Filter Noisy Robotic Sensor Streams

Skild AI robot sensors can produce isolated spikes caused by vibration or transmission noise. Implement a causal median filter that replaces a reading when it differs too much from the recent filtered signal.

Given a list of numeric readings, an odd window_size, and an absolute threshold, process readings from left to right:

1. For the first reading, output the reading unchanged.
2. For every later reading, compute the median of up to the previous window_size output values.
3. If the absolute difference between the current reading and that median is greater than threshold, output the median. Otherwise, output the current reading.
4. The output value becomes part of the history used to process future readings.

Return a list containing the filtered values in their original order.

Formal Specification

• Input: readings, a list of integers or floating-point numbers; window_size, a positive odd integer; and threshold, a nonnegative number.
• Output: A list of numbers with the same length as readings.
• When the available history has an even length, define its median as the average of its two middle values.