WO2011033291A1 - Processing of object detection signals - Google Patents

Processing of object detection signals Download PDF

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Publication number
WO2011033291A1
WO2011033291A1 PCT/GB2010/051532 GB2010051532W WO2011033291A1 WO 2011033291 A1 WO2011033291 A1 WO 2011033291A1 GB 2010051532 W GB2010051532 W GB 2010051532W WO 2011033291 A1 WO2011033291 A1 WO 2011033291A1
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Prior art keywords
remote sensing
return
return remote
pulses
sensing pulse
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PCT/GB2010/051532
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French (fr)
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Peter Graham Challenor
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University Of Southampton
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/95—Radar or analogous systems specially adapted for specific applications for meteorological use
    • G01S13/958—Theoretical aspects
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/66—Radar-tracking systems; Analogous systems
    • G01S13/72—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar
    • G01S13/723—Radar-tracking systems; Analogous systems for two-dimensional tracking, e.g. combination of angle and range tracking, track-while-scan radar by using numerical data
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/882—Radar or analogous systems specially adapted for specific applications for altimeters
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/95—Radar or analogous systems specially adapted for specific applications for meteorological use
    • G01S13/955—Radar or analogous systems specially adapted for specific applications for meteorological use mounted on satellite
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/28—Details of pulse systems
    • G01S7/2806—Employing storage or delay devices which preserve the pulse form of the echo signal, e.g. for comparing and combining echoes received during different periods
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/28—Details of pulse systems
    • G01S7/285—Receivers
    • G01S7/292—Extracting wanted echo-signals
    • G01S7/2923—Extracting wanted echo-signals based on data belonging to a number of consecutive radar periods
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/28—Details of pulse systems
    • G01S7/285—Receivers
    • G01S7/288—Coherent receivers
    • G01S7/2883—Coherent receivers using FFT processing
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/28—Details of pulse systems
    • G01S7/285—Receivers
    • G01S7/32—Shaping echo pulse signals; Deriving non-pulse signals from echo pulse signals
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A90/00—Technologies having an indirect contribution to adaptation to climate change
    • Y02A90/10—Information and communication technologies [ICT] supporting adaptation to climate change, e.g. for weather forecasting or climate simulation

Abstract

A method of processing return remote sensing pulses comprising using Bayes Linear statistics to modify a return remote sensing pulse in light of at least one of data relating to at least one previously processed return remote sensing pulse and data governing the return remote sensing pulse shape/parameters.

