Special Topics in Sports Engineering Smartphone Exercise Files

kalman_filter.m

function [x, P] = kalman_filter(A, B, C, Q, R, x, u, y, P)
% kalman_filter - Returns the next state estimate and its covariance matrix
% using the Kalman Filter predict & update. Note that this implementation is
% not numerically stable, use production code for non-textbook problems.
%
% Syntax: [x, P] = kalman_filter(A, B, C, Q, R, x, u, y, P)
%
% Inputs:
%   A - State matrix, size 5 x 5
%   B - Input matrix, size 5 x 1
%   C - Output matrix, 2 x 5
%   Q - Model covariance matrix, size 5 x 5
%   R - Measurement convariance matrix, size 2 x 2
%   x - Current state, size 5 x 1
%   u - Current input, size 1 x 1
%   y - Current measurement, size 2 x 1
%   P - Current state covariance matrix, size 5 x 5
% Outputs:
%   x - New state, size 5 x 1
%   P - New state covariance matrix, 5 x 5

x = A*x + B*u;
P = A*P*A' + Q;
L = P*C'*inv(C*P*C' + R);
P = (eye(length(x)) - L*C)*P;
x = x + L*(y - C*x);

end

run_kalman_filter.m

data = csvread('smartphone-data.csv', 1, 0);

t = data(:, 1);
v = data(:, 5);
omega = data(:, 6);
a = data(:, 7);
theta_true = data(:, 8);
v_true = data(:, 9);

dt = % 1 x 1
g = 9.81;

A = % 5 x 5
B = % 5 x 1
C = % 2 x 5

Q_scale = 1.0;  % adjust this number, model covariance
R_scale = 1.0;  % adjust this number, measurement covariance

Q = Q_scale*diag([0.0, 0.0, 0.0, 0.0, 1.0]);
R = R_scale*diag([2.5e-01, 9.0e-04]);

% initial P and x
P = diag([1.0e+02, 2.5e-01, 1.0e-04, 4.0e-04, 9.0e-04]);
x = % 5 x 1, initial state

xs = zeros(length(?), 5);  % add correct length of time vector
xs(1, :) = x;
for i=2:length(?) % add correct length of time vector
    u = % 1 x 1, model input
    y = % 2 x 1, actual measurements
    % run the filter for this time step, updating x and P
    [x, P] = kalman_filter(A, B, C, Q, R, x, u, y, P);
    % store the estimated state vector
    xs(i, :) = x;
end

% make some plots
figure();
plot(t, v_true, t, v, '.', t, xs(:, 2));
figure();
plot(t, theta_true, t, xs(:, 4));
figure();
plot(t, omega, '.', t, xs(:, 5));

run_kalman_filter.py

import numpy as np
import matplotlib.pyplot as plt

def kalman_filter(A, B, C, Q, R, x, u, y, P):
    """Returns the next state estimate and its covariance matrix.

    Parameters
    ==========
    A : shape(5, 5)
        State matrix
    B : shape(5, 1)
        Input matrix
    C : shape(2, 5)
        Output matrix
    Q : shape(5, 5)
        Model covariance matrix
    R : shape(2, 2)
        Measurement convariance matrix
    x : shape(5, 1)
        Current state
    u : shape(1, 1)
        Current input
    y : shape(2, 1)
        Current measurement
    P : shape(5, 5)
        Current state covariance matrix

    Returns
    =======
    x : shape(5, 1)
        New state
    P : shape(5, 5)
        New state covariance matrix

    """
    x = A@x + B@u
    P = A@P@A.T + Q
    L = P@C.T@np.linalg.inv(C@P@C.T + R)
    P = (np.eye(len(x)) - L@C)@P
    x = x + L@(y - C@x)
    return x, P


data = np.loadtxt('smartphone-data.csv', skiprows=1, delimiter=',')

t = data[:, 0];
v = data[:, 4];
omega = data[:, 5];
a = data[:, 6];
theta_true = data[:, 7];
v_true = data[:, 8];

dt = # 1 x 1

A = # 5 x 5
B = # 5 x 1
C = # 2 x 5

Q_scale = 1.0  # adjust this number, model covariance
R_scale = 1.0  # adjust this number, measurement covariance

