Square-root UKF for better numerical stability

[fabianhirmann]

In our robotics group we noticed that sometimes the UKF seems to be unstable without any clearly noticeable reason. Unfortunately we don't have (yet) any rosbag at hand when the situation occurred.
However, I just remembered that there exists also a square-root form of the UKF which should have better numerical stability [1] and as far as I noticed in the source code, this variant is not used here.

What do you think about that? Would the square-root UKF be an option to increase general numerical stability or do you think it might not make much difference? Or is this (or ideas from it) already implemented and I didn't see it?

If this feature already exists, feel free to close this feature request.

Thanks,
Fabian

[ayrton04]

It would be hugely helpful if you could provide more details. What version are you using? How is the instability manifesting? What is your configuration? And yes, of course, a bag file (and maybe sample input messages) helps a lot. While it may seem like the instability is without reason, there is usually another cause.

[ayrton04]

Oh, I should also note that this package is no longer adding new features. I would encourage users to switch to fuse.

[fabianhirmann]

Thanks for your quick reply! It is interesting and good to hear that you recommend switching to fuse because we are currently actually in the process of that.

In any case, I spent now some time finding a situation where a strange behavior occurs. Very quickly summarized the pose there suddenly jumps from y = ~0 m to y = ~ -9m and the other data seems fine. We then "resolved" the issue by switching to the EKF which showed no problems like that afterwards when testing it directly at the robot.

Here's the configuration (with the UKF). It is important to note that /initial_current_pose just gets published once at restart and the NDT at /ndt_pose_with_covariance gets feed back the UKF pose and uses this as current pose estimation:
ukf.launch

<?xml version="1.0"?>
<launch>
  <node name="ukf" pkg="robot_localization" type="ukf_localization_node" clear_params="true" respawn="true">

    <param name="predict_to_current_time" value="true"/>
    <param name="dynamic_process_noise_covariance" value="true"/>
    <param name="smooth_lagged_data" value="true"/>
    <param name="history_length" value="2.0"/>

    <param name="frequency" value="50"/>
    <param name="sensor_timeout" value="0.2"/>
    <param name="transform_time_offset" value="0.07"/> 
    <param name="publish_tf" value="true"/>

    <param name="two_d_mode" value="true"/>

    <param name="map_frame" value="map"/>
    <param name="base_link_frame" value="base_link"/>
    <param name="world_frame" value="map"/>

    <param name="use_control" value="true"/>
    <rosparam param="control_config">[true,  false, false,
                                     false, false, true]</rosparam>

    <param name="reset_on_time_jump" value="true"/>

    <param name="print_diagnostics" value="true"/>

    <param name="pose0" value="/initial_current_pose"/>
    <rosparam param="pose0_config">[true,  true,  false,
                                    false, false, true, 
                                    false, false, false, 
                                    false, false, false,
                                    false, false, false]</rosparam>
    <param name="pose0_differential" value="false"/>
    <param name="pose0_relative" value="false"/>

    <param name="pose1" value="/ndt_pose_with_covariance"/>
    <rosparam param="pose1_config">[true,  true,  true,
                                    true,  true,  true, 
                                    false, false, false, 
                                    false, false, false,
                                    false, false, false]</rosparam>
    <param name="pose1_differential" value="false"/>
    <param name="pose1_relative" value="false"/>

    <param name="imu0" value="/imu/data"/>
    <rosparam param="imu0_config">[false, false, false,
                                   false, false, false,
                                   false, false, false,
                                   true, true, true,
                                   true, true, true]</rosparam>
    <param name="imu0_differential" value="true"/>
    <param name="imu0_remove_gravitational_acceleration" value="true"/>
<!-- if can is not working this is bullshit for localization -->
    <param name="odom0" value="/odom"/>
    <rosparam param="odom0_config">[false, false,  false, 
                                    false, false, false, 
                                    true, true,  true, 
                                    true, true, true,
                                    false, false, false]</rosparam>
    <param name="odom0_differential" value="false"/>
    <param name="odom0_relative" value="false"/>

    <remap from="/odometry/filtered" to="/ukf_pose"/>
    <remap from="set_pose" to="~/set_pose"/>

  </node>

</launch>

Excerpt from /ukf_pose (=odometry/filtered). Note the switch of pose at seq=15523:

