Bernoulli taxonomic discrimination method

• US 7,499,833 B1
• Filed: 06/30/2004
• Issued: 03/03/2009
• Est. Priority Date: 07/02/2003
• Status: Active Grant

• Current Assignee: Lockheed Martin Corporation (Martin Marietta Corporation)
• Original Assignee: Lockheed Martin Corporation (Martin Marietta Corporation)
• Inventors: Mingrone, Joseph R., Friesel, Mark A.
• Primary Examiner(s): Bui; Bryan
• Assistant Examiner(s): TEIXEIRA MOFFAT, JONATHAN CHARLES
• Application Number:
  US10/881,115
• Time in Patent Office: 1,707 Days
• Field of Search: 702/179
• US Class Current: 702/179
• CPC Class Codes: G05B 23/0221 Preprocessing measurements, e.g. data collection rate adjustment; Standardization of measurements; Time series or signal analysis, e.g. frequency analysis or wavelets; Trustworthiness of measurements; Indexes therefor; Measurements using easily measured parameters to estimate parameters difficult to measure; Virtual sensor creation; De-noising; Sensor fusion; Unconventional preprocessing inherently present in specific fault detection methods like PCA-based methods

Abstract

A sensor includes transducer(s) for observing a region, and produces raw data representing the observed object. The raw data is processed to produce evidence signals representing one or more characteristics of the object. Taxonomic (type) classification is performed by a method using N Bernoulli trials.

Claims

1. A method for fusing plural evidence data obtained from a sensor, said method comprising the steps of:

observing at least one object with a sensor to produce N sequential samples of evidence data representing characteristics, including at least a characteristic a, of said object at the times of the samples;

determining a probability b_N of obtaining N₁ occurrences of evidence E₁ given that characteristic a was observed, by fusing evidence data employing the equation

$\begin{array}{cc}{b}_N<br><br>\left(N_1|a\right)=\left(\begin{array}{c}N\\ N_1\end{array}\right)<br><br>{p<br><br>\left(E_1|a\right)}^{N_1}<br><br>{p<br><br>\left(E_2|a\right)}^{N-N_1}& \left(2\right)\end{array}$

where;

N is the number of independent observations of the evidence data of characteristic a of the object;

N₁ is the number of times within the group of N samples that evidence E₁ is obtained; and

E₂ is any evidence other than E₁;

determining the likelihood that characteristic a was observed given that evidence E₁ was produced N₁ times during the sequence of observations by employing the equation

$\begin{array}{cc}{B}_N<br><br>\left(a|N_1\right)=\frac{b_N<br><br>\left(N_1|a\right)}{b_N<br><br>\left(N_1|a\right)+b_N<br><br>\left(N_1|b\right)}& \left(3\right)\end{array}$

where B_N(a|N₁) is the likelihood that a was observed given that evidence E₁ occurred N₁ times out of N sequential samples;

b_N(N₁|b) is the likelihood that b was observed given that evidence E₁ occurred N₁ times out of N sequential samples.

2. A method for fusing plural evidence data obtained from a sensor, said method comprising the steps of:

observing at least one object with a sensor to produce N sequential samples of evidence data representing characteristics, including at least a characteristic a, of said object at the times of the samples;

determining a probability b_N of obtaining N₁ occurrences of evidence E₁, and N₂ occurrences E₂, given that characteristic a was observed, by fusing evidence data employing the equation

$\begin{array}{cc}{b}_N<br><br>\left(N_1,N_2|a\right)=\frac{N!}{N_1!<br><br>N_2!<br><br>\left(N-N_1-N_2\right)!}<br><br>{p<br><br>\left(E_1|a\right)}^{N_1}<br><br>{p<br><br>\left(E_2|a\right)}^{N_2}<br><br>{p<br><br>\left(E_3|a\right)}^{N-N_1-N_2}& \left(4\right)\end{array}$

where;

N is the number of independent observations of the evidence data of characteristic a of the object;

N₁ is the number of times within the group of N samples that evidence E₁ is obtained; and

N₂ is the number of times within the group of N samples that evidence E₂ is obtained;

E₃ . . . are any evidence other than E1;

determining the likelihood that characteristic a was observed given that evidence E₁ was produced N₁ times during the sequence of observations by

$\begin{array}{cc}{B}_N<br><br>\left(a|N_1,N_2\right)=\frac{b_N<br><br>\left(N_1,N_2|a\right)}{b_N<br><br>\left(N_1,N_2|a\right)+b_N<br><br>\left(N_1,N_2|b\right)}& \left(5\right)\end{array}$

where B_N(a|N₁,N₂) is the likelihood that a “

a”

was observed given that evidence E₁ occurred N₁ times, and E₂ occurred N₂ times, out of N sequential samples; and

b_N(N₁,N₂|b) is the likelihood that b was observed given that evidence E₁ occurred N₁ times, and E₂ occurred N₂ times, out of N sequential samples.