Q = Q_scale*np.diag([0.0, 0.0, 0.0, 0.0, 1.0])
R = R_scale*np.diag([2.5e-01, 9.0e-04])

P = np.diag([1.0e+02, 2.5e-01, 1.0e-04, 4.0e-04, 9.0e-04])

x = # 5 x 1, initial state

us =  # n x 1 x 1, inputs
ys =  # n x 2 x 1, measurements

xs = np.zeros((len(us), 5, 1)) # n x 5 x 1
for i, (u, y) in enumerate(zip(us, ys)):
    x, P = kalman_filter(A, B, C, Q, R, x, u, y, P)
    xs[i] = x

# make some plots
plt.figure()
plt.plot(t, v_true, t, v, '.', t, xs[:, 1, 0]);

plt.figure()
plot(t, theta_true, t, xs[:, 3, 0]);

plt.figure()
plot(t, omega, '.', t, xs[:, 4, 0]);

smartphone-data.csv

time [s],altitude [m],latitude [deg],longitude [deg],speed [m/s],rate_gyro_z [rad/s],accelerometer_x [m/s/s],true_slope_angle [rad],true_speed [m/s]
0.0,29.349255038655915,34.14528015694175,133.02109942426688,5.0,0.02743613603825991,0.19624320475316748,0.03977464905028287,5.0
0.1,28.98532874791777,34.14530224788589,133.0210677537201,5.0,-0.050001858885091,0.20115685586216087,0.03562063913485901,4.981922246361347
0.2,30.12374256600749,34.145165581670916,133.02100808295805,5.0,-0.014990206694255746,0.19773983621018504,0.031479264841759405,4.968104748684157
0.30000000000000004,29.651512134560015,34.14530215592312,133.02117868846744,5.0,0.024343713701225754,0.22872029208253056,0.027347088343894963,4.958485910241052
0.4,29.7162295894864,34.145327818039526,133.02098691765065,5.0,-0.07914181593345203,0.18268057290285417,0.023220734000403667,4.953008284578877
0.5,29.627047871908914,34.14516285913839,133.0211686071004,5.0,-0.04135677467297087,0.20482025973275425,0.0190968588638307,4.951618031703902
0.6000000000000001,29.66727825395798,34.14528407201074,133.02122356373013,5.0,-0.028509036006478215,0.2132818850708582,0.014972152680128418,4.95426491808181
0.7000000000000001,29.135455821873695,34.14531894979247,133.0210908026624,5.0,0.002360827094701465,0.18189588561354084,0.010843337888656431,4.9609023166377115
0.8,29.476509691217345,34.14513657524417,133.02114513301734,5.0,-0.016837110179394293,0.20977211752802896,0.006707169622181531,4.971487206756135
0.9,29.791863279051945,34.14531889327758,133.02118166503502,5.0,-0.09042887648926684,0.20409333024985823,0.002560435706877716,4.98598017428103
1.0,29.309797156236918,34.145315713274854,133.02110373066606,5.0,-0.03383078390325187,0.18571071790566973,-0.0016000433376738253,5.004345411515768
1.1,28.66937817638784,34.145163520336155,133.02102575528517,5.0,-0.05312921715650932,0.19034361039800496,-0.005776904709968868,5.026607014057085
1.2000000000000002,30.216955430972863,34.14520413668664,133.0210104997868,5.0,-0.07730042473012397,0.19057036597890908,-0.009972792785046307,5.052840232500631
1.3,28.531122766284163,34.14525343463812,133.02110519660508,5.0,-0.03133444968026107,0.18111322083592993,-0.014191613530303357,5.082993727950669
1.4000000000000001,28.575910706433287,34.145252555329975,133.0211630035638,5.0,-0.022343312347815676,0.1769402865573584,-0.018437082723504312,5.1169929224698185
1.5,29.318899535867097,34.145244238958895,133.0211023784559,5.0,-0.05871091464947488,0.17518916497791082,-0.022712692376996406,5.154743018578305
1.6,29.661416127136366,34.14519361258572,133.02095553790605,5.0,-0.019393545734648687,0.16847804289742188,-0.0270217107377098,5.196128999253955
1.7000000000000002,28.940921777650836,34.14521280223687,133.0211357983949,5.0,-0.11935520462982002,0.17512915033994347,-0.03136718228715761,5.241015627932199
1.8,29.336982233838917,34.145212202015635,133.0210622633263,5.0,0.012599858249781722,0.16905921724055178,-0.03575192774143587,5.28924744850607
1.9000000000000001,28.62173476167685,34.14523917906292,133.02126232538825,5.0,-0.07135185732785028,0.14264329585236182,-0.040178544051223564,5.3406487853262075