---
header: 
  seq: 15521
  stamp: 
    secs: 1668179164
    nsecs:  52270412
  frame_id: "map"
child_frame_id: "base_link"
pose: 
  pose: 
    position: 
      x: 2.51339685402
      y: -0.217812746379
      z: -3.36292408851e-16
    orientation: 
      x: 2.9206618638e-16
      y: 3.99149955666e-16
      z: 0.00487644571953
      w: 0.999988110068
  covariance: [0.005806096256140677, 7.410138711661708e-05, -4.920212240563025e-24, -7.672892276544646e-27, -2.4768909011022214e-27, -7.153843514925996e-22, 7.410138711661708e-05, 0.005806096256456419, 5.809839871234253e-24, -2.4063369087586272e-26, 1.7110977177870695e-26, 3.660265857800534e-22, -4.9137498920274544e-24, 5.8033775226986826e-24, 0.0007093626684977179, -4.656985874228941e-30, -2.6205195880960306e-30, 3.292310987939893e-27, 5.251804796007005e-27, -2.4063369087586272e-26, -4.656985874228941e-30, 0.0003552321967841364, 5.886545901792446e-30, 3.850358557956063e-24, -2.5778650968764713e-27, 1.7110977177870695e-26, -2.6074232644741974e-30, 5.892323691625249e-30, 0.0003552321967841364, -4.639770089003693e-24, -7.153843514910589e-22, 3.6602658580470533e-22, 3.494308683483048e-27, 3.8503554027050335e-24, -4.6397732448325e-24, 0.004156899536375154]
twist: 
  twist: 
    linear: 
      x: -0.684915790916
      y: 0.00289079901873
      z: -7.44196371194e-16
    angular: 
      x: 6.90439024977e-16
      y: -4.47657816164e-16
      z: -0.0166656494609
  covariance: [0.0006289534966632125, -8.338966324022164e-21, 2.475887282690459e-25, 8.463239681352977e-28, 1.8971541765345482e-25, 2.8877971455474756e-21, -8.338979248718464e-21, 0.0006289534966632153, -2.5527538892951942e-27, 1.619316755125698e-28, -1.287450287098737e-27, -2.6139110912958914e-23, 2.607153737319235e-25, -2.6537280851634837e-27, 0.0010074330670943453, -1.850481638815866e-30, 1.155172780643464e-30, 1.1662519622787439e-26, 8.463239681382364e-28, 1.1144457757842505e-28, -1.8011778322395527e-30, 0.00025268724277499344, -8.048620147266041e-31, -1.2396627797445045e-27, 1.961777661886492e-25, -1.3379373850328818e-27, 1.155172780643464e-30, -8.050546077210428e-31, 0.00025268724277499344, 7.011732643585256e-27, 2.8877971455474756e-21, -2.6139009938811194e-23, 1.1662519622787439e-26, -1.239662972337499e-27, 7.011757295488544e-27, 0.0005031605693297958]
---
header: 
  seq: 15522
  stamp: 
    secs: 1668179164
    nsecs:  72133780
  frame_id: "map"
child_frame_id: "base_link"
pose: 
  pose: 
    position: 
      x: 2.49977890051
      y: -0.217906915606
      z: 4.00316982356e-16
    orientation: 
      x: 1.29431200022e-16
      y: -3.39787061071e-17
      z: 0.00489450470929
      w: 0.99998802184
  covariance: [0.006277663974161937, 7.410138711439408e-05, 2.3469473021306957e-24, -2.234368376095646e-25, -2.569559407165383e-25, 7.034192659960183e-22, 7.410138711439408e-05, 0.006277663974478703, 8.449500153652612e-24, 7.3464894853186e-27, 1.5339587789947903e-26, 1.270433719015327e-22, 2.340459710046158e-24, 8.44788140799361e-24, 7.103179890176627e-05, 1.6261501742127177e-30, -1.0614863632029536e-30, 4.01199855623784e-29, -2.299118079196892e-25, 7.346489485312722e-27, 1.6261501749474016e-30, 3.592395267821782e-05, -5.077578746733285e-31, -1.4199655907468448e-29, -2.569685624910336e-25, 1.5339587789944965e-26, -1.0607174954906257e-30, -5.077586269897116e-31, 3.592395267821782e-05, -2.455149543676753e-29, 7.034192652048463e-22, 1.2704337269000841e-22, 4.0095357733214547e-29, -1.417500400399662e-29, -1.1905069049943185e-29, 0.004722463712977792]
twist: 
  twist: 
    linear: 
      x: -0.68622585437
      y: 0.000940167766789
      z: 3.56323043987e-16
    angular: 
      x: 3.01809193304e-17
      y: -1.28744727943e-16
      z: -0.00147073552297
  covariance: [0.001125570519004979, -1.7888102071729232e-17, 2.0595580513510176e-26, 1.2006193024151698e-26, -2.902079219080555e-26, -2.14378200373948e-22, -1.7888101968331655e-17, 0.0011255705190042526, -2.3588605069580204e-27, 3.455354458708988e-28, 6.253111016440904e-28, 3.6446267360621416e-25, 2.0592425069889292e-26, -2.3588605069580204e-27, 0.00010020977235367613, -2.2424745863405067e-31, -3.618160327085233e-31, -9.717780276191339e-29, 1.0390605891763699e-26, 3.4238000225001473e-28, -2.211659707230311e-31, 2.566373846234137e-05, -5.756651733725862e-32, -1.2000576348145844e-28, -3.063637932469818e-26, 6.284665467696072e-28, -3.602752887530135e-31, -5.602577338174883e-32, 2.566373846234137e-05, 1.7993742433501154e-28, -2.1437779647639415e-22, 3.6446268593178964e-25, -9.717780276191339e-29, -1.326275379646273e-28, 1.7993742433501154e-28, 4.9583527701333e-05]
