Markov Sequential Detector

US 20080186225A1
Filed: 04/18/2006
Published: 08/07/2008
Est. Priority Date: 04/29/2005
Status: Active Grant

First Claim

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1. A continuous method of detecting a signal s(t) present in a data stream y(t, ω

) dependent on a discrete time variable t and an observation variable ω

, the signal being characterized by a state model x(t) with values in a finite set {x₁, . . . , x_N}, to which there corresponds a finite set {ω

₁, . . . , ω

_N} of N values of the observation variable ω

, this method formulating for each instant t and for each state x_na detection criterion Λ

_n(t),wherein at each instant t the value of the criterion Λ

_n(t) for a state x_nis calculated simultaneously in two different ways;

as being a function of the product of the probability P_nof the state x_n, and of the ratio of the conditional probabilities p₁and p₀of the datum y(t, ω

_n) in the absence and in the presence of a signal,as being a function of the product of one of the N values of the criterion that were calculated at the previous instant t−

1, of the probability of transition P_n,mbetween the state x_mfor which this value was calculated at the instant t−

1 and the state x_nconsidered, and of the ratio of the conditional probabilities p₁and p₀of the datum y(t, ω

_n) in the absence and in the presence of a signal,the larger of the two calculated values being assigned to the criterion of Λ

_n(t).

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Abstract

The present invention relates to the general problem of detection by sonar or radar. It is concerned in particular with the initial detection of a signal of interest in a data stream corresponding to the signal received by such equipment. This initial detection is transmitted to the equipment charged with performing the tracking of the objects of interest that were the subject of a detection. The method considers that a signal of interest is characterized by a state model x(t) with values in a finite set {x₁, . . . , x_N}, to which there corresponds a finite set {ω₁, . . . , ω_N} of N values of an observation variable ω, characteristic of this signal. To detect the presence of a signal of interest the method simultaneously calculates the value of a detection criterion Λ_n(t) in two different ways. The first way, the detection function is calculated is as a function of the product of the probability P_nof the state x_n, and of the ratio of the conditional probabilities p₁and p₀of the datum y(t, ω_n) containing the signal, in the absence and in the presence of a signal. The second way the detection signal is calculated is as a function of the product of one of the N values of the criterion that were calculated at the previous instant t−1, of the probability of transition P_n,mbetween the state x_mfor which this value was calculated at the instant t−1 and the state x_nconsidered, and of the ratio of the conditional probabilities p₁and p₀of the datum y(t, ω_n) in the absence and in the presence of a signal. The larger of the two calculated values is assigned to the criterion of Λ_n(t) which is then compared with a detection threshold.

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14 Claims

1. A continuous method of detecting a signal s(t) present in a data stream y(t, ω
- ) dependent on a discrete time variable t and an observation variable ω
  
  , the signal being characterized by a state model x(t) with values in a finite set {x₁, . . . , x_N}, to which there corresponds a finite set {ω
  
  ₁, . . . , ω
  
  _N} of N values of the observation variable ω
  
  , this method formulating for each instant t and for each state x_na detection criterion Λ
  
  _n(t),wherein at each instant t the value of the criterion Λ
  
  _n(t) for a state x_nis calculated simultaneously in two different ways;
  
  as being a function of the product of the probability P_nof the state x_n, and of the ratio of the conditional probabilities p₁and p₀of the datum y(t, ω
  
  _n) in the absence and in the presence of a signal,as being a function of the product of one of the N values of the criterion that were calculated at the previous instant t−
  
  1, of the probability of transition P_n,mbetween the state x_mfor which this value was calculated at the instant t−
  
  1 and the state x_nconsidered, and of the ratio of the conditional probabilities p₁and p₀of the datum y(t, ω
  
  _n) in the absence and in the presence of a signal,the larger of the two calculated values being assigned to the criterion of Λ
  
  _n(t).
- View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14)
- - 2. The method as claimed in claim 1 further comprisinga step A of initialization where the N values of the detection criterion Λ
    - _nat the instant t₀−
      
      1 preceding the first instant of the data to be processed t₀are fixed at predetermined values,a step B of calculating the N values of the criterion Λ
      
      _nat the current instant t according to the two ways and of determining the maximum value,a step C of detecting by comparison with a threshold the N values of the criterion that were determined at phase B, the overshooting of the detection threshold by a value of the criterion determining the presence of a signal in the state x_ncorresponding to this value of the criterion, at the current instant, steps B and C being carried out in an iterative manner.
  - 3. The method as claimed in claim 1, in which the detection criterion Λ
    - _n(t) is defined by the following relations;
      