2.0,28.77602678940273,34.14519665156262,133.02105350864665,5.0,-0.07375672853114955,0.1411261146470797,-0.04464940440178261,5.395023743200849
2.1,29.151205959852806,34.14515266735049,133.02113517363136,5.0,-0.05418209267198555,0.15239724506541352,-0.04916665821295786,5.452156207395841
2.2,28.29404048977968,34.14521397342533,133.02103465334616,5.0,-0.045087883820343316,0.1431369040648526,-0.05373223113917712,5.51180984363463
2.3000000000000003,29.416321590469543,34.14518229569743,133.02113883128797,5.0,-0.048092291405778836,0.09108039249247948,-0.05834782506945112,5.5737280980982655
2.4000000000000004,29.833478076463425,34.14519411741133,133.02109838502207,5.0,-0.05988963360821839,0.12255864907354859,-0.06301491812737352,5.6376341974254025
2.5,28.72434107236792,34.14519644777341,133.02109493684935,5.0,-0.06957854538301318,0.12472667154080931,-0.0677347646711209,5.703231148712296
2.6,28.89410575848845,34.145113570563964,133.0211788555839,5.0,-0.09494939752505362,0.11983015981135742,-0.07157716540621724,5.77020173951281
2.7,28.64032337654543,34.14517452717872,133.02119237965854,5.0,0.018552641221322906,0.09108689367555235,-0.06985516978670644,5.8382085378384065
2.8000000000000003,29.119408407699073,34.14500313278784,133.0210160776851,5.0,-0.04433186486281754,0.10174577901069665,-0.06811349625258531,5.906893892158153
2.9000000000000004,29.20795686418919,34.14525199440929,133.02100649402564,5.0,0.007468065132514596,0.07935041346164882,-0.06635201665997933,5.975879931398719
3.0,28.597230150350235,34.145163524224394,133.0210028079891,6.04476856494438,-0.009498135398803086,0.07950660983186157,-0.06457068267143257,6.04476856494438
3.1,28.625224327056383,34.14502946302539,133.02100045563046,6.04476856494438,-0.0016206521996081531,0.07810021872301891,-0.06276952575590754,6.113141482637011
3.2,28.642600552546,34.1451894622221,133.02106903273113,6.04476856494438,-0.05003394452499754,0.08294143870904283,-0.060948657188785296,6.180560154776095
3.3000000000000003,28.905571856144455,34.14507828153979,133.02115226454453,6.04476856494438,0.049809155780152395,0.04340104923736859,-0.05910826805186549,6.246565832118714
3.4000000000000004,29.423119808693226,34.14521440736125,133.0210358458253,6.04476856494438,-0.018342955129499714,0.044145254456619536,-0.057248629233366176,6.310679545879555
3.5,28.69651014973521,34.145066824566705,133.02106065739406,6.04476856494438,0.05092948798656975,0.04110642395098102,-0.055370091427924,6.3724021077309105
3.6,28.878209687251264,34.145114391070805,133.02108749482434,6.04476856494438,-0.000723564905541537,0.03864807769503839,-0.053473085136594066,6.431214109802673
3.7,28.98402466840695,34.14509722180211,133.02105073075657,6.04476856494438,0.03314539030708066,0.03891685735024559,-0.05155812066685006,6.48657592468234
3.8000000000000003,29.390788703347614,34.14501649715185,133.0211802599904,6.04476856494438,0.01467549685076643,0.032680480945144336,-0.04962591063733221,6.538246193392969
3.9000000000000004,28.26377845250957,34.14509608196809,133.02107224587905,6.04476856494438,0.004127876084913294,0.016410611320983218,-0.04767787729652914,6.587569031349582
4.0,29.018808534423837,34.145062692042245,133.02095297948577,6.04476856494438,0.0601433709049655,0.010989949550461401,-0.04571502787435793,6.634695431875715
4.1000000000000005,28.770572821677128,34.14499395790999,133.02112509045583,6.04476856494438,-0.03089864886192952,0.010151806036963178,-0.04373825530329076,6.679545135111055
4.2,29.104161219559916,34.14499468816002,133.02106176769934,6.04476856494438,0.029700053303059457,-0.010783103425614891,-0.04174842849058,6.722050093085105
