Genetically Modified Networks: A Genetic Algorithm contribution to Space Geodesy.Application to the transformation of SLR and DORIS EOP time series into ITRF2005.

D. Coulot1, X. Collilieux1, A. Pollet1, P. Berio2, M.L. Gobinddass1,3, L. Soudarin4, P. Willis5,3, J.M. Lemoine6, and H. Capdeville4

(email : David.Coulot@ign.fr) 1 Institut Géographique National – LAREG et GRGS, Marne la Vallée, France - 2 Université Nice Sophia-Antipolis, Observatoire de la Côte d’Azur, Nice, France - 3 Institut de Physique du Globe de Paris, Paris, France

4 Collecte Localisation Satellites, Toulouse, France - 5 Institut Géographique National – Direction Technique, Saint-Mandé, France - 6 Centre National d’Etudes Spatiales – DTP et GRGS, Toulouse, France

Abstract

Solutions analyzed

Prospects

Genetic Algorithms

A

BD

G

Preliminary results for the DORIS technique F

IGN, 15 April 2009N° EGU2009-7988

Referencing of EOP time series C

In this poster, we apply Genetic Algorithms (GA) in order to optimize the referencing of the Earth Orientation Parameters (EOP) with respect to ITRF2005. These EOP are derived from SLR or DORIS data at a daily sampling, simultaneously with weekly station positions. We use an algorithm based on GA to find weekly optimal sub-networksover which applying Minimum Constraints (MC) in order to reference EOP. Each week, the three rotations of the involved terrestrial frames are forced to be zero with respect to ITRF2005 using MC applied over these sub-networks, which are called Genetically Modified Networks (GMN). The Reference System Effects (RSE) are used as objectives to optimize.

Regarding SLR, our approach provides an improvement of 10 % in accuracy for polar motion in comparison to the results obtained with the network specially designed for EOP referencing by the Analysis Working Group (AWG) of the International Laser Ranging Service (ILRS). This improvement of nearly 25 µas represents 50 % of the current precision of the IERS 05 C04 reference series. We also show preliminary results regarding such GMN for the DORIS technique using two different solutions.

Finally, for practical applications, we also test the possible emergence of global core networks to be used for EOP referencing on the basis of the GMN.

Results for the SLR technique E

General algorithm [Michalewicz, 1999]

t=0Initialization (P(t))Evaluation (P(t))do while (not stop_condition) t=t+1 P(t)=selection (P(t-1)) alteration (P(t)) evaluation (P(t))end do

Simple description Context Maximization of the function f(x1,…xn) in [a1,b1]x…x[an,bn] (f =objective function)

Solution coding (example of binary coding) Each parameter xi is encoded into a binary vector of length li

10110100 →xi ( li depends on the required precision for xi )

Codes of each parameter then merged all together

111000101110 111111 nnnnnnnnxx n →1 such merged code = 1 possible solution = 1 individual = 1 chromosome = 1 genotypeTrue values coded by a given genotype = 1 phenotype 1 digit (0 or 1) = 1 gene ( with the coding, nbrgen = l1 + … + ln )

Initial population 1 population of size m = m chromosomes = m individuals { ind1,…,indm }Created by randomly computing the nbrgen genes of the m individuals.

Evaluation and selection (example with roulette wheel)Evaluation of the current population = computation of the m values fj=f(x1

j,…,xnj)

→=→= ∑= F

fpfF jj

m

jj

1

m drawing lots

Selection of m individuals= Intermediate populationfor alteration (crossover and mutation)

Balance between exploitation and exploration

CrossoverCrossover probability pc set. Each individual of intermediate population “tested” wrt. pc. Sub-population of parents (other individuals directly duplicated). Chromosome recombination sub-population of children replacing parents. Children + duplicated individuals = new intermediate population for mutation.

Mutation Mutation probability pm set.Each gene of each individual tested wrt. pm. Mutation of some genes of some individuals.

New population for evaluation.