---
header: 
  seq: 15523
  stamp: 
    secs: 1668179164
    nsecs:  92131853
  frame_id: "map"
child_frame_id: "base_link"
pose: 
  pose: 
    position: 
      x: 0.523457287989
      y: -9.33399802522
      z: 4.17255206081e-16
    orientation: 
      x: -2.62444141014e-16
      y: -8.03243915063e-17
      z: 0.0053265916456
      w: 0.99998581361
  covariance: [0.0022313208500287125, 0.0029051277447315034, 6.1076608953650574e-24, 3.4164877799525615e-25, -2.9376448233823844e-26, 1.695559513306465e-21, 0.0029051277447315034, 0.015002819009560055, -1.2657014477894222e-23, 6.534816499544699e-24, 2.5461247229680536e-24, 3.241275235328249e-20, 6.158551890082675e-24, -1.2669939174965363e-23, 0.0006069628850259633, -2.322346512252891e-30, -1.5550187827479823e-30, -3.230484014493196e-27, 3.416487779892376e-25, 6.534816499562755e-24, -2.296159883540301e-30, 0.0003037916307352352, 1.2824343599663826e-30, -4.890673935239072e-24, -2.978034501748508e-26, 2.5396623744328592e-24, -1.6039377794936103e-30, 1.2816639879886726e-30, 0.00030379163073523523, 5.928538364414603e-24, 1.6956621030894673e-21, 3.24160610757327e-20, -4.025655806955976e-27, -4.8902700369148786e-24, 5.9281407785183714e-24, 0.0019218115747884025]
twist: 
  twist: 
    linear: 
      x: -0.673204279723
      y: -0.00390430047648
      z: -1.55778168143e-15
    angular: 
      x: 8.34753577625e-16
      y: 1.42175936779e-15
      z: -0.0122991511755
  covariance: [0.0005619475157579163, -4.6541897230941434e-20, 7.64172714331215e-25, -4.1119202120569907e-25, -7.01988294219607e-25, -2.0665946512010327e-21, -4.6541897230941434e-20, 0.0005619475157583011, -9.302247794366171e-27, 5.7418944830601904e-27, 8.99110142947504e-27, 2.6047386868768885e-23, 7.124739260466508e-25, -8.494454227419855e-27, 0.0008998844538573786, -4.172334631520508e-30, -8.076579814782312e-30, -2.304736020693708e-26, -4.1119202120569907e-25, 5.7418975645481014e-27, -5.1584107630467725e-30, 0.00022545540039096965, 4.9291594469276656e-30, 1.359142875026069e-26, -7.278376883618891e-25, 8.99110142947504e-27, -7.87936458847706e-30, 4.7319442206224126e-30, 0.00022545540039096965, 1.654264660665149e-26, -2.0665946512010327e-21, 2.604738686879296e-23, -2.4650325566346177e-26, 1.3591231535034384e-26, 1.654225217619888e-26, 0.00044954499024098466]
---
header: 
  seq: 15524
  stamp: 
    secs: 1668179164
    nsecs: 112134695
  frame_id: "map"
child_frame_id: "base_link"
pose: 
  pose: 
    position: 
      x: 0.510019453191
      y: -9.33427325793
      z: 4.21049913685e-16
    orientation: 
      x: -1.81288846127e-15
      y: 1.02409095683e-15
      z: 0.00520358436176
      w: 0.999986461263
  covariance: [0.0026816746193840946, 0.002905127744751815, 5.240284348703036e-23, -4.636555493191139e-25, 4.63856279425496e-25, -2.0900673033498915e-22, 0.002905127744751815, 0.015453172778934786, -1.6156689229912855e-22, 1.2693395701300101e-23, -1.799123019923937e-24, 1.444636951146249e-21, 5.2402029382576174e-23, -1.6156689229912855e-22, 0.0011475246151595726, -5.32327036628632e-31, 2.909694959980236e-30, 9.710877743270655e-28, -4.640594459099941e-25, 1.2690164527032316e-23, -5.325196296230707e-31, 0.0005739365549637336, -1.9752837713614e-29, -3.569981241044416e-23, 4.380068852832139e-25, -1.7991230199299555e-24, 2.1456785510418195e-30, -1.9728185810509513e-29, 0.0005739365549637336, 1.1892130247340382e-22, -2.0900673033479655e-22, 1.4446304887992542e-21, 1.3749352539936473e-27, -3.56998124104441e-23, 1.1892130247340382e-22, 0.0024620997810012066]
twist: 
  twist: 
    linear: 
      x: -0.670605207437
      y: -0.00930010809458
      z: -4.19803081186e-15
    angular: 
      x: 2.1839122056e-16
      y: 2.20837810489e-16
      z: -0.0122991511814
  covariance: [0.0010621548430465896, -1.5747271816920435e-18, -3.2134028093124454e-24, -6.9271602694673625e-25, -1.0575143163780118e-24, -1.7517934000234877e-21, -1.5747272850896185e-18, 0.0010621548430469526, 3.9500600552695515e-24, 1.4435517944523097e-26, 2.442748673698768e-26, 8.496409108260945e-23, -3.2651015975970096e-24, 3.9500600552695515e-24, 0.0017002033818597996, 1.0255191767873153e-29, 7.173703856853576e-30, 5.255706894944469e-26, -6.668666297229662e-25, 1.3627727459064692e-26, 1.0255191767873153e-29, 0.00042548381988559853, 9.382355906671415e-30, 1.097638883859007e-26, -1.083363704357318e-24, 2.4427492899963503e-26, 7.173703856853576e-30, 9.579571132976668e-30, 0.0004254838198855986, 2.189107016903624e-26, -1.7517934000296507e-21, 8.496414156980368e-23, 5.250658185151055e-26, 1.097638883859007e-26, 2.1891070169224318e-26, 0.0008496018292302422]
