# Optimal sensor for measuring object velocity in an open area?

I am trying to measure vertical and horizontal speed of an object attached to a parachute. It will be launched from a low altitude and in an open area, allowing satellite GPS lock.

Data treatment will be post flight, so no real-time or processing power requirements.

Up to now, I have identified two solutions:

• 9-DOF IMU, sensor fusion to get absolute orientation, accelerometer integration to get the velocity vector.
• GPS, ground speed for horizontal speed and elevation for vertical speed. I would probably fuse GPS elevation with a barometer relative altitude to maximize precision.

I have explored the IMU solution up to now, but I have encountered some problems:

• accelerometer integration is very prone to error, since it depends on the absolute orientation, gravity offset removal, numerical integration methods, noise attenuation, drift correction, etc.
• sensor fusion SDKs are pessimistic about inertial navigation performance, which leads me to think that getting velocities from it is easier said than done.

After reading some GPS datasheets, and I have also identified some problems:

• Weather may block GPS satellite signals and accuracy depends highly on the locked number of satellites.
• Update rates are pretty slow, I should not rely on something faster than 2 Hz.

I have the following questions:

• Am I missing another type of sensor that would be easier to implement and get accurate velocity vectors?
• Would the GPS be a more reliable solution than the IMU?
• Am I correct on the assumption the ground speed I get from the GPS is the horizontal speed of the object?

GPS is easiest to implement with lots of off-the-shelf hardware available. With a rugged (shock resistant) receiver, it will be reliable. GPS raw data is cartesian coordinates in earth centered inertial reference frame, receivers convert this to lat/long/height in earth fixed frame (see WGS-84). Postprocessing will allow you to convert to any reference frame you may want.

GPS receivers evaluate distance changes to space vehicles at a high rate, often at 1kHz. Even better, these deltas are more accurate than the position solution (because of ambiguities). Unfortunately, the raw pseudorange data and rates is often not available from consumer grade equipment. The position solution in contrast if often done only at 1Hz, better units do 10 solutions per second. To make things worse, solvers do low-pass filtering on acceleration. This makes the output look better (less noisy), but it is less accurate. If you want accuracy, do not calculate deltas from solutions, instead go for raw pseudoranges and doppler rates (RINEX-format is the keyword to look for).

Weather conditions will probably not be an issue, I assume your parachute is in open sky? Parachute fabric should be transparent to microwaves (is this also true for wet fabric?). The patch antenna should be placed on top to maintain satellite visibility even when spinning.

Jerks on high speed chute deployment can be an issue, your receiver may temporarily loose lock on satellites if line of sight dynamics exceeds $10m/s^2$ (this is due to limited loop bandwidth in the tracking loops and applies even when using raw data).

• Thanks for the very detailed explanation. I was initially thinking to only use the NMEA messages to extract ground speed and altitude. Do you think the ground speed will not correlate to the horizontal displacement of the load attached to the parachute? I was also checking GPS modules, and it seems that GNSS modules, such as the NEO-M8 are quite popular for drone applications these days. Do you think they could help me in any way over GPS-only solutions? Would a SMD antenna be detrimental for satellite lock or accuracy, supposing it is pointed upwards? – gstorto Feb 25 '18 at 23:01
• @gstorto NMEA ground speed will be accurate on average but you may find that it is slow to respond to changes. It may overshoot after sudden speed changes, an effect of the kalman filtering. NEO-M8 is a good one, check for UBX-message type. Performance of PCB-mounted antennas will be OK if you get everything right ... but it's not trivial to get it right. Invest a few grams of payload weight for a separate patch antenna. Passive antenna is OK if the cable is short. – Andreas Feb 25 '18 at 23:20

IMU integration is too unreliable for this unless you spend an astonishing amount of money on the sensors. GPS is the only reliable, compact, cheap way of doing this. You can to some extent get faster updates through "sensor fusion", using a GPS and IMU together, but this requires a lot of computation. On the other hand if this is a parachute its speed will be pretty constant once it's opened.

If you have the space and power and money then other techniques exist like optical or radar ground tracking.

• I was also reaching this conclusion. I will just add to the question that the data treatment will be post flight, since it is only for parachute performance evaluation. I don't think it changes anything in your answer though. – gstorto Feb 25 '18 at 11:34