4.3,28.934604878840634,34.14511353563532,133.02114385172342,6.04476856494438,0.04184051062713352,0.0007791201581662435,-0.03974639231825808,6.762154469717191
4.4,28.4584938603066,34.14516357145351,133.0211124715348,6.04476856494438,0.024275139740674086,-0.0016133372745628996,-0.037732967643137515,6.7998146408164555
4.5,29.64315841641136,34.14505765346557,133.02108222550547,6.04476856494438,0.024467212745136364,-0.00833072827034034,-0.03570895129681103,6.834999194081859
4.6000000000000005,28.67836406850687,34.14504898371229,133.02108729892325,6.04476856494438,0.035435268706487305,-0.022301543129598495,-0.033675116085651366,6.867688929102181
4.7,29.086193691439792,34.145080206178896,133.02102152996537,6.04476856494438,0.014876725073242003,-0.025111143355962103,-0.031632210790811445,6.897876857356023
4.800000000000001,28.202214777331147,34.14507604085541,133.02105984631172,6.04476856494438,0.006114665514421313,-0.026059463594297207,-0.029580960168224257,6.925568202211801
4.9,28.450180943595107,34.144979836169576,133.02091487364098,6.04476856494438,0.06420332117501647,-0.017903343435868305,-0.027522064948602966,6.950780398927753
5.0,28.883454903552522,34.14505782107446,133.0210175287104,6.04476856494438,-0.012717737878376743,-0.004662854556825795,-0.025456201837440774,6.973543094651934
5.1000000000000005,29.540851498782256,34.145154231877676,133.02104643050197,6.04476856494438,0.012692414623038353,-0.016746369875407438,-0.023384023515011024,6.993898148422217
5.2,29.470480818036712,34.14484920948979,133.02100152549923,6.04476856494438,0.07192731345004372,-0.03273150353820682,-0.021306158636367194,7.011899631166298
5.300000000000001,29.410567425759304,34.14507994616729,133.0210570677702,6.04476856494438,0.010428382793720388,-0.026030741074544225,-0.019223211831342867,7.027613825701689
5.4,28.76248612458453,34.14502122993172,133.02108594696887,6.04476856494438,0.05595877880595168,-0.034069563102708166,-0.017135763704551783,7.041119226735718
5.5,28.836882080874002,34.14494545882127,133.02113834767826,6.04476856494438,-0.007893726430722652,-0.030810874314993884,-0.01504437083538767,7.052506540865537
5.6000000000000005,27.85378295822077,34.14504027487776,133.02100644951088,6.04476856494438,0.017602551602162765,-0.03453414233202355,-0.012949565778024454,7.0618786865781145
5.7,29.188454210939604,34.144997925408695,133.02101281654862,6.04476856494438,0.031604743838807015,-0.02341271768292613,-0.01085185706141624,7.069350794250237
5.800000000000001,28.92474571984039,34.14501952677166,133.0210716537407,6.04476856494438,-0.04034975470281493,-0.023456170226680742,-0.00875172918929712,7.0750502061485125
5.9,29.182521871405232,34.14501783693285,133.02093256040519,6.04476856494438,-0.03385743604533995,-0.02423106883452283,-0.0066496426401813635,7.0791164764293635
6.0,28.581409543081676,34.144917529204584,133.0209813734641,7.081701371139036,-0.03933892600468611,-0.027509281847533863,-0.004546033867363353,7.081701371139036
6.1000000000000005,29.02385124091551,34.144866687747395,133.02101963891718,7.081701371139036,-0.04242731792314935,-0.041342930538322574,-0.004271452460684626,7.082968868213591
6.2,28.934472361895256,34.14498669227919,133.02103711382225,7.081701371139036,-0.06134239202248967,-0.03269977974024073,-0.004126635683033597,7.083095157478911
6.300000000000001,29.151521646608117,34.144990835477124,133.02096961427023,7.081701371139036,-0.02016782513577389,-0.031228534182739572,-0.003981794349098432,7.082268640650697
6.4,29.339941132492314,34.14491457417555,133.02101124540118,7.081701371139036,0.019281601856275542,-0.04350248531707281,-0.0038369518690645962,7.080689931334467
