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Advanced Radar to GPS (XYZ)

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Outputs filtered target coordinates, velocity, and acceleration from a radar (that have been processed using an Unscented Kalman Filter UKF). It also maintains the original selected track by finding which of the 8 targets are closest to the estimate (meaning it ignores chaff (anti-chaff) or any other misdetections).

The HUD is only really just a visualization of the radar to GPS. Not much thought went into the system tbh.




In addition to the Kalman filter, it also exploits a weird quirk with SW radars that allow for extra filtering with no added downsides (Time since detection filtering).

The time since detection output of radars isn't actually the time since it first detected a target. Instead, every few ticks the radar takes a snapshot of the azimuth, elevation, and range to each of it's targets. For the next 8 or however many ticks random noise is just applied to this snapshot. Meaning if you were to average the radar data over this period of 8 ticks, you could get a better estimate of the true data.

This time since update period varies with the max range of the radar though. So a radar with 28 km range may have a period of 9 ticks where the radar output is just the same values with random noise applied each tick. A radar with a max range under 2km has no delay (time since detection never starts counting).



Because of this, the Kalman filter may be the optimal solution under some circumstances. Kalman filters are known to be optimal filters for normally distributed noise with linear dynamics. Normally, SW radar noise is uniformly distributed, but by sampling many uniformly distributed variables the resulting average begins to resemble a normal distribution. The more points sampled (higher time since detection/max radar range) the more it approaches a normal distribution.

However, a normal Kalman filter would still suffer since it assumes a linear transformation from measurement space to state space. To get from polar radar coordinates (azimuth, elevation, range) to global cartesian coordinates, a bunch of non-linear trig functions have to be used. Filters like the extended Kalman filter (EKF) and unscented Kalman filter (UKF) account for these non-linear transforms.

The main reason I picked the UKF over the EKF, is just because the UKF was less work for this application. Like for the EKF you have to figure out a bunch of partial derivatives (or write some program to compute them for you), but for the UKF it doesn't require any background work. The UKF samples a bunch of points surrounding the position estimate, and then converts these points to the radar's polar coordinates. Doing so, we can get better estimate of variance.


-Constant-turn state transition matrix (instead of acceleration based transition matrix)

By toggling 1, the radar will enter a mode where it'll lock the first target it picks up. It will then try to maintain this lock even if other targets enter the FOV.

"Process Noise"
If you find that the Kalman filter estimate is too unresponsive try increasing the process noise property value.
Likewise, if you want the filter to give a more accurate (but unresponsive) value try lowering process noise.

"Initial Covariance"
I've also added a dropdown for the initial covariance, a higher value will start the estimate off with more sensitivity (keep in mind that no matter what you set this initial value to it'll eventually converge to the same covariance).

"Timeout (seconds)"
If the radar is no longer detecting a target, it'll keep predicting where that target will be until it times out.




Feel free to re-upload this radar system on your own vehicles, so long as you provide the link to this WS page.