Particle filtering and navigation system using measurement correlation

Patent metadata

Field	Value
Publication number	US-12511583-B2
Application number	US-202017783363-A
Country	US
Kind code	B2
Filing date	Dec 7, 2020
Priority date	Dec 13, 2019
Publication date	Dec 30, 2025
Grant date	Dec 30, 2025

Abstract

Disclosed is a box-regularized particle filtering process which includes an Epanechnikov kernel smoothing step. For this purpose, the process uses a special method for generating random numbers that follow an Epanechnikov probability density function. The process can be performed autonomously in a navigation system using correlation measurement, in particular on board an aircraft such as an aircraft, a flying drone or any self-propelled aerial carrier.

First claim

The invention claimed is:

1 . A box-regularized particle filtering method, for predicting a state of a system by a set of state intervals with weights associated with said state intervals, to form a probability distribution that characterizes the state of the system, said system being a land, air, sea or space vehicle that is provided with a navigation system using measurement correlation, the method comprising:
iteratively measuring accelerations and angular velocities of the vehicle using an inertial system to obtain measurements of accelerations and angular velocities used to obtain the set of state intervals of the vehicle, each of the set of state intervals comprising position, speed and attitude coordinates of said vehicle; and repetitively applying a sequence of steps to the set of state intervals with the associated weights for updating the state intervals and said associated weights, the sequence of steps comprising a smoothing step that consists in modifying at least one of the state intervals by applying random modifications to one of: (i) a set of interval bounds, and (ii) center values and interval lengths, that determine the state interval according to state coordinates of the system in order to correct at least one drift of the inertial system by using measurement correlation between the set of state intervals and the updated set of state intervals, wherein the random modifications relating to each state interval to be modified, which is identified by an integer index i, are determined by:
generating a first random value, denoted β i and comprised between 0 and 1, the values 0 and 1 being permitted, according to a statistical-distribution beta law with a first parameter equal to d and a second parameter equal to 2, where d is a number of state coordinates of the system,
generating 2·d second random values, denoted ν k,i , each according to a normal statistical distribution law with zero mean value and standard deviation equal to unity, where k is another integer index that varies from 1 to 2·d and identifies the interval bounds, or center values and interval lengths, for each state interval,
calculating a first number, denoted ξ i , according to the first formula: ξ i =[Σ k=1 to 2·d (ν k,i ) 2 ] 1/2 ,
calculating a second number, denoted α i , according to the second formula: α i =β i 1/2 /ξ i , and
calculating 2·d third numbers, denoted ε k,i , according to the third formula: ε k,i =ν k,i ·α i , and
wherein the random modifications that are applied to the state interval i are proportional to the 2·d third numbers ε k,i , with a proportionality coefficient that is non-zero and common to said random modifications.

2 . The method according to claim 1 , wherein, all the interval bounds, or center values and interval lengths, which determine the state interval i, are modified by:
combining the random modifications that relate to said state interval i using a square matrix of dimension 2·d, to obtain 2·d combinations of random modifications, and then adding said combinations of random modifications that are obtained one-to-one to the interval bounds, or center values and interval lengths, of the state interval i.

3 . The method according to claim 2 , wherein the matrix that is used to combine the random modifications is such that the product of said matrix multiplied by a transpose of said matrix is equal to a mean product matrix, said mean product matrix being square of dimension 2·d, and having as coefficients mean values that are calculated over all the state intervals, of products of the interval bounds, or center values or interval lengths, taken in pairs separately for each state interval.

4 . The method according to claim 3 , wherein each first random value β i is generated using an algorithm that combines:
a generation of two random numbers each according to a uniform statistical distribution law, and
at least one acceptance criterion that is based on the two random numbers, such that, in a case in which said at least one acceptance criterion is satisfied, a first of the two random numbers is used to calculate the first value β i , and in a case in which the at least one acceptance criterion is not satisfied, the generation of the two random numbers is recommenced.

5 . The method according to claim 3 , wherein each second random value ν k,i is calculated as a sum of several initial random values, each of said initial random values being generated according to a uniform statistical distribution law.

6 . The method according to claim 2 , wherein each first random value β i is generated using an algorithm that combines:
a generation of two random numbers each according to a uniform statistical distribution law, and
at least one acceptance criterion that is based on the two random numbers, such that, in a case in which said at least one acceptance criterion is satisfied, a first of the two random numbers is used to calculate the first value β i , and in a case in which the at least one acceptance criterion is not satisfied, the generation of the two random numbers is recommenced.

7 . The method according to claim 2 , wherein each second random value ν k,i is calculated as a sum of several initial random values, each of said initial random values being generated according to a uniform statistical distribution law.

8 . The method according to claim 1 , wherein each first random value Bi is generated using an algorithm that combines:
a generation of two random numbers each according to a uniform statistical distribution law, and at least one acceptance criterion that is based on the two random numbers, such that, in a case in which said at least one acceptance criterion is satisfied, a first of the two random numbers is used to calculate the first value β i , and in a case in which the at least one acceptance criterion is not satisfied, the generation of the two random numbers is recommenced.

9 . The method according to claim 8 , wherein each of the two random numbers is generated using a method of the shift register type with linear feedback.

10 . The method according to claim 9 , wherein each second random value ν k,i is calculated as a sum of several initial random values, each of said initial random values being generated according to a uniform statistical distribution law.

11 . The method according to claim 8 , wherein each second random value ν k,i is calculated as a sum of several initial random values, each of said initial random values being generated according to a uniform statistical distribution law.

12 . The method according to claim 1 , wherein each second random value ν k,i is calculated as a sum of several initial random values, each of said initial random values being generated according to a uniform statistical distribution law.

13 . The method according to claim 1 , wherein respective estimations of each first number ξ i and of each second number α i are obtained, where X is a positive or zero variable number and α is an exponent value equal to 2 or ½, by:
writing the number X in the form X=(1+m)·2 ex , where ex is a negative, positive or zero integer, and m is a mantissa comprised between 0 and 1, the value 0 and being permitted, so that a binary representation of the number X is:
I(X)=L·(m+ex+B), where L=2 n with n being a number of bits of a binary writing of the mantissa m, and B being a positive or zero constant number, referred to as bias,
calculating a binary representation of X α in the form:
I(X α )=α·I(X)+L·(1−α)·(B−σ), where σ is a constant number the value of which is recorded, and
obtaining the estimation of the value of X α from the binary representation

Assignees

• Office National Detudes Rech Aerospatiales

Inventors

• Merlinge Nicolas
• Audebert Clément
• Dahia Karim
• Herisse Bruno
• Allard Jean-Michel

Classifications

• G06F17/18

  for evaluating statistical data {, e.g. average values, frequency distributions, probability functions, regression analysis (forecasting specially adapted for a specific administrative, business or logistic context G06Q10/04)} · CPC title

• G06F7/584

  using finite field arithmetic, e.g. using a linear feedback shift register · CPC title

• G06F18/2415

  based on parametric or probabilistic models, e.g. based on likelihood ratio or false acceptance rate versus a false rejection rate · CPC title

• G06N20/10 Primary

  using kernel methods, e.g. support vector machines [SVM] · CPC title

• G01C21/165 Primary

  combined with non-inertial navigation instruments · CPC title