---
header: 
  seq: 15525
  stamp: 
    secs: 1668179164
    nsecs: 132174730
  frame_id: "map"
child_frame_id: "base_link"
pose: 
  pose: 
    position: 
      x: 0.496502427268
      y: -9.33445328561
      z: 7.2506020285e-18
    orientation: 
      x: -1.15712965488e-16
      y: -1.07066706907e-16
      z: 0.00520725195995
      w: 0.999986442172
  covariance: [0.0031370906678349943, 0.0029051277447155253, 5.389597199551624e-24, 2.2531142459642485e-27, -3.7028625537542297e-26, 1.7844204710599855e-22, 0.0029051277447155253, 0.015908588827376325, -5.1142635035496175e-23, -8.316855628015845e-25, -1.143611319017067e-24, 8.495131894732004e-21, 5.3903923713440864e-24, -5.111759343492084e-23, 0.0005260842094079927, 5.950973064879654e-32, 1.004643299896373e-31, -5.666917898123223e-28, 2.2404924715042222e-27, -8.316855628015845e-25, 6.57216070358299e-32, 0.00026350328319612026, 1.305807629370104e-31, -8.252138373136527e-28, -3.622083197059598e-26, -1.1177619248762895e-24, 1.0036878580880246e-31, 1.273548302805205e-31, 0.00026350328319612026, -1.2610195816191032e-27, 1.7846789649994824e-22, 8.493477508263349e-21, -5.666979527881444e-28, -7.74726739379508e-28, -1.2854742696809546e-27, 0.003007248189521408]
twist: 
  twist: 
    linear: 
      x: -0.673448906229
      y: -0.00417529931829
      z: -2.35055030995e-16
    angular: 
      x: -9.53420401768e-17
      y: 9.08896706633e-17
      z: -0.00892513192139
  covariance: [0.0015630820549466843, -2.017709628459276e-16, -3.1604923306774617e-26, 4.7722350477987014e-26, -8.389131383074156e-26, 2.4749197987901994e-21, -2.0177096615465006e-16, 0.0015630820549476163, 2.6482060588269366e-27, 4.48355804425976e-29, -1.1914316789163701e-28, 3.402839768370254e-24, -3.1604923306774617e-26, 2.6482060588269366e-27, 0.0007726410255542452, 5.366122307548936e-32, -2.3905605434706565e-32, 2.074704180731261e-28, 5.41846990255946e-26, 5.114646768431978e-29, 5.250566510885702e-32, 0.0001938445586181354, -9.053617407964608e-33, 6.530114187760075e-29, -8.389131385481569e-26, -1.1914316789163701e-28, -2.195560136601449e-32, -8.283245430232135e-33, 0.0001938445586181354, -6.766940430445533e-28, 2.4749181832092285e-21, 3.4044553555041466e-24, 1.5698332013898135e-28, 1.4814043944190682e-29, -6.766940911928019e-28, 0.0003856011361552342]
---
header: 
  seq: 15526
  stamp: 
    secs: 1668179164
    nsecs: 152184963
  frame_id: "map"
child_frame_id: "base_link"
pose: 
  pose: 
    position: 
      x: 0.482324364217
      y: -9.33444041474
      z: -2.20841140514e-15
    orientation: 
      x: 4.61045734583e-16
      y: -1.3948233309e-16
      z: 0.00500666265469
      w: 0.999987466586
  covariance: [0.0036129268994044314, 0.0029051277447221724, 1.586725237725492e-23, -3.6728220857661395e-26, -2.8192772242086126e-26, 4.892053859441254e-22, 0.0029051277447221732, 0.016384425058996958, 8.334157691478946e-25, -1.0725738930446765e-24, 6.636687057430474e-25, 4.674899653074446e-21, 1.5866848480471447e-23, 7.300181925787661e-25, 0.0010981683553175372, -6.0532941117063016e-30, 5.565889391030502e-30, 4.5202124299616587e-26, -3.04678207146738e-26, -1.0208751047601122e-24, -5.26443320648529e-30, 0.0005493574490545619, -1.482946463552752e-30, -1.2475360828515881e-23, -3.4655120777468575e-26, 6.636687057430474e-25, 5.57821534267458e-30, -1.4891094393719212e-30, 0.0005493574490545619, 7.925769108607216e-25, 4.892051839957336e-22, 4.674899653462713e-21, 4.6868592961895974e-26, -1.2475335584966867e-23, 7.941924995353582e-25, 0.0035795846214019384]
twist: 
  twist: 
    linear: 
      x: -0.687211928896
      y: 0.00117929434732
      z: -1.65839564303e-15
    angular: 
      x: -1.16670141396e-16
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header: 
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header: 
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header: 
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header: 
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---
header: 
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twist: 
  twist: 
    linear: 
      x: -0.693107342042
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      x: 1.18530584449e-16
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---

