A simple low-resource usage Kalman Filter using shared resources Written with MyHDL: the future of HDL
I was faced to filter a noisy temperature measurement, but it was for a legacy Altera EP1C6 device, without Hardware Multipliers. There was no real speed requirement as the filter was to feed a PID running at a slow rate of 10 to 50Hz. So I opted to use a bit-serial multiplier and re-use this for the 3 calculations. As there where also additions to be done, I wanted to re-use the adder from the multiplier to do these as well. After a while it turned out that we can get away with one large adder to do the multiplications and to do the additions without actually doing the additions :)
There are plentiful resources on the web, so I'm not going to cover much more than the bare necessities to explain what I've done. The basic formula is:
y(n) = a.y(n-1) + b.x(n)For a true Kalman Filter the coefficients a and b are variable and adapted in time. To keep the resource usage and development time low, I implemented the filter with a fixed gain. It then effectively becomes a low pass filter. I use fixed values for a and b, in this case 0.99121 and 0.000879. The sum of a and b is 1. If smaller the filter doesn't reach the average value, if it is more it will overshoot, or oscillate.
The above formula is normally calculated in Floating Point Arithemetic which at best is problematic in any FPGA except the latest $1k+ devices ... Instead I used 'Scaled Integer Arithmetic'. A scaling factor of about 1000 is usually a good starting point, so I chose to scale by 1024. The above coefficients then become 1015 and 9 respectively. The formula then becomes:
y(n) = (a.y(n-1) + b.x(n)) / 1024The division by 1024, the 'scaling', has the side effect of rounding (by truncation) towards negative infinity, so I will make it round to the nearest integer by adding half of the scaling factor before doing the scaling operation:
y(n) = (a.y(n-1) + b.x(n) + 1024/2 ) / 1024Now, go read the code. I made an extra effort in adding readable comments.