Description

PROCESSING OF OBJECT DETECTION SIGNALS
Technical Field
The present invention relates generally to processing of object detection signals, and in particular, although not exclusively, to methods for tracking/re-tracking waveforms from radar altimeters or similar remote sensing instruments .
Background
A radar altimeter is a satellite (or aircraft) remote sensing instrument that measures the height of the satellite above the Earth's surface by transmitting a narrow pulse of radar energy from the satellite to the Earth and measuring the time it takes to return to the satellite. Reflections from the crests of the waves return earlier than the mean sea surface, whereas reflections from wave troughs come back later. It will be appreciated that the pulse is in fact a chirp in the frequency domain and that the waveform which is analysed is the Fourier transform of the returned pulse.
The shape of the pulse is modified in the reflection process (for example by its interaction with the sea surface) and contains information on other geophysical parameters, such as the significant wave height and wind speed over the ocean. These observations are used to derive geophysical parameters such as sea surface height, significant wave height and wind speed. The applications of these parameters include the calculation of gravity over the ocean, geostrophic ocean currents, tides and sea state for safety at sea and design conditions. Obtaining estimates of these parameters from the radar returns involves tracking (or re- tracking if done off-line) the radar returns (or waveforms) . This process involves fitting a theoretical model of the expected waveform shape to the recorded waveform. This is currently done mainly by least-squares or maximum likelihood on single waveforms.
Currently, each waveform (the averaged radar return received at the satellite or aircraft) is tracked separately. No external or pre-existing information about what we expect its parameters to be is used. This does not exploit the fact that we know that the properties on the Earth's surface are continuous, for example we know that sea surface height or significant wave height varies smoothly across the ocean. There may also be external information for example model forecasts or other satellite instruments that we wish to include in the processing of the reflected pulses. We have appreciated that by not considering such information the current estimates of satellite altitude, significant wave height etc are not as accurate as they could be. We have in particular appreciated that there is information about the value of the parameters that govern the waveform shape which comes either from other waveforms previously tracked or from external sources, such as weather forecasting models or other satellite instruments. Broadly, a preferred embodiment of the invention may be viewed as a method to utilise this information using Bayes Linear methods in the tracking/re-tracking of the waveforms.
Summary According to a first aspect of the invention there is provided a method of processing return remote sensing pulses comprising using Bayes Linear statistics to modify a return remote sensing pulse in light of at least one of data relating to at least one previously processed return remote sensing pulse and data governing the return remote sensing pulse shape/parameters. According to a second aspect of the invention there is provided a data processor arranged to process return remote sensing pulses, the processor configured to use Bayes Linear statistics to modify a return remote sensing pulse in light of at least one of data relating to a previously processed remote sensing pulse and data governing the return remote sensing pulse shape/parameters.
According to a third aspect of the invention there are provided machine readable instructions for execution by a data processor, the instructions such that the processor operative to use Bayes Linear statistics to modify a return remote sensing pulse in light of at least one of data relating to a previously processed return remote sensing pulse and data influential on the return remote sensing pulse shape/parameters.
Brief description of the drawings Various embodiments of the invention will now be described, by way of example only, with reference to the following drawings in which:
Figure 1 is a flow diagram,
Figure 2 is a plot of a prior waveform,
Figure 3 is a plot of return data, Figure 4 is a plot of posterior data, and
Figure 5 is a flow diagram.
Detailed description
Below is described one embodiment of the invention using the Bayes Linear Update. The overall aim to include information from previous waveforms in the tracking of the ith. Moreover, this is to be achieved without inducing spurious correlation that would come from conventional smoothing where we perform a weighted average along track. There are two forms of uncertainty in the return signal. First there is thermal noise. This is the signal that would be received if we transmitted nothing and is the background radiation at the radar frequency. It can be described as white (but non-Normal) noise within the pulse and is independent from pulse to pulse. The second source of noise is the fading noise. This is the noise on the actual received signal. For a single pulse this is an exponential distribution. To reduce the variance, a number of pulses are averaged to give a single mean waveform.
In Bayes Linear methods we use a version of Bayes theorem that only updates the first two moments (means and variances) rather than the full portability distribution. This is given by this pair of matrix equations:
Figure imgf000005_0001
Where:
E(0|w) is the (adjusted) expectation, V(0|w) is the (adjusted) variance matrix,
0 is a vector of the parameters,
E(0 is our prior expectation for the geophysical parameters before we see the data. This will come from previously analysed waveforms or from external sources or a combination (e.g. a weighted mean) of both w is the measured waveform as a vector, with the value at bin τ with w(z) . w(Q) is the theoretical waveform (for example the Brown model).
V(0) is the variance (as a measure of uncertainty) of the estimates
V(w(0)) is the variance matrix of the theoretical waveform. If we assume a Gamma distribution for the waveform values this is w (0)/«. Normally we assume that the individual bins are uncorrelated so this is a diagonal matrix with diagonal terms given by win or E(w(Q))/n (where n is the number of pulses averaged in creating the waveform being tracked), n typically being 20 to 100.
Cov (0, w(0)) is the covariance matrix between 0 and the theoretical waveform values. Cov (w (0),0) = Cov (0, w(0))T E(w(0)) is the expected value of the waveform.
Looking at each term in (2) , the first term is our prior expectation of the values of the parameters or in other words our belief about the value of the parameters before we collect the waveform. The second term relates to how these beliefs are modified by the data. This (second) term has three components. Starting from the right we have (w- E(w(Q)) . This is the difference between the measured value waveform (w) and our expectation of the waveform E(w(Q)) . This difference is weighted by its variance V(w(0)) . This weighted difference is in the space of the waveform so we need to convert this into a correction in 0 space. This is achieved by multiplying by the Cov (0,w(0)) , which can be thought as the amount that 0 changes for a given change in w.
Two terms, E(w(0)) and Cov (0,w(0)) , need to be further expanded using a scaled Taylor series expansion, as shown in the Appendix. An example is now shown of use of the Bayes Linear Update using a simplified form of the full Brown model. This has four parameters: σ0 (the amplitude of the waveform) , h( the position of the waveform in the window = the sea surface height), Hs (the slope of the leading edge = the significant wave height) and tn the thermal noise. The simplified model is given by:
(Note we have dropped the Θ from w and replaced it with a τ (to represent time) in this section for clarity) .
Figure imgf000007_0001
Erf ( ) is defined by:
Figure imgf000007_0002
V (W(T)) is equal to E(w( ))/np where np is the number of radar pulses averaged into a single waveform. Giving w(x) a χ2 distribution with np degrees of freedom.
For the Taylor series approximation to the moments we need to have the gradient and Hessian of the waveform with respect to each of the parameters. For a particular value of τ these are given by:
Figure imgf000007_0003
Figure imgf000008_0001
Figure imgf000009_0001
Reference is now made to Figure 1 which is a flow diagram 100 showing a simplified exposition of how the Bayes Linear Update methodology is implemented by a data processor executing suitable machine-readable instructions. As can be seen, the process is essentially cyclic, with previous predicted values being used to modify a subsequent return signal. In this way, each predicted value takes account of previous predicted values. At step 101, the previous predicted waveform shape, referred to as the posterior, is assigned as the prior for the next received return data. As shown at step 102, the process of determining the next predicted waveform then commences. At step 103, the next return pulse of radar data is determined. At step 104, the pulse is modified by using equations (2) and (3) and the posterior to determine a predicted waveform and uncertainty, given by expectation and variance, respectively. These values then form the (new) posterior values. The process continues, working through each return pulse sequentially. Reference is now made to Figure 2 which shows an example plot of a prior waveform. The steps shown in Figure 1, combine the prior with the received return data (shown in Figure 3) using equations (2) and (3) to produce the posterior, shown in Figure 4. It will appreciated that although in Figure 1 the process is referred to in relation to waveform shapes, the process can also be performed in relation to the parameters of the waveform, as illustrated in Figure 5 by steps 201 to 205 of flow diagram 200.
Some of the significant advantages of the tracking/re-tracking using the Bayes Linear update methodology are as follows. The method is fast because there is no non-linear optimisation involved, just simple matrix algebra
The method works with any parametric form for a waveform including those used in costal areas, where specular reflections from 'bright' targets may be included
The method provides both estimates and uncertainty on the geophysical parameters.
The method allows statistical tests to be easily constructed to distinguish between different waveform models. This is of particular relevance in coastal analysis where we will want to test for the presence of bright targets.
The method being Bayesian means that it is naturally sequential.
Figure imgf000011_0001