6.5,29.703166017001543,34.14486748364515,133.02099572373177,7.081701371139036,0.0014209214413551357,-0.030477504731585163,-0.003692130000610247,7.07857185502556
6.6000000000000005,29.15876861870949,34.144911990492226,133.0208615950071,7.081701371139036,-0.06544543515892473,-0.04206403861894391,-0.0035473488489062327,7.076139449109132
6.7,29.24272404838235,34.14489555655268,133.0209065656782,7.081701371139036,0.07148131321482805,-0.03646948636158421,-0.0034026268666160894,7.073629962860159
6.800000000000001,29.40772147920002,34.14495224261369,133.02095759437285,7.081701371139036,0.04631450303257414,-0.03190945742321859,-0.003257980853896044,7.071292857443435
6.9,29.3141775123176,34.14489737780459,133.02087655407905,7.081701371139036,0.06937912128718897,-0.02595315741666299,-0.0031134259583950187,7.069389805913574
7.0,28.78660674922436,34.14491531977582,133.02100338980526,7.081701371139036,-0.008740152399793977,-0.03697837066396006,-0.002968969968207149,7.068128711727557
7.1000000000000005,27.735920210280405,34.144909558688745,133.02097103590668,7.081701371139036,0.04887020614501261,-0.02988351293668244,-0.0028245557266821566,7.0669382034062345
7.2,28.791556011155976,34.14482036296013,133.02103315015847,7.081701371139036,0.06981443049586732,-0.04166391041337182,-0.002680167391093455,7.06561929399491
7.300000000000001,29.35081411344261,34.14501632810638,133.02095145238667,7.081701371139036,0.023086516396053008,-0.02351870058533126,-0.0025358075086423758,7.064173318778519
7.4,28.214634663189287,34.14479525854635,133.02099158329278,7.081701371139036,-0.041008875905307225,-0.01977584009265334,-0.0023914786048564096,7.062601604011104
7.5,29.18761390726787,34.14493893158244,133.02092485746368,7.081701371139036,-0.016466911767226547,-0.01912933649679279,-0.0022471831835892135,7.060905466915815
7.6000000000000005,29.01851790215398,34.14501194526334,133.02085561648562,7.081701371139036,0.006262631959040779,-0.024088667491270307,-0.002102923727020606,7.059086215684914
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563.1,21.51187976360403,34.128012118012286,133.0160681217155,5.107637001595482,-0.007709072922448356,0.2053841553565853,0.026150170341512416,4.8665329638626424
563.2,20.248873308471833,34.12795520315843,133.01603963885879,5.107637001595482,0.02135825683297257,0.22163191619690042,0.025655437810504972,4.861565746889014
563.3000000000001,20.32455760323077,34.12786050167516,133.0161689076738,5.107637001595482,-0.03787484592856381,0.22581808688683164,0.02516117535884217,4.857148601719376
563.4,20.36958509074962,34.12787698807493,133.01621193980407,5.107637001595482,0.04656571589673524,0.22160915197874198,0.024667336328719702,4.853266362118353
563.5,19.552595501105912,34.12786409580283,133.01613591037335,5.107637001595482,-0.021783005184211068,0.2180293489568635,0.024173932125115462,4.849809022614196
563.6,20.99090311082839,34.12786955500207,133.01621589282226,5.107637001595482,0.020918213779297916,0.22182835146527632,0.02368090723887681,4.8467731054202305
563.7,19.949816451990472,34.12795623241769,133.01622582101425,5.107637001595482,0.02774434800887646,0.2324093910996784,0.023188191145210202,4.844180174493962
563.8000000000001,20.07053482756946,34.127972626336934,133.0161391743239,5.107637001595482,0.027100165798307086,0.2191750847598416,0.02269571545156547,4.842049318510128
563.9,20.473153927261652,34.12795813470976,133.01607732546478,5.107637001595482,-0.017780119125024724,0.20807377299112442,0.0222034138976368,4.840397150860696
564.0,19.711635988272665,34.12788456502155,133.0160800238295,4.839237809654857,-0.03864561943954069,0.21780195723324475,0.021711222355360847,4.839237809654857