Excerpt from /odom:

---
header: 
  seq: 12421
  stamp: 
    secs: 1668179164
    nsecs:  27654299
  frame_id: "odom"
child_frame_id: "base_link"
pose: 
  pose: 
    position: 
      x: 2.86502911409
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twist: 
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---
header: 
  seq: 12422
  stamp: 
    secs: 1668179164
    nsecs:  52652068
  frame_id: "odom"
child_frame_id: "base_link"
pose: 
  pose: 
    position: 
      x: 2.848275218
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twist: 
  twist: 
    linear: 
      x: -0.675093216896
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---
header: 
  seq: 12423
  stamp: 
    secs: 1668179164
    nsecs:  77658289
  frame_id: "odom"
child_frame_id: "base_link"
pose: 
  pose: 
    position: 
      x: 2.83151649312
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    orientation: 
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twist: 
  twist: 
    linear: 
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    angular: 
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---
header: 
  seq: 12424
  stamp: 
    secs: 1668179164
    nsecs: 102669491
  frame_id: "odom"
child_frame_id: "base_link"
pose: 
  pose: 
    position: 
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twist: 
  twist: 
    linear: 
      x: -0.68061909318
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---
header: 
  seq: 12425
  stamp: 
    secs: 1668179164
    nsecs: 127678690
  frame_id: "odom"
child_frame_id: "base_link"
pose: 
  pose: 
    position: 
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twist: 
  twist: 
    linear: 
      x: -0.686366370916
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---
header: 
  seq: 12426
  stamp: 
    secs: 1668179164
    nsecs: 152717707
  frame_id: "odom"
child_frame_id: "base_link"
pose: 
  pose: 
    position: 
      x: 2.78045916334
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    orientation: 
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twist: 
  twist: 
    linear: 
      x: -0.688804016113
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    angular: 
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---
header: 
  seq: 12427
  stamp: 
    secs: 1668179164
    nsecs: 177785789
  frame_id: "odom"
child_frame_id: "base_link"
pose: 
  pose: 
    position: 
      x: 2.76317974081
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    orientation: 
      x: 0.0
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twist: 
  twist: 
    linear: 
      x: -0.694472379684
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    angular: 
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---
header: 
  seq: 12428
  stamp: 
    secs: 1668179164
    nsecs: 202690660
  frame_id: "odom"
child_frame_id: "base_link"
pose: 
  pose: 
    position: 
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    orientation: 
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twist: 
  twist: 
    linear: 
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    angular: 
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---
header: 
  seq: 12429
  stamp: 
    secs: 1668179164
    nsecs: 227699352
  frame_id: "odom"
child_frame_id: "base_link"
pose: 
  pose: 
    position: 
      x: 2.72887280301
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    orientation: 
      x: 0.0
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  covariance: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
twist: 
  twist: 
    linear: 
      x: -0.688087749481
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    angular: 
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  covariance: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
---
header: 
  seq: 12430
  stamp: 
    secs: 1668179164
    nsecs: 252675604
  frame_id: "odom"
child_frame_id: "base_link"
pose: 
  pose: 
    position: 
      x: 2.71202447333
      y: 0.446303588003
      z: 0.0
    orientation: 
      x: 0.0
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      z: -0.0615773688555
      w: 0.998102313215
  covariance: [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
twist: 
  twist: 
    linear: 
      x: -0.679718207121
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    angular: 
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---