Claims

1. A method of processing return remote sensing pulses comprising using Bayes Linear statistics to modify a return remote sensing pulse in light of at least one of data relating to at least one previously processed return remote sensing pulse and data governing the return remote sensing pulse shape/parameters.
2. A method as claimed in claim 1 which comprises using data resulting from at least an immediately preceding processed return remote sensing pulse.
3. A method as claimed in any preceding claim which comprises modifying the return remote sensing pulse to produce an expectation of the return remote sensing pulse.
4. A method as claimed in claim 4 comprising determining an uncertainty of the expectation of the return remote sensing pulse.
5. A method as claimed in any preceding claim which comprises determining an adjusted expectation of the return remote sensing pulse given by:
Figure imgf000012_0001
in which,
E(0|w) is the adjusted expectation of the return signal, Θ is a vector of geophysical parameters, E(0J is a prior expectation for the geophysical parameters, w is the measured return signal as a vector, w(0) is the theoretical waveform,
V(w(0)) is the variance matrix of the theoretical waveform, E(w(0)) is the expected value of the waveform, and,
Cov (0, w(0)) is the covariance matrix between 0 and the theoretical waveform values
6. A method as claimed in claim 5 which comprises determining a variance of the return the return remote sensing pulse given by
Figure imgf000013_0001
in which,
V(0|w) is an adjusted variance matrix,
V(0(0)) is the variance (as a measure of uncertainty) of the estimates,
Cov (0, w(0)) is the covariance matrix between 0 and the theoretical waveform value. Cov (w (0),0) = Cov (0, w(0))T.
V(w(0)) is the variance matrix of the theoretical waveform,
7. A method as claimed in any preceding claim in which return remote sensing pulses are processed in the sequence in which they are received.
8. A method as claimed in any preceding claim in which the return remote sensing pulses are radar pulses.
9. A method as claimed in any preceding claim comprising processing pulses from radar altimeter pulses.
10. A method as claimed in any preceding claim in which the return remote sensing pulses are pulses which have been reflected from a sea surface.
11. A method as claimed in any preceding claim in which the return remote sensing pulses are pulses which have been reflected from a costal region.
12. A data processor arranged to process return remote sensing pulses, the processor configured to use Bayes Linear statistics to modify a return remote sensing pulse in light of at least one of data relating to a previously processed return remote sensing pulse and data governing the return remote sensing pulse shape/parameters.
13. Machine readable instructions for execution by a data processor, the instructions such that the processor operative to use Bayes Linear statistics to modify a return remote sensing pulse in light of at least one of data relating to a previously processed return remote sensing pulse and data governing the return remote sensing pulse shape/parameters.
PCT/GB2010/051532 2009-09-15 2010-09-13 Processing of object detection signals WO2011033291A1 (en)

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Cited By (2)

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CN102721644A (en) * 2012-06-21 2012-10-10 中国科学院对地观测与数字地球科学中心 Method and device for processing remote sensing data of water environment
CN109581363A (en) * 2018-12-03 2019-04-05 中国电波传播研究所（中国电子科技集团公司第二十二研究所） A kind of detection of small size space junk and parameter extracting method based on incoherent scattering radar

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102721644A (en) * 2012-06-21 2012-10-10 中国科学院对地观测与数字地球科学中心 Method and device for processing remote sensing data of water environment
CN102721644B (en) * 2012-06-21 2014-07-23 中国科学院对地观测与数字地球科学中心 Method and device for processing remote sensing data of water environment
CN109581363A (en) * 2018-12-03 2019-04-05 中国电波传播研究所（中国电子科技集团公司第二十二研究所） A kind of detection of small size space junk and parameter extracting method based on incoherent scattering radar

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