I am trying to obtain an estimated speed from the IMU data stream of an OAK-D-POE camera. The basic math is simple: velocity = acceleration/dt, in theory, is the average velocity of the camera (on a specific axis) over the time interval dt relative to the previous period dt.

If acceleration is negative, the speed in the interval dt will be negative and vice versa.

Thus, the velocity relative to the ground is the sum of the relative speeds.

Obviously, this approach can produce errors derived from inaccurate data produced by the IMU, and so filters and corrections must be introduced, such as setting the speed to zero when there is no lateral or vertical acceleration, which indicates that the camera is stationary.

However, from the tests I have done, I get absolutely incorrect data.

Has anyone tried and found a solution?

    SDV
    dvelocity = acceleration*dt
    Generally, you are integrating over time, so little errors in measurements will cause drift over time.

    SDV when there is no lateral or vertical acceleration, which indicates that the camera is stationary.

    Or moving at the same velocity.

    Can you demo the data? How quickly are the results completely wrong?

    Thanks,
    Jaka

        `Hi. Im using this code:

        #!/usr/bin/env python3

        import cv2

        import depthai as dai

        import time

        import numpy as np

        import csv

        # Create pipeline

        pipeline = dai.Pipeline()

        # Define sources and outputs

        imu = pipeline.create(dai.node.IMU)

        xlinkOut = pipeline.create(dai.node.XLinkOut)

        xlinkOut.setStreamName("imu")

        # enable ACCELEROMETER_RAW at 500 hz rate

        imu.enableIMUSensor(dai.IMUSensor.LINEAR_ACCELERATION, 500)

        # enable GYROSCOPE_RAW at 400 hz rate

        imu.enableIMUSensor(dai.IMUSensor.GYROSCOPE_CALIBRATED, 400)

        # it's recommended to set both setBatchReportThreshold and setMaxBatchReports to 20 when integrating in a pipeline with a lot of input/output connections

        # above this threshold packets will be sent in batch of X, if the host is not blocked and USB bandwidth is available

        imu.setBatchReportThreshold(1)

        # maximum number of IMU packets in a batch, if it's reached device will block sending until host can receive it

        # if lower or equal to batchReportThreshold then the sending is always blocking on device

        # useful to reduce device's CPU load and number of lost packets, if CPU load is high on device side due to multiple nodes

        imu.setMaxBatchReports(10)

        # Link plugins IMU -> XLINK

        imu.out.link(xlinkOut.input)

        # Function to write data to CSV

        def write_to_csv(data, filename='imu_data.csv'):

        with open(filename, mode='a', newline='') as file:

    writer = csv.writer(file)

    writer.writerow(data)

        # Write CSV header

        write_to_csv(['Timestamp (ms)', 'Delta t (ms)', 'Accel X (m/s2)', 'Accel Y (m/s2)', 'Accel Z (m/s2)', 'Velocity X (km/h)', 'Velocity Y (km/h)', 'Velocity Z (km/h)'])

        # Pipeline is defined, now we can connect to the device

        with dai.Device(pipeline) as device:

        def timeDeltaToMilliS(delta) -> float:

    return delta.total_seconds() \* 1000

# Output queue for imu bulk packets

imuQueue = device.getOutputQueue(name="imu", maxSize=50, blocking=False)

baseTs = None

velocity = np.array([0.0, 0.0, 0.0])

lastTs = None

while True:

    imuData = imuQueue.get()  # blocking call, will wait until new data has arrived

    imuPackets = imuData.packets

    for imuPacket in imuPackets:

        acceleroValues = imuPacket.acceleroMeter

        acceleroTs = acceleroValues.getTimestampDevice()

        if baseTs is None:

            baseTs = acceleroTs

        acceleroTs = timeDeltaToMilliS(acceleroTs - baseTs)

        # Calculate time difference

        currentTs = acceleroTs / 1000.0  # convert to seconds

        if lastTs is not None:

            dt = currentTs - lastTs

            # Read acceleration

            acceleration = np.array([acceleroValues.x, acceleroValues.y, acceleroValues.z])

