FDS
Why Smoothing?
on January 5, 2017

Occasionally I have been asked why parameters in the POLARIS software are described as “Smoothed”. You will find Smoothed versions of Latitude and Longitude, Altitude STD, Gross Weight and soon to be Pitch and Roll (we are adding these to provide cosmetic improvements for visualisation displays). It’s a bit of a history lesson, so makes a gentle start to the New Year.

## Anti-Submarine Warfare

Well of course this has to do with helicopters. When a helicopter is chasing a submarine at sea (daft thing to say “at sea” – how many submarines have you seen going down the road? anyway, I digress) there are a number of different ways to find the submarine.

These include sonobuoys which can be dropped from fixed wing or rotary wing aircraft, Magnetic Anomaly Detectors (MAD) which are towed behind the aircraft to keep clear of the aircraft’s magnetic field, and dunking sonars. Here helicopters come into their own, as they can hover over a spot in the sea and winch the sonar into the sea at the required depth. (Thermal layers in the sea make sound waves bend so it is important to be able to listen at the correct depth).

All the helicopter has to do is to sit in a stable hover and keep the cable going straight down and the sonar detector at the required depth. Easy.

## Inertial Height Smoothing

OK. As you will have learned, things can get complicated. There are waves and wind to contend with. Let’s do waves first.

Imagine the helicopter in a hover 40ft over the waves. The radio altimeter is showing anything from 30ft to 50ft as the 20ft high waves pass under the aircraft. If we just try to hold height on this signal, the aircraft will be trying to climb and descent constantly and we won’t hold the sonobuoy at a constant depth. Let alone the stress on the engines and the seasick crew.

The solution is to use accelerometers to detect the motion of the aircraft and establish a smooth height signal to control the aircraft. When the Wessex, the first Anti-Submarine Warfare (ASW) helicopters with an autopilot, came into service, there were no digital computers so the problem of resolving the vertical acceleration was solved mechanically. A set of three orthogonal accelerometers were fixed to a platform that was held level using two gyroscopes. One gyroscope held the platform level when the aircraft pitched up and down and the other held it level when the aircraft rolled left and right.

The vertical accelerometer signal could then be integrated twice (using analogue operational amplifier integrators) to produce a smoothed height signal. An error signal formed by comparing the radio altitude with the computed height was fed back into the circuitry to ensure that, in the long term, the smoothed height was equal to the radio height. This equipment was called the height smoother, and hence why I started using this term when we processed height and position data in POLARIS.

## Control Theory

For those of you brave enough, there was a further integral stage to allow for accelerometer errors, so the overall transfer function was in fact:

Where hs is the smoothed altitude, hr is the radio altitude, AZ is the vertical acceleration, the ks are constants and s is the Laplace operator. I have pretended units don’t exist, so you can see that a change in Az results in double integration (1/s2) transformation to the smoothed height, but the long term ratio between the smoothed and radio heights is unity.

## Smoothing Velocity

These helicopters were also fitted with Doppler radars to detect motion across the water, and the lateral and longitudinal accelerometers provided smoothed lateral and fore-aft velocity signals that ignored the horizontal motion of the waves. When used for Search And Rescue (SAR) operations, some autopilots include a positional trimming system so that the winch operator can move the aircraft over the person being rescued.

For ASW, the autopilot position system holds the aircraft over the dunked sonar. To achieve this the winch provides cable angle and depth information. For a given cable angle, a deeper sonar is displaced further from the helicopter position, so the more corrective motion was needed to get back “on top” of the sonar. This leads to an interesting control law with variable gains which, as the sonar is being raised, tends to zero gain as you need only very small helicopter movements to keep over the sonar as it nears the surface.

## Terminology

We could have used the words “Filtered”, “Processed” or “Adjusted” but as long as you know something has been done to change the signal from that recorded, any of these adjectives is sensible. In our case we have used “Smoothed” and now you know the history behind this.

TTFN

Dave

P.S. I tried hard to find a copy of an old photo I had, but it’s lost somewhere. The photo shows an ASW helicopter in the hover taken through the periscope of the submarine being hunted on an exercise. It was evidently a hot day, and you can see the legs of all the crew members (pilot, co-pilot, sonar operator) hanging out of the open door.

It was a single engine helicopter with a single channel autopilot. Just don’t think about the failure cases…