Certain sensors are to trigger a signal based on the rate of change of the value rather than a threshold.

For instance, heat detectors in fire alarms are supposed to trigger an alarm quicker if the rate of temperature rise is higher: A temperature rise of 1K/min should trigger an alarm after 30 minutes, a rise of 5K/min after 5 minutes and a rise of 30K/min after 30 seconds.

I am wondering how this is implemented in embedded systems, where resources are scares. Is there a clever data structure to minimize the data stored?

The naive approach would be to measure the temperature every 5 seconds or so and keep the data for 30 minutes. On these data one can calculate change rates over arbitrary time windows. But this requires a lot of memory.

I thought about small windows (e.g. 10 seconds) for which min and max are stored, but this would not save much memory.

CodePudding user response：

From a mathematical point of view, the examples you have described can be greatly simplified:

1K/min for 30 mins equals a total change of 30K

5K/min for 5 mins equals a total change of 25K

Obviously there is some adjustment to be made because you have picked round numbers for the example, but it sounds like what you care about is having a single threshold for the total change. This makes sense because taking the integral of a differential results in just a delta.

However, if we disregard the numeric example and just focus on your original question then here are some answers:

First, it has already been mentioned in the comments that one byte every five seconds for half an hour is really not very much memory at all for almost any modern microcontroller, as long as you are able to keep your main RAM turned on between samples, which you usually can.

If however you need to discard the contents of RAM between samples to preserve battery life, then a simpler method is just to calculate one differential at a time.

In your example you want to have a much higher sample rate (every 5 seconds) than the time you wish to calculate the delta over (eg: 30 mins). You can reduce your storage needs to a single data point if you make your sample rate equal to your delta period. The single previous value could be stored in a small battery retained memory (eg: backup registers on STM32).

Obviously if you choose this approach you will have to compromise between accuracy and latency, but maybe 30 seconds would be a suitable timebase for your temperature alarm example.

You can also set several thresholds of K/sec, and then allocate counters to count how many consecutive times the each threshold has been exceeded. This requires only one extra integer per threshold.

CodePudding user response：

In signal processing terms, the procedure you want to perform is:

1. Apply a low-pass filter to smooth quick variations in the temperature
2. Take the derivative of its output

The cut-off frequency of the filter would be set according to the time frame. There are 2 ways to do this.

1. You could apply a FIR (finite impulse response) filter, which is a weighted moving average over the time frame of interest. Naively, this requires a lot of memory, but it's not bad if you do a multi-stage decimation first to reduce your sample rate. It ends up being a little complicated, but you have fine control over the response.
2. You could apply in IIR (Infinite impulse response) filter, which utilizes feedback of the output. The exponential moving average is the simplest example of this. These filters require far less memory -- only a few samples' worth, but your control over the precise shape of the response is limited. A classic example like the Butterworth filter would probably be great for your application, though.