Robot Sensor Simulator for Calibration and Sensor Fusion

Controls

Choose a smooth or stepped truth signal, then adjust sample rate, quantization, random noise, drift, bias, dropouts, and filter memory. Compare raw data with moving-average, low-pass, median, and complementary estimates. Presets make noisy, biased, and unreliable sensor behavior repeatable.

Theory

Every sensor has a measurement range, resolution, accuracy, bandwidth, latency, and failure behavior. Datasheet accuracy describes only part of the system; mounting, temperature, supply noise, electromagnetic interference, and surface properties often dominate real results.

Fusion works when sensors contribute complementary information and their uncertainty is represented honestly. Combining two biased measurements does not automatically create truth. Start with calibration, timestamps, coordinate frames, and data-quality checks.

Algorithm

1. Timestamp and range-check every sample at the acquisition boundary.
2. Convert raw units using calibration scale, offset, and axis alignment.
3. Reject impossible jumps or mark them invalid instead of inventing data.
4. Apply the lightest filter that meets the downstream noise requirement.
5. Transform measurements into a common frame and fuse them using known uncertainty.
6. Log raw and processed values so failures remain reproducible.

Source code

An exponential low-pass filter is useful when its time constant is chosen deliberately:

class LowPass:
    def __init__(self, alpha):
        self.alpha = alpha
        self.value = None

    def update(self, sample):
        if self.value is None:
            self.value = sample
        else:
            self.value += self.alpha * (sample - self.value)
        return self.value

Record the raw sample beside the filtered result. Otherwise an attractive plot can hide clipping, dropouts, and calibration errors.

Assumptions and hardware differences

This lab is an educational signal model, not a specific sensor datasheet. Noise is seeded Gaussian or uniform with a dial you control; a real IMU or ToF sensor adds temperature-dependent bias, non-Gaussian spikes and bus timing jitter that this model simplifies. Sampling is perfectly periodic here, but on a microcontroller loop timing and interrupt latency make timestamps essential — which is why every processing mode in the controls compares truth, raw samples and the estimate together. Filtering looks attractive on a plot, yet every smoother adds lag that will later appear as control delay on hardware; the same trade is covered in the sensor noise tutorial.

Circuit diagram

Confirm bus voltage, pull-up requirements, addresses, and maximum cable length before connecting multiple sensors.

Guided experiments

The dials in this lab exist to let you produce each sensor fault deliberately, then see which tool fixes it. Doing that once is worth a great deal of reading.

1. Prove that filtering cannot fix a bias

Set noise to zero and bias to a clear offset. Now try every filter in turn — moving average, low-pass, median. None of them move the estimate toward the truth, because all three attenuate variation and a bias does not vary.

Then set bias to zero and noise high, and watch the same filters work well. This is the single most useful distinction in sensor work: noise, bias and drift look alike on a plot and need three different fixes, and more filtering never cures a bias.

2. Watch a mean smear a spike that a median rejects

Turn on dropouts or spikes, and compare a moving average against a median of the same window.

Ultrasonic and time-of-flight noise is not Gaussian — it is occasional wild values against an otherwise steady signal. That is exactly the case an average handles worst.

3. Measure what the lag costs you

Switch to the stepped truth signal and lower the filter’s alpha (or lengthen the window). The estimate gets smoother and arrives later. Read the delay off the plot at each setting:

The last row produces a beautifully smooth trace and steers a robot on where the obstacle was 15 cm ago. Always check the lag in the units the robot cares about, not in samples — this is the most common way a well-intentioned filter makes a robot worse.

4. See what fusion can and cannot do

Set one source noisy-but-unbiased and the other smooth-but-drifting, and watch the complementary estimate take the good half of each. Then give both sources the same bias and watch the fused estimate inherit it exactly.

Fusion exploits errors that are independent. A common-mode error survives untouched, which is why calibration comes before fusion rather than after it.

What you should observe

Taking it to hardware

The practical procedure for a real sensor is short: hold it still against a known input, log a few thousand timestamped samples, and plot both the time series and a histogram. The histogram is the part people skip and the most informative — Gaussian noise makes a bell, outliers make a bell with a few points far out in the tails, and those two need different filters. The full method is in sensor noise, bias, and filtering.