How to increase 1d-data resolution though interpolating in between measurements? - numpy

Question

I'm developing a pythong script where I receive angular measurements from a motor which has a low resolution encoder attached to it. The data I get from the motor has a very low resolution (about 5 degrees division in between measurments). This is an example of the sensor output whilst it is rotating with a constant speed (in degrees):
sensor output = ([5, 5, 5, 5, 5, 10, 10, 10, 10 ,10, 15, 15, 20, 20, 20, 20, 25, 25, 30, 30, 30, 30, 30, 35, 35....])
As you can see, some of these measurements are repeating themselves.
From these measurements, I would like to interpolate in order to get the measurements in between the 1D data-points. For instance, if I at time k receive the angular measurement theta=5 and in the next instance at t=k+1 also receive a measurement of theta=5, I would like to compute an estimate that would be something like theta = 5+(1/5).
I have also been considering using some sort of predictive filtering, but I'm not sure which one to apply if that is even applicable in this case (e.g. Kalman filtering). The estimated output should be in a linear form since the motor is rotating with a constast angular velocity.
I have tried using numpy.linspace in order to acheive what I want, but cannot seem to get it to work the way I want:
# Interpolate for every 'theta_div' values in angle received through
# modbus
for k in range(np.size(rx)):
y = T.readSensorData() # take measurement (call read sensor function)
fp = np.linspace(y, y+1, num=theta_div)
for n in range(theta_div):
if k % 6 == 0:
if not y == fp[n]:
z = fp[n]
else:
z = y
print(z)
So for the sensor readings: ([5, 5, 5, 5, 5, 10, 10, 10, 10 ,10, 15, 15, 20, 20, 20, 20, 25, 25, 30, 30, 30, 30, 30, 35, 35....]) # each element at time=k0...kn
I would like the output to be something similar to:
theta = ([5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17.5, 20...])
So in short, I need some sort of prediction and then update the value with the actual reading from the sensor, similar to the procedure in a Kalman filter.

Answer 1

why dont just make a linear fit?
import numpy as np
import matplotlib.pyplot as plt
messurements = np.array([5, 5, 5, 5, 5, 10, 10, 10, 10 ,10, 15, 15, 20, 20, 20, 20, 25, 25, 30, 30, 30, 30, 30, 35, 35])
time_array = np.arange(messurements.shape[0])
fitparms = np.polyfit(time_array,messurements,1)
def line(x,a,b):
return a*x +b
better_time_array = np.linspace(0,np.max(time_array))
plt.plot(time_array,messurements)
plt.plot(better_time_array,line(better_time_array,fitparms[0],fitparms[1]))