Analytical estimation of performance of a sensor system

• US 7,167,810 B2
• Filed: 07/12/2002
• Issued: 01/23/2007
• Est. Priority Date: 08/06/2001
• Status: Active Grant

• Current Assignee: Telefonaktiebolaget LM Ericsson
• Original Assignee: Telefonaktiebolaget LM Ericsson
• Inventors: Kronhamn, Thomas, Andersson, .ANG.ke
• Primary Examiner(s): Assouad; Patrick J
• Application Number:
  US10/485,806
• Publication Number:
  US 20040243344A1
• Time in Patent Office: 1,656 Days
• Field of Search: None
• US Class Current: 702/182
• CPC Class Codes: G01S 13/726 Multiple target tracking
• CPC Class Codes: G01S 7/4004 of parts of a radar system

Abstract

The invention relates to a method for an analysis tool for analysis of the sensor performance of a system of sensors, which method comprises analytical calculation of a sensor system'"'"'s measurement characteristics at each point in a given geographical area. The method comprises obtaining performance parameters from N sensors that are in the system. The method is characterized in that a set of analytical performance parameters for the system is calculated by the performance parameters being fused irrespective of the different measurement characteristics of the sensors in the system with regard to the given performance parameters and in that the analytical parameters are used in the analysis of the performance of the sensor system. The invention also relates to a device for use of the method and to the use of the method and the device.

Claims

1. A method for analyzing performance of a system of sensors, which method comprises analytical calculation of a sensor system'"'"'s measurement characteristics at each point in a given geographical area, the method comprising:

obtaining performance parameters from N_S sensors that are in the system, the performance parameters comprising;

p_ss,j=a detection probability per scan for targets with a particular target area for the sensor N_S=i;

R_j=measurement accuracy expressed as a covariance matrix for the sensor N_S=i;

T_j=searching time for a search area for the sensor N_S=i, and;

P_fa,j=a probability of false alarms for a sensor N_s=i;

calculating a set of analytical performance parameters for the system using the performance paramaeters being fused, the calculating of the analytical performance parameters being performed irrespective of different measurement charictaristics of the sensor in the system, the calculating of the analytical performance parameters including evaluating the following expressions;

$\begin{array}{cc}{T}_j={\left(\underset{i=1}{\overset{N_S}{\sum <br><br>}}<br><br><br><br>T_i^{-1}\right)}^{-1}& \left(7<br><br>\text{-}<br><br>2\right)\\ \frac{1}{T_{e<br><br><br><br>j}}=\underset{i=1}{\overset{N_S}{\sum <br><br>}}<br><br>\frac{p_{s<br><br><br><br>s,i}}{T_i}<br><br>& \left(7<br><br>\text{-}<br><br>3\right)\\ p_{s<br><br><br><br>s,j}=\frac{T_j}{T_{e<br><br><br><br>j}},<br><br>& \left(7<br><br>\text{-}<br><br>4\right)\\ \frac{1}{T_{e<br><br><br><br>i}}=\frac{p_{s<br><br><br><br>s,i}}{T_i}<br><br>& \left(7<br><br>\text{-}<br><br>5\right)\\ <br><br>{\mathrm{\mu <br><br>}}_i=\frac{T_{e<br><br><br><br>j}}{T_{e<br><br><br><br>i}}<br><br>& \left(7<br><br>\text{-}<br><br>6\right)\\ <br><br>R_j={\left\{\underset{i=1}{\overset{N_S}{\sum <br><br>}}<br><br>{\mathrm{\mu <br><br>}}_i<br><br>R_i^{-1}\right\}}^{-1}<br><br>& \left(7<br><br>\text{-}<br><br>7\right)\\ <br><br>p_{f<br><br><br><br>a,j}=\left\{\underset{i=1}{\overset{N_s}{\sum <br><br>}}<br><br>\frac{p_{f<br><br><br><br>a,i}}{T_i}\right\}<br><br>T_j& \left(7<br><br>\text{-}<br><br>8\right)\end{array}$

where

$T_j,\frac{1}{T_{e<br><br><br><br>j}},$

p_ss,j, μ

_i, R_j and p_fa,j comprise the analytical performance parameters, where N_s stands for the number of sensors in the system, and where the subscript j stands for joint;

using the analytical performance parameters for analysis of the sensor system'"'"'s performance.

