Output of the localize algorithm as .csv and some R code to analyze the results. The test uses a multilateration technique and minimizes the STD. The idea is that the point with the lowest STD (localized_STD) is the point with the lowest localization error (error_m). In Addition some noise (..._n) was simulated.

locAlg_DA.r

# read the csv file
df <- read.csv(file = "locResults_small_mNoise5_mSigRnd8.csv")

# use ggplot for plotting
require(ggplot2)

# show histogramms
ggplot(df, aes(x=error_m)) +
  geom_histogram(bins=20,
                 colour="dark gray", fill="black") +
  scale_x_continuous(name = "Remaining error [m] per localization") +
  ggtitle("Histogram remaining error")

ggplot(df, aes(x=localized_std)) +
  geom_histogram(bins=20,
                 colour="dark gray", fill="black") +
  scale_x_continuous(name = "Remaining STD per localization") +
  ggtitle("Histogram remaining standart deviation")

# perform normality tests
shapiro.test(df$localized_std)
# OUTPUT
# 	Shapiro-Wilk normality test
# data:  df$localized_std
# W = 0.84849, p-value < 2.2e-16


shapiro.test(df$error_m)
# OUTPUT
# 	Shapiro-Wilk normality test
# data:  df$error_m
# W = 0.82922, p-value < 2.2e-16


# Person should not be used, since data is not
# normal distributed?

cor.test(x = df$localized_std, y = df$error_m)
# OUTPUT
# 	Pearson's product-moment correlation
# data:  df$localized_std and df$error_m
# t = 42.617, df = 998, p-value < 2.2e-16
# alternative hypothesis: true correlation is not equal to 0
# 95 percent confidence interval:
#  0.7802119 0.8242905
# sample estimates:
#       cor 
# 0.8033488 


# spearman as the correct test for corellation?
cor.test(x = df$localized_std, y = df$error_m, method = "s")
# OUTPUT
# 	Spearman's rank correlation rho
# data:  df$localized_std and df$error_m
# S = 36685000, p-value < 2.2e-16
# alternative hypothesis: true rho is not equal to 0
# sample estimates:
#       rho 
# 0.7798916 

# scatterplot for both variables
ggplot(df, aes(x = localized_std , y = error_m)) +
  geom_point(alpha=0.2) +
  scale_x_continuous(name = "remaining standart deviation (STD)") +
  scale_y_continuous(name = "error in [m] from original source") +
  ggtitle("Relation of location error ~ standart deviation (STD)",
          subtitle = paste0("Spearman's rho = ",round(cor(df$localized_std,
                                             df$error_m, method = "s"),2)))

locResults_large_mNoise5_mSigRnd8.csv

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