            # Integrate acceleration to get velocity

            velocity += acceleration \* dt

            # Convert velocity to km/h

            velocity_kmh = velocity \* 3.6

            imuF = "{:.1f}"

            print(f"Delta t: {imuF.format(dt \* 1000)} ms")

            print(f"Accelerometer [m/s^2]: x: {imuF.format(acceleroValues.x)} y: {imuF.format(acceleroValues.y)} z: {imuF.format(acceleroValues.z)}")

            print(f"Velocity [km/h]: x: {imuF.format(velocity_kmh[0])} y: {imuF.format(velocity_kmh[1])} z: {imuF.format(velocity_kmh[2])}")

            # Write data to CSV

            write_to_csv([currentTs \* 1000, dt \* 1000, acceleroValues.x, acceleroValues.y, acceleroValues.z, velocity_kmh[0], velocity_kmh[1], velocity_kmh[2]])

        lastTs = currentTs

    if cv2.waitKey(1) == ord('q'):

        break\`

        And this is part of the data collected:

        Timestamp (ms),Delta t (ms),Accel X (m/s2),Accel Y (m/s2),Accel Z (m/s2),Velocity X (km/h),Velocity Y (km/h),Velocity Z (km/h)

        7.3629999999999995,7.3629999999999995,1.41015625,0.0234375,-0.0625,0.037378729687499994,0.0006212531249999999,-0.001656675

        9.718,2.3549999999999995,1.453125,0.015625,-0.44140625,0.0496983234375,0.0007537218749999999,-0.005398917187499999

        12.235,2.5170000000000003,0.42578125,-0.21484375,-0.609375,0.0535564125,-0.0011930203125000002,-0.0109205859375

        14.815999999999999,2.581,0.31640625,-0.19921875,-0.546875,0.0564963328125,-0.00304408125,-0.0160019296875

        17.194999999999997,2.3789999999999956,-1.046875,-0.09765625,-0.87890625,0.047530476562500014,-0.0038804484374999984,-0.02352923437499999

        19.754,2.5590000000000055,-1.5625,0.015625,0.18359375,0.033136101562499985,-0.003736504687499998,-0.021837895312499984

        22.226,2.4719999999999986,-1.4921875,0.0234375,0.19921875,0.019856826562499992,-0.003527929687499998,-0.020065007812499983

        24.621000000000002,2.3950000000000014,-1.2734375,0.04296875,0.1015625,0.008877248437499987,-0.003157453124999998,-0.019189335937499982

        28.909,4.287999999999997,0.27734375,-0.0859375,0.58203125,0.013158548437499985,-0.0044840531249999965,-0.010204635937499991

        31.405,2.4960000000000053,1.203125,0.1171875,-0.1796875,0.023969348437500006,-0.003431053124999994,-0.011819235937499993

        37.138999999999996,5.733999999999996,1.52734375,0.10546875,-0.29296875,0.05549738906249998,-0.0012539249999999958,-0.017866814062499993

        54.576,17.437,-1.12109375,0.078125,0.0,-0.014877253125000026,0.003650231250000005,-0.017866814062499993

        64.731,10.154999999999998,1.28125,0.109375,0.05859375,0.03196268437499997,0.007648762500000004,-0.015724743749999992

        78.067,13.336,-0.9453125,0.07421875,0.2109375,-0.013421390625000034,0.011211975000000004,-0.005597718749999991

        89.89800000000001,11.831000000000008,1.26171875,-0.01953125,-0.19140625,0.040317229687500004,0.010380107812500003,-0.013750017187499996

        99.652,9.754,-1.20703125,-0.0390625,-0.03125,-0.002066948437499989,0.009008451562500004,-0.014847342187499998

        113.319,13.666999999999998,1.5625,0.09375,-0.30078125,0.0748099265625,0.013621064062500002,-0.029646140624999994

        121.965,8.646,-0.33984375,-0.14453125,-0.6640625,0.0642320859375,0.009122442187500003,-0.050315484375

        129.46699999999998,7.501999999999967,-1.515625,0.0859375,-0.04296875,0.023299298437500178,0.011443373437499993,-0.05147594999999999

        136.97799999999998,7.511000000000018,1.0859375,0.06640625,0.33984375,0.05266261406250025,0.013238971874999996,-0.042286710937499965