      $\begin{matrix} Λ_{n} (t_{0} - 1) = 0, \\ Λ_{n} (t) = \max {\begin{matrix} F (K_{2} \cdot \frac{p_{1} (y (t, ω_{n}))}{p_{0} (y (t, ω_{n}))} \cdot \max_{1 \leq m \leq N} {P_{n, m} \cdot Λ_{m} (t - 1)}), \\ F (K_{1} \cdot \frac{p_{1} (y (t, ω_{n}))}{p_{0} (y (t, ω_{n}))} P_{n}) \end{matrix}} \end{matrix}$ where t₀is the first instant of the data to be processed, ω
      
      _nis the locus in the observation space corresponding to the state x_n, where p₁and p₀represent the conditional probability laws for the data y(t, ω
      
      ) in the absence and in the presence of a signal, where F is an increasing function, and where K₁and K₂are two arbitrarily chosen factors.
  - 4. The method as claimed in claim 3, for which the factor K₁or the factor K₂is regulated so as to maintain a reinitialization rate for the recursive calculation of Λ
    - _nthat is determined by the condition;
      
      $F (K_{1} \cdot \frac{p_{1} (y (t, ω_{n}))}{p_{0} (y (t, ω_{n}))} P_{n}) > F (K_{2} \cdot \frac{p_{1} (y (t, ω_{n}))}{p_{0} (y (t, ω_{n}))} \cdot \max_{1 \leq m \leq N} {P_{n, m} \cdot Λ_{m} (t - 1)}),$ near to a specified value R.
  - 5. The method as claimed in claim 4 for which R is equal to 0.5.
  - 6. The method as claimed in claim 1 applied to the initialization of sonar tracks on spectral lines on the basis of observation data y(t, ω
    - ) for which ω
      
      is a frequency datum.
  - 7. The method as claimed in claim 1 applied to the initialization of sonar tracks on spectral lines on the basis of observation data y(t, ω
    - ) for which ω
      
      is a data pair (frequency, bearing).
  - 8. The method as claimed in claim 2 applied to the initialization of sonar tracks on spectral lines on the basis of observation data y(t, ω
    - ) for which ω
      
      is a frequency datum.
  - 9. The method as claimed in claim 4 applied to the initialization of sonar tracks on spectral lines on the basis of observation data y(t, ω
    - ) for which ω
      
      is a frequency datum.
  - 10. The method as claimed in claim 2 applied to the initialization of sonar tracks on spectral lines on the basis of observation data y(t, ω
    - ) for which ω
      
      is a data pair (frequency, bearing).
  - 11. The method as claimed in claim 4 applied to the initialization of sonar tracks on spectral lines on the basis of observation data y(t, ω
    - ) for which ω
      
      is a data pair (frequency, bearing).
  - 12. The method as claimed in claim 2 in which the detection criterion Λ
    - _n(t) is defined by the following relations;
      
      $\begin{matrix} Λ_{n} (t_{0} - 1) = 0, \\ Λ_{n} (t) = \max {\begin{matrix} F (K_{2} \cdot \frac{p_{1} (y (t, ω_{n}))}{p_{0} (y (t, ω_{n}))} \cdot \max_{1 \leq m \leq N} {P_{n, m} \cdot Λ_{m} (t - 1)}), \\ F (K_{1} \cdot \frac{p_{1} (y (t, ω_{n}))}{p_{0} (y (t, ω_{n}))} P_{n}) \end{matrix}} \end{matrix}$ where t₀is the first instant of the data to be processed, ω
      
      _nis the locus in the observation space corresponding to the state x_n, where p₁and p₀represent the conditional probability laws for the data y(t, ω
      
      ) in the absence and in the presence of a signal, where F is an increasing function, and where K₁and K₂are two arbitrarily chosen factors.
  - 13. The method as claimed in claim 12 for which the factor K₁or the factor K₂is regulated so as to maintain a reinitialization rate for the recursive calculation of Λ
    - _nthat is determined by the condition;
      
      $F (K_{1} \cdot \frac{p_{1} (y (t, ω_{n}))}{p_{0} (y (t, ω_{n}))} P_{n}) > F (K_{2} \cdot \frac{p_{1} (y (t, ω_{n}))}{p_{0} (y (t, ω_{n}))} \cdot \max_{1 \leq m \leq N} {P_{n, m} \cdot Λ_{m} (t - 1)}),$ near to a specified value R.
  - 14. The method as claimed in claim 13 for which R is equal to 0.5.

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Current Assignee
Thales SA
Original Assignee
Thales SA
Inventors
Didier, Billon

Granted Patent

US 7,649,806 B2
Time in Patent Office

Days
Field of Search
US Class Current

342/195
CPC Class Codes

G01S 13/66   Radar-tracking systems; Ana...

G01S 15/66   Sonar tracking systems

G01S 7/2923   based on data belonging to ...

Markov Sequential Detector

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Markov Sequential Detector

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