564.1,20.34326578138958,34.127867190298716,133.01618017075447,4.839237809654857,0.010381650667609104,0.22935293762505563,0.02121907882891952,4.838582957719035
564.2,21.761229399189972,34.12793277723207,133.01609524745683,4.839237809654857,0.006000098748413849,0.23903014891556762,0.020726923454738137,4.838441782596884
564.3000000000001,20.40372233155151,34.127871529766175,133.01614494183193,4.839237809654857,-0.027096812898609268,0.21636897373433883,0.02023469850148634,4.838820996549282
564.4,20.356427950208694,34.12792181356898,133.01613743928874,4.839237809654857,0.022944890867184372,0.23198236642088743,0.019742348370077184,4.83972483655434
564.5,20.98486021283511,34.12788274902752,133.01615876750182,4.839237809654857,-0.016863249241742248,0.22859784645875425,0.01924981959366758,4.8411550643073955
564.6,20.81367666399898,34.12789767483274,133.01613087306484,4.839237809654857,0.0019260593403404823,0.2211943573021647,0.018757060837658775,4.843110966221016
564.7,20.326308546054626,34.12793215933714,133.01612653858686,4.839237809654857,-0.008024833475285958,0.2191622750024186,0.01826402289969542,4.845589353424997
564.8000000000001,20.953550486794708,34.12804144579297,133.01619266043636,4.839237809654857,-0.09131447212284007,0.2231296684512879,0.0177706587096665,4.848584561766363
564.9,20.017748481933765,34.127872316326545,133.01608850926323,4.839237809654857,-0.0004847511195540076,0.23387662165734258,0.017276923329705318,4.852088451809363
565.0,21.243818429012176,34.1279142671086,133.01618803859301,4.839237809654857,0.05395510187058862,0.21634016545418416,0.016782773954186737,4.856090408835486
565.1,20.823861815925433,34.1278914377196,133.01624605071763,4.839237809654857,-0.006462770683004326,0.23148272806607506,0.016288169909732732,4.860577342843441
565.2,20.70432815458394,34.12794442775118,133.0161484958434,4.839237809654857,0.025539112131128618,0.22564879206069874,0.01579307265520729,4.865533688549166
565.3000000000001,20.688260700919532,34.127780455841496,133.01615384145327,4.839237809654857,-0.03313405384146894,0.19850228060596656,0.015297445781718254,4.870941405385829
565.4,21.482953089193984,34.12780756874024,133.0161494797573,4.839237809654857,0.022552527836659522,0.21738846627944328,0.014801255012619202,4.876779977503821
565.5,21.016876313597084,34.1278246798085,133.01620385785708,4.839237809654857,-0.0019182041426083363,0.20792802386561682,0.01430446820350433,4.8830264137707795
565.6,20.409687304771108,34.1279037123407,133.01619504212027,4.839237809654857,0.035179464473501953,0.21375028507253857,0.013807055342214481,4.889655247771555
565.7,20.489810900612525,34.127678005766384,133.01619123243964,4.839237809654857,0.07714945820059517,0.21384154089016016,0.013308988548833434,4.896638537808228
565.8000000000001,20.861415800905434,34.12782710069372,133.01623562694567,4.839237809654857,0.06353104213935983,0.21193125088161635,0.012810242075689308,4.903945866900114
565.9,20.635435038310362,34.127926106662954,133.01624308594327,4.839237809654857,-0.03513423171603407,0.20951277311839672,0.01231079230735362,4.911544342783741
566.0,21.15107467539707,34.12779669612108,133.0161368476608,4.839237809654857,0.048918476201858005,0.19591246906614138,0.011810617760641282,4.919398597912898
566.1,20.09260804374147,34.127778568822,133.01619175765197,4.839237809654857,0.012632097474427863,0.20051579006837172,0.011309699084612483,4.9274707894585745
566.2,20.225406347603258,34.12778535311875,133.01619942575275,4.839237809654857,0.0030199570829680866,0.20973538853257884,0.01080801906056987,4.935720599308998
566.3000000000001,20.85100525000072,34.12791255663527,133.01611020018413,4.839237809654857,-0.004224277935806914,0.2122826533675527,0.010874669310983005,4.944105234069624
