Methods and devices for determining the impulse response of propagation channels involving emitters, reflectors and sensors that are fixed or mobile

A method for determining one or more parameters of an impulse response of a propagation channel involving emitters, reflectors or sensors that are fixed or mobile, and for detecting and for determining the position and kinematic parameters of the emitters and reflectors, in a system comprising N sensors configured to receive signals from said emitters or reflections from said reflectors, with N being an integer greater than or equal to 2, the method comprising:

• determining an ambiguity function based on coupling of a spatial analysis and a delay-distance/Doppler-kinematic analysis;
• determining at least one sufficient statistic Ĉ(l,m,K) corresponding to a correlation between a known signal s(kTe) corresponding to a complex envelope of an emitted signal that is subjected to a transformation associated with assumptions regarding the positions and kinematic parameters of the emitters, reflectors and sensors and regarding fluctuations of propagation, and an output of a space filter w(l,m), where l symbolizes a set of temporal assumptions reduced to a delay or a distance and m symbolizes a set of frequency assumptions reduced to a Doppler or a relative speed, wherein:
• the space filter w(l,m) is input observations xm((k+1)Te), where 0≦k≦K−1 and Te is a sampling period of the sensor receiving the signals,
• values of the pair (l,m) are determined by comparing a value of a statistic for the pair (l,m) with a detection threshold value, and
• m indexes variables xm and rxms;
• and
• for each delay assumption l and each Doppler assumption m:
• estimating the vector {circumflex over (r)}xms(lTe) from K samples s(kTe) from the emitted signal and from the K samples that are offset in frequencies, where xm((k+l)Te)=x((k+l)Te)exp[−j2πm(k+l)/K], 0≦k≦K−1;
• estimating the matrix {circumflex over (R)}xm(lTe) from the K samples that are offset in frequencies, where xm((k+l)Te)=x((k+l)Te)exp, 0≦k≦K−1;
• calculating the sufficient statistic according to
• Ĉ(l,m,K)(1/{circumflex over (π)}s){circumflex over (r)}xms(lTe)†{circumflex over (R)}xm(lTe)−1{circumflex over (r)}xms(lTe), where {circumflex over (π)}s
• is defined by a least squares estimate of an average power of the K samples;
• setting the detection threshold for a predetermined false alarm probability;
• comparing the sufficient statistic Ĉ(l,m,K) with the detection threshold and, if the sufficient statistic Ĉ(l,m,K) exceeds the detection threshold, ordering detection of the emitter or of the reflector in the distance/Doppler pair (l, m);
• estimating a relative delay and distance of the emitter or of the reflector based on the temporal assumptions symbolized by l;
• estimating a relative Doppler and speed of the emitter or of the reflector based on the frequency assumptions symbolized by m;
• and
• estimating a spatial cell of the emitter or of the reflector from a directing vector ĥs on an antenna of the emitted signal, the directing vector ĥs being defined.