sm4sd-Package: sm4sd: A package for computing the conductivity of the pore...

In 4301350/sm4sd: Statistical Modeling for Sensor Data

Description

The sm4sd provides several methods to extract the pore water electrical conductivity based on data including Hilhorst model (deterministic model) and time-varying dynamic linear model approach.

Details

Salt concentration of bulk is a strong indicator for world's agricultural productivity. One way to mesure it is through determining the pore water conductivity of soil, σ_p. According to Hilhorst, σ_p can be determined from the equation:

$\sigma$_p=ε_pσ_b/(ε_b-ε_σb=0)

where

• ε : electrical permittivity,

• σ : electrical conductivity,

• p : pore water,

• b : bulk soil.

The values ε_b and σ_b can be mesured in the bulk soil using a dielectric sensor; ε_p is a function of temperature; and ε_σb=0 appear as a offset of the linear relationship between ε_b and σ_b depending on soil type. In his work, he recommended using 4.1 as a generic offset.

Once the offset is fixed, this model is deterministic. The producer of capacitance soil moisture sensors 5TE recommends the use the an offset ε_σb=0 of 6 while another study found that this value is appropriate and does not present a good linear relationship between ε_b and σ_b Giving the randomness, Basem, Jose and Gerd described a statistical approach using the time-varying dynamic linear model (dlm). In this work, they considered the offset ε_σb=0 as an unknow parameter which is also estimaded by the model. The model can be formulated as follow:

$y$_t = A_tx_t + v_t $$

$x$_t = x_t-1 + w_t $$

where

• y_t

  is an 1-dimensional vector, representing the observation at time t, ε_b;

• x_t

  is an 2-dimensional uncorrelated vector, representing the state at time t, (x₁, x₂)_t, and

  • x₁

    is the offset ε_σb=0,

  • x₂

    is related to the product of σ_b, ε_p;

• A_t

  , for our specific model, is 2-dimension vector (1, σ_b × ε_p)_t;

• v_t, w_t

  are white noise random variable with their own covariance matrix.

The sm4sd contrains several classes:

• RS: raw signal class with 3 raw inputs, σ_b, ε_b and ε_p;

• SM-class: signal model class, it contains the RS and it's virtual, it means you can't create directly an instance with this class;

• SM.dlm: dynamic linear model for raw signal, it contains SM-class and the extra parameters for the model definition;

• SM.dlm.fitted: fitted dynamic linear model;

• SM.HL: Hilhorst model;

• SM.rnn: Recurrent Neural Network model for σ_b simulation.

For more details, check the class definitions.

4301350/sm4sd documentation built on June 14, 2020, 4:22 p.m.