2. The method according to claim 1, wherein probabilities for different events that concern a tracking procedure are calculated by using a calculated measurement rate,

$\frac{1}{T_j},$

the detection probability, p_ss,jand the probability of false alarms, p_fa,j, for the sensor system together with Markov analysis.

3. The method according to claim 1, wherein a filter for the sensor system is calculated by using a calculated effective measurement rate,

$\frac{1}{T_{\mathrm{ej}}},$

for the system.

4. The method according to claim 3, wherein:

the expressions are used to calculate the sensor system'"'"'s measurement characteristics in order to calculate with a filter the sensor system'"'"'s tracking performance for tracking measured objects;

the filter for the system gives a covariant matrix, P, which is read off as a covariance matrix that gives the tracking accuracy of the sensor system at each point in a given area.

5. The method according to claim 3, wherein the sensor system'"'"'s stationary characteristics are calculated by a filter'"'"'s stationary state being calculated at each point over a given area, which calculation comprises the expression.

6. The method according to claim 3, wherein the sensor system'"'"'s dynamic characteristics are calculated by a filter being calculated based on parallel target paths of a target with given values of speed and course, which calculation also comprises the expression.

7. The method according to claim 1, wherein an adaptive sensor is regarded as a sensor system.

8. A device for analytical calculation of a sensor system'"'"'s performance, the sensor system comprising N_S sensors, the device comprising:

means for combining performance parameters in the form of measurement characteristics from the respective sensors, the performance parameters comprising;

p_ss,j=a detection probability per scan for targets with a particular target area for the sensor N_S=i;

R_i=mearsurement accuracy expresses as a covariance matrix for the sensor N_S=i;

T_i=searching time for a search area for the sensor N_S=i, and;

p_fa,j=a probability of false alarms for a sensor N_s=i;

means for fusing the performance parameters by weighting measurement contributions of the respective said sensorsr;

means for calculating analytical performance parameters for the sensor system, independently of different measurement characteristics of the sensors in the system the calculating of the analytical performance parameters including evaluating the following expression;

$\begin{array}{cc}{T}_j={\left(\underset{i=1}{\overset{N_S}{\sum <br><br>}}<br><br><br><br>T_i^{-1}\right)}^{-1}& \left(7<br><br>\text{-}<br><br>2\right)\\ \frac{1}{T_{e<br><br><br><br>j}}=\underset{i=1}{\overset{N_S}{\sum <br><br>}}<br><br>\frac{p_{s<br><br><br><br>s,i}}{T_i}<br><br>& \left(7<br><br>\text{-}<br><br>3\right)\\ p_{s<br><br><br><br>s,j}=\frac{T_j}{T_{e<br><br><br><br>j}},<br><br>& \left(7<br><br>\text{-}<br><br>4\right)\\ \frac{1}{T_{e<br><br><br><br>i}}=\frac{p_{s<br><br><br><br>s,i}}{T_i}<br><br>& \left(7<br><br>\text{-}<br><br>5\right)\\ <br><br>{\mathrm{\mu <br><br>}}_i=\frac{T_{e<br><br><br><br>j}}{T_{e<br><br><br><br>i}}<br><br>& \left(7<br><br>\text{-}<br><br>6\right)\\ <br><br>R_j={\left\{\underset{i=1}{\overset{N_S}{\sum <br><br>}}<br><br>{\mathrm{\mu <br><br>}}_i<br><br>R_i^{-1}\right\}}^{-1}<br><br>& \left(7<br><br>\text{-}<br><br>7\right)\\ <br><br>p_{f<br><br><br><br>a,j}=\left\{\underset{i=1}{\overset{N_s}{\sum <br><br>}}<br><br>\frac{p_{f<br><br><br><br>a,i}}{T_i}\right\}<br><br>T_j& \left(7<br><br>\text{-}<br><br>8\right)\end{array}$

where

$T_j,\frac{1}{T_{e<br><br><br><br>j}},$

p_ss,j,μ

_i, R_i and p_fa,i comprised the analyticcal performance parameters, where N_Sstands for the number of sensors in the system, and where the subscript j stands for joint; and

means for using the analytical performance parameters for analysis of the sensor systems'"'"'s performance.