Excerpt from /ndt_pose_with_covariance:

---
header: 
  seq: 2376
  stamp: 
    secs: 1668179163
    nsecs: 925950000
  frame_id: "map"
pose: 
  pose: 
    position: 
      x: 2.59750509262
      y: -0.219114094973
      z: 0.0
    orientation: 
      x: 0.0
      y: 0.0
      z: 0.00530391058631
      w: 0.999985934167
  covariance: [0.002, 4.091662975931129e-05, 0.0, 0.0, 0.0, 0.0, 4.09166297592987e-05, 0.002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.01, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.01, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.01, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
---
header: 
  seq: 2377
  stamp: 
    secs: 1668179164
    nsecs:  19899000
  frame_id: "map"
pose: 
  pose: 
    position: 
      x: 2.54609394073
      y: -0.222047418356
      z: 0.0
    orientation: 
      x: 0.0
      y: 0.0
      z: 0.00547032416823
      w: 0.999985037665
  covariance: [0.003911485769314464, 0.006595565954900154, 0.0, 0.0, 0.0, 0.0, 0.006595565954934102, 0.008746897099994409, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.01, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.01, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.01, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
---
header: 
  seq: 2378
  stamp: 
    secs: 1668179164
    nsecs: 227426000
  frame_id: "map"
pose: 
  pose: 
    position: 
      x: 0.282901406288
      y: -9.90779304504
      z: 0.0
    orientation: 
      x: 0.0
      y: 0.0
      z: 0.00486808678127
      w: 0.999988150795
  covariance: [0.002, 8.120300276689795e-05, 0.0, 0.0, 0.0, 0.0, 8.120300276687302e-05, 0.002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.01, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.01, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.01, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
---

From the rosbags that I found unfortunately there was no messages on topics /imu/data and /initial_current_pose recorded.

We are using ROS melodic and robot_localization was installed using rosdep (the robot is currently not here so I can't tell which exact version was used).

If there is anything else I can provide, please let me know. Already now thanks for your great help!