566.4,20.512186197362,34.127926006954375,133.01621260156395,4.839237809654857,0.013077358483824148,0.18922092203478005,0.011032151172030115,4.952579425063127
566.5,19.732631340870583,34.12784247545596,133.01605353367538,4.839237809654857,-0.02612250539979798,0.21727589266892758,0.01118988344480272,4.96109542832944
566.6,20.162918223471788,34.12791762354606,133.01633103116242,4.839237809654857,-0.03861035413483333,0.19285624486747088,0.011347868848594561,4.969603024625695
566.7,21.098930760344565,34.12786227082531,133.01615875483452,4.839237809654857,0.038397041082491486,0.18920957010552297,0.011506109435451915,4.978049519426262
566.8000000000001,21.0668679330649,34.12779725419289,133.0161257017092,4.839237809654857,0.017755092382590765,0.19323989291405325,0.011664606590173019,4.986379742922743
566.9,20.626789295588065,34.12776980201253,133.01621761728677,4.839237809654857,0.044666485759127864,0.19802247272307327,0.011823361030308073,4.994536050023956
567.0,20.331060803535973,34.12781348992391,133.01616721389615,5.002458320355975,-0.014254853882614753,0.2076480657026581,0.011982372806159668,5.002458320355975
567.1,20.535968630504307,34.12788105891354,133.01618584577713,5.002458320355975,-0.002276953063293095,0.1804241041338951,0.012141641300782503,5.010083958262079
567.2,21.40252552242946,34.12785764614486,133.01620247048038,5.002458320355975,-0.02640679044653087,0.17288287830509338,0.012301165229983087,5.017347892802782
567.3000000000001,20.517904576881108,34.127840287321895,133.01631021527803,5.002458320355975,-0.02563206512689912,0.21117521232344716,0.012460942642320186,5.024182577755827
567.4,20.47900410228061,34.12779825535534,133.01614657304606,5.002458320355975,0.012425608752110953,0.1973985297438497,0.012620970919104371,5.030517991616178
567.5,19.940252997102455,34.12784894859312,133.01622597570562,5.002458320355975,-0.015759428212628903,0.1831052366554178,0.012781286665884474,5.036810461378845
567.6,20.700146708688315,34.1278048726402,133.01620719163517,5.002458320355975,0.03606136367885277,0.18838418328019813,0.012941932623764538,5.04373041862512
567.7,20.173902084397522,34.12785118080758,133.01629600343503,5.002458320355975,0.012016762286947166,0.19353832750050068,0.01310287950538725,5.051085730427904
567.8000000000001,20.634732742977732,34.127712742471665,133.01616843656592,5.002458320355975,-0.027880247849657796,0.1933870765844221,0.013264097851190076,5.058686571197163
567.9,20.36256575437268,34.1277843872438,133.01618243908092,5.002458320355975,0.006645685106332774,0.18989648666814585,0.013425558824889562,5.066355457087318
568.0,19.901861289083932,34.12763805878506,133.01616044057377,5.002458320355975,-0.04114102984457453,0.173665592682259,0.013587234213482784,5.073927245997274
568.1,20.57085444189033,34.127812162344256,133.016279025056,5.002458320355975,0.05328135471140608,0.17116673984400854,0.013749096427245606,5.081249137570371
568.2,20.724066038633193,34.1277616483866,133.0161859640814,5.002458320355975,-0.0002921755255161204,0.20273892674359878,0.01391111849973399,5.088180673194415
568.3000000000001,21.260104830550237,34.1277404571716,133.01628774840893,5.002458320355975,-0.06551039774591773,0.17602792173190557,0.014073274087783845,5.094593736001675
568.4,20.329876543956384,34.12780430985614,133.01620993670946,5.002458320355975,0.016484301055867887,0.18425447291364816,0.01423553747151016,5.100372550868872
568.5,20.266541264794842,34.12782821681267,133.01624301452986,5.002458320355975,-0.010673781250535806,0.18572081511997607,0.014397883554308306,5.105413684417208
568.6,20.461367642567676,34.127734377621415,133.016272

xtra_kalman.m