I am working on a project that involves multiple sensors for measuring the one-dimensional position of a small car. Each sensor has its own error distribution, which is not necessarily Gaussian.
To be more specific, for example, I have two sensors, A and B:
Sensor A measures the car at position 3 with a certain known non-Gaussian error distribution.
Sensor B measures the car at position 4 with another known non-Gaussian error distribution.
If I know the specific error distributions for these two sensors, can I fuse them to get a more accurate estimate of the car's real position distribution by multiplying these two distributions together?
If this approach of cumulative multiplication is considered valid, could you please point me to any relevant literature or references?
I initially looked into Kalman filtering as it's a widely used technique for sensor data fusion. However, I found two key limitations with applying it to my problem:
Kalman filtering assumes Gaussian error distributions, but my sensors have known, non-Gaussian error characteristics. Kalman filtering is generally focused on estimating the expected value of the state (in my case, the position of the vehicle). However, I'm interested in the entire distribution of the vehicle's position to better understand the uncertainty involved.