%% Lookup table for the critical value of the ambiguity-resolved detector (ARD) [1]
%
% --------------------------------------------------------------------------------------------------
% This file provides a lookup table of the ARD critical value for the short-baseline 
% double-difference GNSS observation model and its equivelence.
%
% How to use
%   - Find the table corresponding to the number of frequencies of the model
%   - Find the index of the specifed significance level alpha, i_alpha
%   - Find the index of the ambiguity-known redundancy of the model from ra_list, i_ra
%   - Obtain the polynomial coefficients from the table
%      - x0_i = x0(i_ra, i_alpha)
%      - x1_i = x1(i_ra, i_alpha)
%      - x2_i = x2(i_ra, i_alpha)
%   - Compute the integer-bootstrapping success rate of the float ambiguity estimator [2], P_{SR}
%   - Compute the ARD critical value
%         k = x0_i + x1_i*(1-P_{SR}) + x2_i*(1-P_{SR})^2
%
% --------------------------------------------------------------------------------------------------
% Copyright: Geoscience & Remote Sensing department @ TUDelft | 11/2024
% --------------------------------------------------------------------------------------------------
% Created by
%   05/11/2024  - Chengyu Yin
% --------------------------------------------------------------------------------------------------
% Reference
% [1] Teunissen, P. J. G. (2024). The ambiguity-resolved detector: a detector for the mixed-integer 
%   GNSS model. Journal of Geodesy, 98(9), 1-16.
% [2] Teunissen, P. J. G.(1998). Success probability of integer GPS ambiguity rounding and bootstrappi
%   ng. Journal of Geodesy, 72, 606-612.
% --------------------------------------------------------------------------------------------------

Single-frequency
alpha: [0.0010 0.0050 0.0100 0.0500]
ra_list: [7;9;11;13;15;17;19;21;23;25;27;29;31]

a0:
[24.3218863479 20.2777398750 18.4753069066 14.0671404493];
[27.8771648713 23.5893507813 21.6659943335 16.9189776046];
[31.2641336202 26.7568489165 24.7249703113 19.6751375727];
[34.5281789749 29.8194712237 27.6882496105 22.3620324948];
[37.6972982184 32.8013206458 30.5779141669 24.9957901397];
[40.7902167069 35.7184656590 33.4086636050 27.5871116383];
[43.8201959645 38.5822565549 36.1908691293 30.1435272056];
[46.7970380416 41.4010647714 38.9321726835 32.6705733409];
[49.7282324664 44.1812752500 41.6383981189 35.1724616269];
[52.6196557762 46.9278901601 44.3141048962 37.6524841335];
[55.4760202057 49.6449152990 46.9629421248 40.1132720694];
[58.3011734898 52.3356177859 49.5878844729 42.5569678043];
[61.0983060811 55.0027038800 52.1913948332 44.9853432804];

a1:
[-44.9086889072 -31.7189321339 -25.9414333728 -13.1963145695];
[-35.6281526781 -25.1953266587 -20.6437933588 -10.8904602290];
[-37.6589364080 -25.9149318463 -20.9517791438 -10.5078054274];
[-35.8712427887 -24.1676396789 -19.4193541520 -9.4976383446];
[-34.0234631812 -22.3905726278 -17.6149547733 -8.1126145097];
[-29.9673003389 -19.7899544400 -15.5778106252 -7.2564644145];
[-26.9304714616 -16.8315647503 -12.9383146591 -5.3715838709];
[-23.3921936365 -13.9618842278 -10.3049830093 -3.7727407570];
[-19.3282895141 -10.9589541601 -7.9189058067 -2.6464457373];
[-14.9539023565 -7.8949399510 -5.4318670952 -1.5125932269];
[-11.2384043005 -5.5553718008 -3.6134547344 -0.7804364159];
[-7.6657122073 -3.2495745653 -2.0370952272 -0.2861077503];
[-5.2526514074 -1.7755322729 -0.8539796914 0.2072313999];