ReferencesBizouard, C., D. Gambis (2008) The combined solution C04 for Earth Orientation Parameters consistent with the International Reference Frame 2005. Proceedings of the GRF2006 Meeting, Munich, Germany, IAG Springer series publication, in press.Coulot, D., P. Berio, R. Biancale, S. Loyer, A.M. Gontier (2007) Toward a direct combination of space-geodetic techniques at the measurement level: Methodology and main issues. Journal of Geophysical Research 112: B05410 DOI: 10.1029/2006JB004336.Coulot, D., A. Pollet, X. Collilieux, P. Berio (2009a) Genetically Modified Networks: A Genetic Algorithm contribution to Space Geodesy. Application to the referencing of the SLR Earth Orientation Parameters with respect to ITRF. Journal of Geodesy, in revision.Coulot, D., M.L. Gobinddass, L. Soudarin (2009b) Genetically Modified Networks: Application to the DORIS technique. Advances in Space Research DORIS special issue, in preparation.Deb, K., S. Agrawal, A. Pratap, T. Meyarivan (2002) A Fast and Elitist Multi-Objective Genetic Algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2): 182-197.Goldberg, D.E. (1989) Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley, Reading, MA.Holland, J.H. (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, MI.Konak, A., D.W. Coit, A.E. Smith (2006) Multi-Objective optimization using genetic algorithms: A tutorial. Reliability Engineering and System Safety 91: 992-1007.Michalewicz, Z. (1999) Genetic Algorithms + Data Structures = Evolution Programs. Third edition, Springer-Verlag, Berlin Heidelberg New York.Sillard, P., C. Boucher (2001) A review of algebraic constraints in terrestrial reference frame datum definition. Journal of Geodesy 75: 63-73.

- One SLR solution provided by ASI (Agenzia Spaziale Italiana) Analysis Centre.- Two DORIS solutions provided by IGN (Institut Géographique National) and by LCA (CNES (Centre National d’Etudes Spatiales) – CLS (Collecte Localisation Satellites)) Analysis Centres.Weekly SINEX files retrieved from the CDDIS archiving facilities. Solution Technique Total number

of stationsWeekly number

of stationsTime span

ASI v10 SLR 77 19 +/- 3 1993.0 – 2008.3IGN wd08 DORIS 145 45 +/- 3 1993.0 – 2009.0

LCA wd21 DORIS 139 44 +/- 4 2000.0 – 2009.0

SLR station distribution for the ASI solution

DORIS beacon distribution for the IGN solution

For any given station/beacon,definition of presence P by P=(total occurrence)/(total number of weeks)

In both maps,

• = 75 < P ≤ 100 %• = 50 < P ≤ 75 %• = 25 < P ≤ 50 %• = P ≤ 25 %

Referencing of EOP time series C

Referencing EOP wrt. ITRF= each week, computing a solutionof station positions and EOP withapplication of minimum constraints (MC) over a given network for the three rotations RX, RY, RZ with respect to ITRF2005.Graph = Differences, with IERS05 C04 series, of xp daily seriescomputed with loose constraintsvs. xp daily series computed withMC. Minimum constraints daily EOP series aligning.

Graph = Differences between yp daily seriescomputed with MC applied over the “ASI” network and yp daily series computed with MC applied over the “ILRS” network. -“ASI” network = network made up by all SLRstations available each week in ASI solution.- “ILRS” network = network made up by SLRstations available each week which belongto the lLRS AWG list of core stations.

Influence of the network used for applying MC on EOP series precision. GA used to find weekly optimal sub-networks for MC application.

- Direct search for a mean “long-term” network of core stations for both techniques.- Similar tests to be carried out for GPS. Study of such approach for VLBI, albeit not with GA.- Improvement of AG: convergence speed, evolutionary program [Michalewicz, 1999], etc.- Comparison of AG with other stochastic approaches : simulated annealing, particle swarm optimization (Ant Colony Optimization), etc.

GA = Evolutionary algorithms, i.e. stochastic algorithms that emulate the evolution theory by using genetic operators such as chromosome selection and crossover (recombination) and gene mutation and the rule of survival of the fittest in probabilistic terms. Main idea = to make populations of possible solutions of a given optimization problem evolve in order to obtain the global optimum of the problem.

