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Reliable Doppler Estimation in Asynchronous Moving ISAC Devices via IMU Integration

Zaman Bhalli, Jacopo Pegoraro, Gianmaria Ventura, Paolo Casari, Michele Rossi

arXiv:2609.39576v1eess.SP

TL;DR

Bistatic Doppler estimation with asynchronous clocks and a mobile transmitter is complicated by clock offsets and transmitter motion, while existing geometric solutions can depend on available static paths. This paper uses an EKF to fuse transmitter IMU readings with wireless channel estimates and jointly estimate target Doppler and transmitter motion. Simulations report median Doppler error below 1.2% for a smartphone-grade IMU and 5° angle-of-departure noise.

  • Problem

    In asynchronous bistatic ISAC with a mobile transmitter, clock offsets and transmitter motion complicate target-Doppler estimation, while geometric solutions can require concurrently available static reference paths.

    Source: §I · p. 1

  • Method

    An EKF tightly couples wireless-channel measurements with transmitter IMU readings to jointly track target Doppler and transmitter speed and orientation.

    Source: §I · p. 1, §III · p. 3

  • Results

    Median Doppler error remains below 1.2% of the true target Doppler with a smartphone-grade IMU (σω = 10−2 rad/s) and 5° angle-of-departure noise.

    Source: §V · p. 6

  • Takeaways & Limitations

    The EKF continues producing estimates when static scatterers are highly intermittent or absent over extended periods, where prior ISAC solutions do not work.

    Source: §V · p. 6

Abstract

from arXiv · show

We present an Integrated Sensing And Communication (ISAC) framework for the joint estimation of the Doppler frequency of a passive mobile target in a bistatic scenario with clock-asynchronous nodes and where the Receiver (RX) is static but the Transmitter (TX) is mobile. In such a setup, previous geometric solutions are integrated with an Inertial Measurement Unit (IMU) device at the TX, coming up with a truly joint data fusion and estimation algorithm based on extended Kalman filtering. The approach jointly estimates the target Doppler frequency, along with the speed and direction of motion of the TX and it is robust to the unavailability of static paths between the TX and RX pair, a condition that makes previous solutions ineffective. The developed extended Kalman filter strikes a balance between the accuracy of ISAC and the IMU reliability. The proposed solution is validated via numerical simulations, obtaining a median Doppler error of 1.2% with a smartphone-grade IMU under realistic operating conditions.

I. INTRODUCTION

The paper addresses target-Doppler estimation in bistatic ISAC with asynchronous clocks and a mobile transmitter, where clock offsets and transmitter motion complicate the path phases. It proposes jointly fusing ISAC measurements and transmitter IMU readings to track the target Doppler and transmitter motion despite intermittent static scatterers.

A. Reference Scenario

  • Asynchronous clocks introduce timing, carrier-frequency, and phase offsets, while transmitter motion adds Doppler to every path and entangles it with target Doppler.The scenario has a mobile transmitter and a static receiver; target and transmitter velocities are independent.Source: §I · p. 1, A. Reference Scenario · p. 2

I. INTRODUCTION

  • Prior work either assumes static devices for asynchronous clocks or uses moving devices in monostatic-like arrangements unaffected by the stated offsets.The proposed setting instead combines a static receiver with a mobile transmitter and asynchronous nodes.Source: §I · p. 1
  • Earlier approaches require enough concurrently available reference paths, including at least two static scatterers or four receivers in the cited geometric solutions.Scatterers can appear and disappear as the scene changes, causing measurement dropouts.Source: §I · p. 1
  • Open-loop IMU integration accumulates bias and drift, while a prior ISAC integration treated IMU speed as known rather than jointly estimating it.The proposed tightly coupled filter lets ISAC and IMU measurements correct one another.Source: §I · p. 1
  • The EKF jointly tracks target Doppler and transmitter speed and orientation, using ISAC and IMU measurements even when no static scatterer paths are available.ISAC re-anchors accumulated IMU drift when scatterers return; IMU measurements sustain estimation between those returns.Source: §I · p. 1

A. Reference Scenario

  • The modeled receiver observes LoS and target paths assumed always available, while up to Ns static-scatterer paths may be absent.The transmitter carries the IMU, and its velocity and orientation contribute Doppler to every path.Source: A. Reference Scenario · p. 2

B. Channel Model

The channel model represents discretized CIR observations as visible-path components affected by phase and timing offsets. Its Doppler geometry separates transmitter-induced shifts on each path from the target Doppler, making transmitter speed and orientation alongside target Doppler the estimation unknowns.

