How can I find process noise and measurement noise in a Kalman filter if I have a set of RSSI readings?

Question

im have RSSI readings but no idea how to find measurement and process noise. What is the way to find those values?

Answer 1

Not at all. RSSI stands for "Received Signal Strength Indicator" and says absolutely nothing about the signal-to-noise ratio related to your Kalman filter. RSSI is not a "well-defined" things; it can mean a million things:

Defining the "strength" of a signal is a tricky thing. Imagine you're sitting in a car with an FM radio. What does the RSSI bars on that radio's display mean? Maybe:

• The amount of Energy passing through the antenna port (including noise, because at this point no one knows what noise and signal are)?
• The amount of Energy passing through the selected bandpass for the whole ultra shortwave band (78-108 MHz, depending on region) (incl. noise)?
• Energy coming out of the preamplifier (incl. Noise and noise generated by the amplifier)?
• Energy passing through the IF filter, which selects your individual station (is that already the signal strength as you want to define it?)?
• RMS of the voltage observed by the ADC (the ADC probably samples much higher than your channel bandwidth) (is that the signal strength as you want to define it?)?
• RMS of the digital values after a digital channel selection filter (i.t.t.s.s.a.y.w.t.d.i?)?
• RMS of the digital values after FM demodulation (i.t.t.s.s.a.y.w.t.d.i?)?
• RMS of the digital values after FM demodulation and audio frequency filtering for a mono mix (i.t.t.s.s.a.y.w.t.d.i?)?
• RMS of digital values in a stereo audio signal (i.t.t.s.s.a.y.w.t.d.i?) ?
• ...

as you can imagine, for systems like FM radios, this is still relatively easy. For things like mobile phones, multichannel GPS receivers, WiFi cards, digital beamforming radars etc., RSSI really can mean everything or nothing at all.

You will have to mathematically define away to describe what your noise is. And then you will need to find the formula that describes your exact implementation of what "RSSI" is, and then you can deduct whether knowing RSSI says anything about process noise.

Answer 2

A Kalman Filter is a mathematical construct for computing the expected state of a system that is changing over time, given an initial state and noisy measurements of that system. The key to the "process noise" component of this is the fact that the system is changing. The way that the system changes is the process.

Your state might change due to manual control or due to the nature of the system. For example, if you have a car on a hill, it can roll down the hill naturally (described by the state transition matrix), or you might drive it down the hill manually (described by the control input matrix). Any noise that might affect these inputs - wind, bumps, twitches - can be described with the process noise.

You can measure the process noise the way you would measure variance in any system - take the expected dynamics and compare them with the true dynamics to generate a covariance matrix.