        144.459,7.481000000000016,0.73046875,-0.0078125,-0.06640625,0.0723353062500003,0.013028568749999997,-0.044075137499999965

        160.09,15.631000000000006,-0.0234375,-0.046875,0.62109375,0.0710164406250003,0.010390837499999996,-0.009125198437499954

        171.66400000000002,11.574000000000002,0.578125,-0.19921875,-0.3125,0.09510482812500029,0.0020901093749999943,-0.022145948437499955

        179.61599999999999,7.951999999999987,-1.48046875,0.01171875,0.1640625,0.05272315312500036,0.002425584374999994,-0.017449298437499962

        191.409,11.792999999999997,1.421875,0.05859375,0.01953125,0.11308857187500036,0.0049131703124999935,-0.016620103124999966

        192.086,0.6770000000000109,1.421875,0.05859375,0.01953125,0.11655396562500041,0.005055974999999995,-0.016572501562499963

        209.376,17.29,-1.48828125,0.01171875,0.2578125,0.02391738750000041,0.005785396874999994,-0.0005252203124999636

        221.906,12.529999999999985,1.55859375,0.13671875,0.0546875,0.09422243437500033,0.011952506249999988,0.0019416234375000336

        238.209,16.30300000000001,-0.78125,0.05859375,0.16015625,0.0483702468750003,0.01539142031249999,0.011341321875000039

        256.839,18.62999999999998,-0.38671875,-0.16015625,-0.58984375,0.022433793750000323,0.004650060937500002,-0.02821831874999992

        274.304,17.465000000000007,1.81640625,0.05859375,-0.17578125,0.1366385203125004,0.008334084375000004,-0.039270389062499925

        289.566,15.261999999999997,-1.44921875,0.05859375,-0.0625,0.05701380468750041,0.011553412500000002,-0.04270433906249993

        296.78900000000004,7.2230000000000345,1.3671875,0.046875,0.1875,0.0925645078125006,0.012772293750000009,-0.0378288140624999

        316.753,19.96399999999998,-1.3359375,0.09765625,0.1015625,-0.003449854687499325,0.019790887500000003,-0.03052947656249991

        339.51,22.756999999999973,-1.8515625,0.01953125,0.2734375,-0.15513948281249915,0.0213909890625,-0.008128054687499938

        359.321,19.81100000000002,-0.47265625,-0.2109375,0.1015625,-0.18884913749999918,0.006347010937499982,-0.0008846578124999297

        374.20799999999997,14.886999999999983,-0.23046875,0.046875,-0.234375,-0.20120069531249915,0.00885919218749998,-0.013445564062499917

        379.108,4.9000000000000155,2.09375,0.078125,0.1484375,-0.16426694531249902,0.010237317187499984,-0.010827126562499907

        386.581,7.473000000000008,-1.0,-0.02734375,0.3984375,-0.19116974531249906,0.009501693749999984,-0.0001080421874998969

        403.961,17.380000000000006,2.1875,0.02734375,-0.81640625,-0.05430224531249899,0.011212537499999986,-0.051188948437499916

        421.554,17.592999999999968,-1.36328125,0.0546875,0.9453125,-0.14064539062499884,0.01467615937499998,0.008682229687499975

        439.448,17.89400000000002,-1.48828125,-0.05859375,-0.0625,-0.23651808749999897,0.010901643749999976,0.00465607968749997

        452.866,13.417999999999985,3.04296875,0.171875,-1.26953125,-0.08952809062499911,0.01920403124999997,-0.05666837343749997

        468.518,15.652,-1.39453125,0.15234375,0.42578125,-0.16810602187499912,0.027788174999999967,-0.03267679218749996

        476.21599999999995,7.697999999999983,2.58203125,0.21875,-0.96875,-0.09655070624999929,0.03385034999999996,-0.059523567187499904

        494.28,18.064000000000025,-2.140625,0.14453125,1.81640625,-0.23575640624999947,0.04324927499999997,0.05859805781250026

        503.908,9.628000000000025,3.078125,0.11328125,-1.515625,-0.1290661312499992,0.047175693749999977,0.006065282812500121