9. The device according to claim 8, further comprising means for calculating a filter'"'"'s stationary state at each point over a given area.

10. The device according to claim 8, further comprising means for calculating a filter'"'"'s dynamic characteristics on the basis of parallel target paths for a target with given values for speed and course.

11. The device according to claim 8, wherein at least one of the sensors in the sensor system is a passive sensor.

12. The device according to claim 8, wherein at least one of the sensors in the sensor system is an active sensor.

13. The device according to claim 8, wherein at least one of the sensors in the sensor system is an adaptive sensor.

14. The device according to claim 8, wherein at least one of the sensors in the sensor system is a radar unit.

15. A computer program product comprising instructions stored on computer-readable memory which, when executed perform the steps of:

obtaining performance parameters from N_S sensors that are in a sensor system, the performance parameters comprising;

p_ss,i=a detection probability per scan for targets with a particular target area for the sensor N_S=i;

R_i=measurement accuracy expressed as a covariance matrix for the sensor N_S=i;

T_i=searching time for a search area for the sensor N_S=i, and;

P_fa,i=a probability of false alarms for a sensor N_S=i;

calculating a set of analytical performance parameters for the system using the performance parameters being fused, the calculating of the analytical performance parameters being performed irrespective of different measurement characteristics of the sensors in the system, the calculating of the analytical performance parameters including evaluating the following expressions;

$\begin{array}{cc}{T}_j={\left(\underset{i=1}{\overset{N_S}{\sum <br><br>}}<br><br><br><br>T_i^{-1}\right)}^{-1}& \left(7<br><br>\text{-}<br><br>2\right)\\ \frac{1}{T_{e<br><br><br><br>j}}=\underset{i=1}{\overset{N_S}{\sum <br><br>}}<br><br>\frac{p_{s<br><br><br><br>s,i}}{T_i}<br><br>& \left(7<br><br>\text{-}<br><br>3\right)\\ p_{s<br><br><br><br>s,j}=\frac{T_j}{T_{e<br><br><br><br>j}},<br><br>& \left(7<br><br>\text{-}<br><br>4\right)\\ \frac{1}{T_{e<br><br><br><br>i}}=\frac{p_{s<br><br><br><br>s,i}}{T_i}<br><br>& \left(7<br><br>\text{-}<br><br>5\right)\\ <br><br>{\mathrm{\mu <br><br>}}_i=\frac{T_{e<br><br><br><br>j}}{T_{e<br><br><br><br>i}}<br><br>& \left(7<br><br>\text{-}<br><br>6\right)\\ <br><br>R_j={\left\{\underset{i=1}{\overset{N_S}{\sum <br><br>}}<br><br>{\mathrm{\mu <br><br>}}_i<br><br>R_i^{-1}\right\}}^{-1}<br><br>& \left(7<br><br>\text{-}<br><br>7\right)\\ <br><br>p_{f<br><br><br><br>a,j}=\left\{\underset{i=1}{\overset{N_s}{\sum <br><br>}}<br><br>\frac{p_{f<br><br><br><br>a,i}}{T_i}\right\}<br><br>T_j& \left(7<br><br>\text{-}<br><br>8\right)\end{array}$

where

$T_j,\frac{1}{T_{e<br><br><br><br>j}},$

p_ss,j, μ

_i, R_j and p_fa,j comprise the analytical performance parameters, where N_S stands for the number of sensors in the system, and where the subscript j stands for joint.