a2:
[148.6514410253 94.2162578521 71.1557123657 23.7686546361];
[87.4256092793 50.8634722250 35.8582421697 8.5666508923];
[106.6886985016 61.2059217836 43.1377392086 9.5794985915];
[87.6872810097 45.4448931439 29.9301384796 2.5834353093];
[84.2743681693 40.6644196817 24.2353651754 -2.2727072639];
[59.7856042274 26.7801555637 14.2841888801 -4.4629512240];
[45.0628519173 12.9031918595 2.5613083534 -11.9041458904];
[28.9180900446 0.4543771880 -8.6902088386 -17.7191240101];
[12.5523574246 -9.5506005940 -15.4141290309 -18.5316370001];
[-5.1393390719 -20.2174097037 -23.1000962817 -20.1488259104];
[-19.0894634134 -26.5943317607 -27.0690096493 -19.9000257775];
[-29.1158591649 -30.8485000877 -27.7417611253 -16.8110512863];
[-37.1109885606 -34.7628494422 -30.7120658994 -17.4201272416];


Dual-frequency
alpha: [0.0010 0.0050 0.0100 0.0500]
ra_list: [13;17;21;25;29;33;37;41;45;49;53;57;61;65]

a0:
[34.5281789749 29.8194712237 27.6882496105 22.3620324948];
[40.7902167069 35.7184656590 33.4086636050 27.5871116383];
[46.7970380416 41.4010647714 38.9321726835 32.6705733409];
[52.6196557762 46.9278901601 44.3141048962 37.6524841335];
[58.3011734898 52.3356177859 49.5878844729 42.5569678043];
[63.8700985223 57.6484452559 54.7755397601 47.3998839191];
[69.3464524962 62.8833354537 59.8925000451 52.1923197301];
[74.7449383984 68.0527264554 64.9500713352 56.9423871468];
[80.0767320108 73.1660608182 69.9568320658 61.6562333763];
[85.3505646086 78.2307080867 74.9194743085 66.3386488630];
[90.5734123053 83.2525512052 79.8433381223 70.9934528338];
[95.7509538325 88.2363754100 84.7327657051 75.6237484694];
[100.8878853069 93.1861353141 89.5913444907 80.2320978488];
[105.9881430896 98.1051438110 94.4220790079 84.8206454977];

a1:
[-23.6426713770 -17.7590945952 -15.2576998324 -9.5821106995];
[-26.8309712736 -17.7368140562 -14.0888237022 -6.9708057169];
[-22.6327932611 -13.6233858260 -10.1936320303 -4.0014888898];
[-15.4873076889 -8.3739584925 -5.8700221140 -1.8170916679];
[-8.8707697870 -4.0494186054 -2.4888647754 -0.4222372942];
[-4.0814476749 -1.4043660179 -0.7189037240 -0.0140166486];
[-3.3787917450 -1.4939102469 -1.1740427809 -0.5768592005];
[-1.5437013850 -0.9633290307 -0.7162076232 -0.4863126033];
[-2.1004072598 -1.6161798506 -1.4980683784 -1.0522659140];
[-2.9183883116 -2.2604615469 -2.0265322893 -1.4172186605];
[-3.3182794127 -2.7220128000 -2.4559072408 -1.6319323405];
[-3.3462252011 -2.6617862666 -2.3924460069 -1.6044803421];
[-3.8605413726 -3.1892904201 -2.9296839180 -1.9757964518];
[-4.5414995563 -3.2680444775 -2.9232935074 -1.9497343989];

a2:
[58.0969471089 39.1344491780 31.4862571751 15.2389802327];
[50.0792032763 21.4524811561 11.2929560318 -3.4667176034];
[26.7659966940 0.4588581170 -7.6341915024 -15.4542821141];
[-1.8994766895 -17.5415155474 -20.7729487825 -18.6818665745];
[-24.4976413463 -28.5560344794 -27.4760516683 -17.9465216189];
[-34.2333340246 -29.2161576962 -24.8440693708 -12.8087692024];
[-27.1912174358 -20.6479484482 -15.6730009950 -7.0246095380];
[-23.0052614862 -13.7721336402 -10.7337233203 -4.2685534390];
[-13.9054884872 -7.3634317380 -4.7996239602 -1.6363609786];
[-4.9023735881 -1.7939406006 -0.7937030835 0.2443682293];
[0.5678915111 2.3760194775 2.6553868217 1.4560275373];
[0.7213117281 1.0437028470 1.3223336075 0.4602810057];
[2.9967787987 3.2603152557 3.1252178117 1.1828073404];
[5.1378167244 2.0811805424 1.8957469883 0.1126502891];