        511.344,7.435999999999998,-1.74609375,-0.23046875,-0.88671875,-0.17580836249999918,0.04100613749999998,-0.017671823437499873

        531.3919999999999,20.047999999999956,1.65625,-0.01171875,-1.0078125,-0.056272162499999424,0.040160362499999984,-0.0904084734374997

        597.305,65.913,0.30078125,0.10546875,-0.46484375,0.01509925781250057,0.06518670468749999,-0.2007097593749997

        647.981,50.67600000000005,0.609375,0.0078125,-0.75390625,0.12626973281250067,0.06661196718749998,-0.33824759062499987

        658.712,10.730999999999934,2.015625,-0.3671875,-2.0390625,0.2041365515625002,0.052426926562500066,-0.4170198374999994

        673.918,15.206000000000053,-0.58984375,0.0625,-0.171875,0.17184756093750012,0.05584827656250008,-0.4264285499999994

        694.723,20.804999999999964,-0.58984375,0.15234375,2.76171875,0.1276694437500002,0.06725851875000005,-0.21958133906249977

        711.073,16.349999999999977,-1.5,-0.328125,-0.9453125,0.03937944375000033,0.047945081250000084,-0.27522243281249975

        723.533,12.460000000000026,-0.03125,0.15234375,-0.41796875,0.03797769375000033,0.0547786125000001,-0.29397083906249977

        733.524,9.990999999999971,2.96484375,0.0859375,-1.9453125,0.14461600781250003,0.05786957812500009,-0.3639390609374996

        746.26,12.73600000000008,-1.3359375,0.2578125,0.39453125,0.08336380781249964,0.06969017812500017,-0.3458499609374995

        753.544,7.283999999999957,2.734375,-0.0390625,-1.2734375,0.15506568281249922,0.06866586562500018,-0.3792425484374993

        760.985,7.441000000000031,1.91796875,-0.14453125,0.36328125,0.20644346249999942,0.06479422031250016,-0.3695111156249993

        772.745,11.759999999999993,0.2890625,0.08203125,-0.0859375,0.21868121249999942,0.06826709531250016,-0.3731493656249993

        778.3919999999999,5.646999999999958,1.8984375,0.015625,-1.0,0.25727492812499914,0.06858473906250015,-0.3934785656249991

        795.9209999999999,17.529000000000018,-3.234375,0.1015625,0.79296875,0.05317163437499892,0.07499377968750016,-0.34343874843749905

        807.79,11.869000000000018,1.8359375,-0.203125,1.03125,0.13161830624999907,0.06631457343750015,-0.299375085937499

        819.5519999999999,11.76199999999994,-2.48828125,0.09375,0.46484375,0.026256515624999605,0.07028424843750013,-0.27969211406249916

        843.433,23.881000000000043,-3.05078125,0.12109375,0.75390625,-0.23602402968750083,0.08069487187500014,-0.21487758749999902

        850.829,7.395999999999958,1.10546875,-0.078125,-0.203125,-0.20659026093750102,0.07861474687500015,-0.22028591249999901

        858.428,7.599000000000022,1.98828125,-0.21484375,1.10546875,-0.15219804375000084,0.07273739531250013,-0.19004426718749892

        878.398,19.97000000000004,1.484375,0.02734375,-0.76171875,-0.04548335625000062,0.07470319218750014,-0.24480575156249904

        886.02,7.622000000000018,-0.078125,-0.26953125,-1.22265625,-0.047627043750000625,0.06730747031250012,-0.27835446093749916

        903.433,17.41300000000001,1.140625,-0.0234375,-0.13671875,0.02387508749999942,0.06583824843750011,-0.28692492187499913

        920.848,17.414999999999957,-1.67578125,0.10546875,3.40234375,-0.08118634218750033,0.0724505062500001,-0.07361838281249965

        936.812,15.963999999999977,-0.171875,-0.0390625,-0.90625,-0.09106406718750032,0.0702055687500001,-0.12570093281249958

        955.748,18.936000000000064,0.875,0.0,-0.08203125,-0.03141566718750012,0.0702055687500001,-0.13129297031249962

