirical covariance function
pls see Moritz: Advanced Physical Geodesy, 1980. Or see Heiskanen & Moritz: Physical
Geodesy, 1967? Chapter 7.7
- Badges
- Science topic