Triple-frequency
alpha: [0.0010 0.0050 0.0100 0.0500]
ra_list: [21;27;33;39;45;51;57;63;69;75;81;87;93;99]

a0:
[46.7970380416 41.4010647714 38.9321726835 32.6705733409];
[55.4760202057 49.6449152990 46.9629421248 40.1132720694];
[63.8700985223 57.6484452559 54.7755397601 47.3998839191];
[72.0546629520 65.4755709035 62.4281210162 54.5722277589];
[80.0767320108 73.1660608182 69.9568320658 61.6562333763];
[87.9679804756 80.7466589540 77.3859620161 68.6692939123];
[95.7509538325 88.2363754100 84.7327657051 75.6237484694];
[103.4423773199 95.6492974805 92.0100236141 82.5287265415];
[111.0550655627 102.9962090773 99.2275154706 89.3912078725];
[118.5990947638 110.2855833636 106.3929229297 96.2166707535];
[126.0825583332 117.5242218736 113.5124104704 103.0095087122];
[133.5120737925 124.7176828230 120.5910145128 109.7733093503];
[140.8931342732 131.8705778492 127.6329129011 116.5110472809];
[148.2303591651 138.9867834509 134.6416168558 123.2252214534];

a1:
[-19.0624069925 -14.1736540517 -12.0871388167 -7.5834147016];
[-18.3375339135 -12.8480944010 -10.6140604781 -5.8864207184];
[-14.7968172008 -9.6352686388 -7.6057830155 -3.7007129694];
[-10.3859367085 -6.3977072311 -4.8743980168 -2.1302622908];
[-7.1326462138 -4.0549137097 -2.9879917940 -1.2833717453];
[-4.7237308982 -2.8587644259 -2.3074600818 -1.2831716301];
[-6.4201982230 -5.0546316357 -4.6175392100 -3.2183274869];
[-6.1265913972 -4.8235482004 -4.2139063679 -3.0303915492];
[-7.5668794898 -6.0683839129 -5.3928295129 -3.8602226808];
[-8.1525998240 -6.3674143213 -5.6747352935 -4.1270691246];
[-8.0350380016 -6.4997249953 -5.8967632047 -4.3497323551];
[-8.5812327900 -6.9398093452 -6.2690956497 -4.5277310714];
[-8.8622526063 -7.4664369881 -6.6665276832 -4.9532794829];
[-8.6324891778 -7.1093241529 -6.3635459357 -4.8165153301];

a2:
[40.6597834320 24.5372737370 18.2380977390 6.6985029580];
[29.2511053055 13.1650562558 7.3200069103 -2.6156953185];
[10.4308567395 -2.0446565500 -6.1104550423 -10.6580001357];
[-7.0111177147 -12.6290940948 -13.9483892921 -13.0669016309];
[-15.6586558798 -17.3844040777 -17.0529675184 -12.3107673448];
[-14.0687450623 -12.4859837085 -11.1497227522 -6.9381289103];
[-3.1657172044 -0.0722458719 1.6369974961 1.6753005415];
[0.8596974257 0.2432573055 -0.3059544852 -0.1721594930];
[11.0953821767 8.0305158471 6.6374393647 3.1708644413];
[13.7413756303 8.7055612586 7.0182024196 3.7946621388];
[11.9968923423 7.5635896735 6.7151714945 3.5282355020];
[13.8466521843 10.3061530245 9.0463734923 4.4172718815];
[14.5814397206 11.4971676704 9.3046640485 5.3709847275];
[7.1301596146 6.1875187119 4.1379202596 1.3203176378];