        963.6289999999999,7.880999999999916,1.66015625,-0.26953125,-0.76171875,0.01568562187499938,0.06255853593750019,-0.15290414999999938

        975.7679999999999,12.13900000000001,-0.28515625,0.046875,0.01953125,0.0032241796874993662,0.0646069921875002,-0.15205062656249937

        991.317,15.549000000000035,-1.609375,0.046875,-0.9296875,-0.08686283906250084,0.0672308859375002,-0.20409118593749948

        1015.6400000000001,24.323000000000093,0.22265625,0.0078125,0.71875,-0.06736643437500077,0.0679149703125002,-0.14115542343749923

        1034.039,18.39899999999983,2.453125,0.0,-1.76953125,0.09511973437499774,0.0679149703125002,-0.25836280312499815

        1043.08,9.041000000000077,-1.359375,-0.10546875,-0.78515625,0.05087534062499737,0.06448221562500017,-0.2839177546874984

        1053.598,10.518000000000027,0.8046875,-0.01171875,1.19921875,0.08134467187499744,0.06403848750000017,-0.23850957656249827

        1060.4560000000001,6.858000000000031,2.828125,-0.01171875,0.5,0.15116768437499775,0.06374916562500017,-0.2261651765624982

        1069.37,8.913999999999866,-2.01953125,-0.125,-0.046875,0.08636011874999872,0.05973786562500023,-0.2276694140624982

        1078.0590000000002,8.689000000000169,-0.859375,0.3515625,0.328125,0.05947852499999819,0.07073488125000044,-0.21740553281249797

        1100.688,22.629000000000012,-1.37890625,0.19921875,1.41796875,-0.052853245312501865,0.08696411718750044,-0.10189155937499791

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        1147.934,14.741000000000115,-2.5078125,0.0078125,0.77734375,-0.20556225000000744,0.0696599296875007,-0.08412129843749913

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        1295.698,10.542999999999969,-0.8515625,-0.12890625,0.390625,-0.2737098562500094,0.052962707812500655,-0.04774409999999795

        1311.107,15.409000000000006,2.0390625,0.04296875,-0.91796875,-0.1605981656250093,0.05534628750000065,-0.09866602968749798

        1322.545,11.43800000000006,0.18359375,-0.30859375,-0.796875,-0.15303836250000927,0.04263938437500059,-0.13147879218749814

        1332.675,10.129999999999972,-0.44140625,0.1484375,1.78125,-0.16913556562500923,0.04805260312500057,-0.06652016718749831

        1346.958,14.283000000000046,-0.9765625,-0.2890625,0.1640625,-0.2193492375000094,0.03318935625000053,-0.058084270312498285

        1357.845,10.886999999999869,-2.0703125,0.29296875,0.69921875,-0.3004914093750084,0.04467173906250039,-0.030679649999998615

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        As you can see there i negative speed while the camere nevere move backward

        I suspect that the camera timestamp is not correct.

        I've made many other try changing the way dt is evaluate, using acceleroValues.getTimestamp()

        but values are totally unreliable leading to very high speed or negative speed

        @jakaskerl shouldn't the speed node included in Depthai by the team? Or we can get accurate speed from the same node (IMU). If LUXONIS Team themselves work on this.
        Kind Regards!

        I've made others tests and I found something odd.

        These are timestamps taken using 15Hz acquisition frequency:

        Timestamp (ms) Delta t (ms)
        0 0
        59,922 59,922
        119,826 59,904
        179,751 59,925
        239,489 59,738
        299,436 59,947
        359,638 60,202
        419,441 59,803

        All intervals are around 60 ms but at 15 Hz, it should be 66 ms

        if there are 6 ms of error on 66 then there is a 10% of error.

        Is it possible that for some reason the interval reported is shorter than the real?

        Hi @SDV
        What you have sent seems like standard drift due to integration error. Nothing you can do about it without sensor fusion, but that is part of VIO.
        Did you move the device when recording the data you have sent? I can confirm using your script, the accelerometer stays pretty much as 0.0 +/- 0.1 when stationary.

        Thanks,
        Jaka

        • SDV replied to this.

          jakaskerl yes. It was recorded with the camera mounted on a car