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A Nonlinear Least Squares Approach to Time of Death Estimation Via Body Cooling
Author(s) -
Rodrigo Marianito R.
Publication year - 2016
Publication title -
journal of forensic sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.715
H-Index - 96
eISSN - 1556-4029
pISSN - 0022-1198
DOI - 10.1111/1556-4029.12875
Subject(s) - exponential function , nonlinear system , non linear least squares , dimension (graph theory) , bivariate analysis , function (biology) , mathematics , thermocouple , algorithm , least squares function approximation , statistics , computer science , estimation theory , mathematical analysis , engineering , physics , quantum mechanics , evolutionary biology , estimator , pure mathematics , electrical engineering , biology
The problem of time of death (TOD) estimation by body cooling is revisited by proposing a nonlinear least squares approach that takes as input a series of temperature readings only. Using a reformulation of the Marshall–Hoare double exponential formula and a technique for reducing the dimension of the state space, an error function that depends on the two cooling rates is constructed, with the aim of minimizing this function. Standard nonlinear optimization methods that are used to minimize the bivariate error function require an initial guess for these unknown rates. Hence, a systematic procedure based on the given temperature data is also proposed to determine an initial estimate for the rates. Then, an explicit formula for the TOD is given. Results of numerical simulations using both theoretical and experimental data are presented, both yielding reasonable estimates. The proposed procedure does not require knowledge of the temperature at death nor the body mass. In fact, the method allows the estimation of the temperature at death once the cooling rates and the TOD have been calculated. The procedure requires at least three temperature readings, although more measured readings could improve the estimates. With the aid of computerized recording and thermocouple detectors, temperature readings spaced 10–15 min apart, for example, can be taken. The formulas can be straightforwardly programmed and installed on a hand‐held device for field use.