Sensor Model for simulations at system level

Through this behavioral modeling, simulations of different kinds of sensors can be carried out, as long as their behavior is somehow classic

Independently of the sensor type, a generic measurement model can be described as:
y_t = (scale factor)x_t + c1x^2_t + c2x^3_t + beta + eta
where:
x_t - sensor input at time step t,
y_t - sensor output at t,
alpha - scale factor typically equal to 1,
bias - typically equal to 0,
c1 ,c2 - nonlinearity coefficients typically equal to zero,
eta_t - stochastic errors affecting measurements.

The proposed model can be customized to reflect the behavior of a given sensor described by the aforementioned model, using parameters extracted from its datasheet or experimental characterization results such as a PSD graph or an ADEV graph. Parameters from a datasheet, an ADEV graph or a PSD graph can be implemented straightforwardly into the sensor model by using the sensor's model mask. Assuming that the input signal is scaled in a given unit (x in Units), blocks of the sensor model are:

1. Scale Factor. This block multiplies the system input by a factor, which may be temperature-dependent and/or affected by random variations. The required parameters to this block are then the typical scale factor constant, its standard deviation, and its temperature coefficients.

2. Nonlinearity. This block implements second-order and third-order nonlinearities of the scale factor using two coefficients c1 (for x^2) and c2 (for x^3). Both factors can be temperature-dependent and/or affected by random variations. For this block, the required parameters are c1, c2 and their linear temperature coefficients.

3.Bias. This block adds a constant value to the input signal. This bias can be temperature-dependent and/or affected by random variations. Parameters required for this block are the typical bias given as an equivalent input signal (in Units) and typically equal to zero, standard deviation (in Units), and its temperature coefficients.

4. White Noise. Matlab Simulink block Band-Limited White Noise is used to generate white noise added to measurements. This block is parametrized using information from an ADEV graph, a PSD graph, or a datasheet.

5. 1/f noise and 1/f^2 Noise. Also known as pink and brown noise, respectively. These colored noises are generated by filtering a white noise sequence with an infinite impulse response (IIR) filter. Then, depending on the denominator of the transfer function, 1/f or 1/f^2 noise is obtained. These blocks are parameterized using information from an ADEV graph or a PSD graph.

6. Bandwidth. To limit the bandwidth, a first-order low-pass filter is used in the proposed sensor model but higher order filters could be implemented. The cut-off frequency of this filter can be the cut-off frequency of the sensor itself or, more likely, the cut-off frequency of the antialiasing filter included before the analog to digital converter. Therefore, the parameter of this block is the cut-off frequency given in Hz.

7. Saturation. Saturation Matlab Simulink block is used to set the sensor full scale (i.e. the measurement range of input signal). Parameters are upper and lower bounds given in equivalent input signal (in Units).

8. Sensitivity. This block permits to map sensor model measurements into the electrical domain. This is carried out by applying a gain function that relates physical signal units to its electrical representation. Usually, this output is required in signal processing at hardware level. The output of this block is typically given in V or A. Moreover, the output could be also converted in the time domain in the form of a variable frequency (Hz) or a variable duty cycle of a PWM signal for example.

9. Quantization. This block gives a discrete output to the system. For this, the Quantizer Matlab Simulink block is used. The parameter required for this block is the quantization interval given in Units. The output of this block is also given in Units.