Alteration = Crossover and mutation

In our study, binary coding : 1 chromosome = the weekly network involved in the considered week.If gene = 0 : The station is not considered. If gene = 1 : The station is considered.Objectives = Reference System Effects (RSE) [Sillard and Boucher, 2001] for the three rotations after the MC application over the network corresponding to the considered chromosomes.For rotations RX and RY, RSE provided by EOP [Coulot et al., 2007].Three objectives use of a Multi-Objective GA (MOGA) [Konak et al., 2006].Use of the Non dominated Sorting GA (NSGA-II) [Deb et al., 2002] which provides a set of optimalsolutions (instead of one single optimal solution) on the basis of the non dominance Pareto relation. We choose the solution corresponding to the minimal Euclidian distance in objective space.

Network Weekly RSERX RY RZ

Biasxp yp

W. St. Dev.xp yp

WRMSxp yp

Weekly numberof stations

ASI 94 87 5 -2 88 324 301 324 314 19 +/- 3ILRS 53 54 6 -17 120 287 246 287 275 12 +/- 2GMN 30 30 5 -8 109 265 220 265 247 8 +/- 2

Table = Brief description of the solutions

Table = Median values of the weekly RSE for the three rotations, deduced from EOP for RX and RY and from station positions for RZ. Statistics of the differences between the daily EOP series and the IERS 05 C04 series. Solutions computed with MC for the three rotations, applied wrt. ITRF2005, over the networks ASI and ILRS and the GMN. All values provided in µas. Improvement of 8–10% for GMN wrt. ILRS regarding W. St. Dev. and WRMS. Improvement of 25 µas = 50 % of precision of IERS05C04 [Bizouard and Gambis, 2008]

(C≥75)&(P≥50)(C≥50)&(P≥25)

7090

7110

7210

78497501

7810

7832

78397840

7843

8834

7080 7105

7403

78357837

79397941

ILRS AWG core stations are underlined.

+ 17 stations always missing (22%)1831 1864 1873 1884 1885 1893 19537123 7249 7358 7404 7410 7548 78057847 7848

Majority of the stations used by GMN belongs to the list of ILRS core stations. If we use the 11 stations 7090 7110 7210 7849 7501 7810 7832 7839 7840 7843 8834 as a global reference network, we obtain difference WRMS of 282 and 267 µas for xp and yp. Possible emergence of mean reference network for EOP referencing from GMN. If objectives are RSE only deduced from station positions for GMN, we obtain difference WRMSof 373 and 338 µas for xp and yp. RSE deduced from EOP = rigorous criteria for EOP referencing [Coulot et al., 2009a]

Prospects for DORIS [Coulot et al., 2009b] : - Possible emergence of a core network of sites/stations from GMN.- Reference system effect for stations only to be studied.- Computation over the whole period of time for LCA wd21 solution to be carried out.

Presence P defined by P=(total occurrence)/(total number of weeks)Choice C defined byC=(occurrence in GMN)/ (occurrence in ASI netw.)

(C≥75)&(P≥75) (C≥75)&(P≥25)(C≥25)&(P≥25)

Map = Mean network emerging from weekly GMN with choice and presence criteria.

GMN provide an improvement of nearly 30 µas regarding weighted standard deviations and WRMS of the differences of EOP wrt. IERS 05C04 series, for both solutions IGN and LCA.

Map = Mean network emerging from weekly GMN with choice and presence criteria for IGN wd08.

(C≥75)&(P≥50)(C≥50)&(P≥25)

GMN mainly use 55 sites (70 %) for the DORIS technique.

All these results must be confirmed. xp pole coordinate

yp pole coordinate

IERS sites are considered, not DORIS beacons.

(C≥75)&(P≥75) (C≥75)&(P≥25)(C≥25)&(P≥25)+ 8 sites always missing (10%)10077 40476 41708 92722 92802 4200539601 39801