PE1-3.5 Adaptive Thresholding & CFAR Detection

What this is and why it exists

Everything so far assumed you know the noise level, because the threshold was set against it. In radar you do not.

Clutter varies with terrain, weather, sea state and look angle, and it varies while the radar is running. A threshold set in advance is either blind or is alarming constantly.

The vocabulary

• Clutter — unwanted returns from the ground, sea, rain or anything that is not the target.
• Non-stationary — having statistics that change with position or time.
• Cell under test — the range or angle cell currently being examined for a target.
• Reference cells — the neighbouring cells used to estimate the background level.
• Guard cells — cells beside the one under test, excluded from the estimate.
• CFAR — constant false alarm rate detection.
• Cell-averaging CFAR — estimating the background as the average of the reference cells.
• Greatest-of CFAR — taking the larger of the two sides' averages.
• Ordered-statistic CFAR — ranking the reference cells and taking one at a chosen position.
• Clutter edge — a boundary where the background level changes abruptly.

The mental model

A fixed threshold is safe only if the noise level never moves. Set it for quiet background and a patch of sea clutter fills the display with false alarms. Set it for the clutter and every target over quiet ground is missed. Neither setting is wrong; the assumption behind having one setting is wrong.

The answer is to estimate the background from the data itself, and set the threshold relative to that estimate. Then when the background rises, the threshold rises with it, and the false alarm rate stays where you put it. The name says precisely what is held constant.

Cell-averaging is the standard method. Take the cells surrounding the one being tested and average them to estimate the local background. Multiply that by a factor which sets the false alarm rate, and use the result as the threshold.

One detail matters more than it looks. The cell under test is excluded from its own reference set. If a target is present, including that cell would raise the estimated background, which raises the threshold, which makes the target harder to detect. A strong target would help hide itself. Guard cells beside it are excluded too, because a real target spreads slightly and would otherwise contaminate the estimate the same way.

Target models come in here. Whether a target's return fluctuates from look to look changes the detection performance substantially. A detection probability quoted without naming the assumed model is not a complete statement.

Every variant of the method estimates the background differently, and each fails in a different place.

Cell-averaging fails at a clutter edge. When the cell under test sits at a boundary, half the reference cells come from quiet ground and half from heavy clutter. The average lands between them, so the threshold is too low on the clutter side and false alarms appear along the edge. Greatest-of takes the larger of the two sides' averages instead, which fixes that particular failure.

Cell-averaging also fails with several targets close together. A second target inside the reference window inflates the estimated background and masks the first. Ordered-statistic ranks the reference cells and takes one at a chosen position, so a few unusually large cells do not move the estimate at all. That fixes the multiple-target failure, and it costs a little performance in uniform clutter.

That is the useful shape of the topic. There is no best variant. Each is a different answer to which failure you are most worried about.

What you should now be able to explain or do

Explain why a fixed threshold cannot work in varying clutter. State what CFAR holds constant and how it does so. Describe cell-averaging and explain why the cell under test and its guard cells are excluded. Say why the target model has to be stated with any detection probability. Name the failure each variant addresses, and say what it gives up.

Check yourself