B. Channel Model

  • The CIR model includes the LoS and target paths plus whichever static-scatterer paths are visible; only LoS and target paths need to be identified separately from static paths.The CIR is estimated from 5G NR DM-RS pilots and converted from CFR by IDFT at period T.Source: B. Channel Model · p. 2

C. Doppler Geometry

  • The path phase includes transmitter Doppler and common CFO, while target Doppler contributes only on the target path.The transmitter-induced Doppler differs by path because the transmitter is the common origin of the propagation paths.Source: B. Channel Model · p. 2, C. Doppler Geometry · p. 2
  • The transmitter-induced shift depends on transmitter speed and the angle between its velocity and each path; for LoS, that angle is the transmitter orientation η.The target Doppler remains a single quantity rather than being expanded into geometric components; fd, v, and η are jointly estimated.Source: C. Doppler Geometry · p. 2

D. Measured Phase Model

The measured phase model tracks Doppler through path-phase changes while accounting for clock offsets and residual noise; static-scatterer phases are available only when those paths are visible. The transmitter IMU supplies noisy yaw-rate and acceleration samples that are integrated from an initialized speed and orientation.

D. Measured Phase Model

  • The phase model combines a common phase term for phase and carrier-frequency offsets with path-specific Doppler contributions and residual noise.Path-amplitude phase is treated as constant over a sufficiently short time window; scatterer paths are intermittent, unlike LoS and target paths.Source: D. Measured Phase Model · pp. 2–3

E. IMU Modeling

  • A rigidly mounted 9-DoF IMU measures transmitter yaw rate and longitudinal acceleration under a 2D motion model.Its discrete samples include noise and slowly varying biases; the biases are modeled as random walks.Source: E. IMU Modeling · p. 3
  • The IMU quality is parameterized by gyroscope noise, with the other noise terms scaled from it.The stated scaling is σa = 10 σω and σb,x = σx/10 for x ∈ {ω, a}.Source: E. IMU Modeling · p. 3
  • Open-loop integration yields speed and orientation estimates whose errors combine initialization error with accumulated error that increases over time.The initial speed and orientation estimates are obtained by averaging noisy GNSS speed-over-ground and magnetometer readings collected during a boot interval.Source: E. IMU Modeling · p. 3

F. Noise Characterization

The filter must balance ISAC phase errors against IMU errors, which have different characteristics. ISAC phase reliability depends on path strength, while open-loop IMU error accumulates over time.

F. Noise Characterization

1) ISAC Phase Noise:

  • ISAC phase noise stems from CIR estimation noise and is modeled as Gaussian.The phase-noise variance depends on path amplitude and is anchored to the LoS because the estimated CIR scale is arbitrary and only amplitude ratios are identifiable.Source: 1) ISAC Phase Noise · p. 3
  • Stronger paths carry cleaner extracted phases, so the phase measurements are not equally reliable.The stated model uses communication SNR measured on the LoS as its reference.Source: 1) ISAC Phase Noise · p. 3

2) IMU Noise:

The IMU error model treats the heading and speed errors as uncorrelated because they arise from separate sensor noise and integration chains.

2) IMU Noise:

  • The ηimu and vimu errors are mutually uncorrelated because separate gyroscope and accelerometer noise and integration chains feed them.t is the time since the last fix in the accuracy expressions.Source: 2) IMU Noise · p. 3

III. METHODOLOGY

The methodology generates ISAC and IMU measurements, then fuses them in an EKF. Its ISAC measurements use path-phase differences and AoD-based geometry, but framewise geometric solving requires at least two visible scatterers.

III. METHODOLOGY

  • The core method generates ISAC and IMU measurements in separate chains and fuses both through an EKF.The ISAC chain reduces estimated CIR to phase measurements; the IMU chain produces samples through open-loop integration.Source: §III · p. 3

A. ISAC Measurements

  • Referencing each CIR path phase to LoS and differencing adjacent frames cancels common phase offset and CFO, while path-length phase cancels under short-window constancy.Of the extracted phases, Ns[k] + 1 remain useful.Source: A. ISAC Measurements · pp. 3–4
  • The working equation reexpresses per-path geometry through measured AoDs and TX orientation, while target Doppler appears only in the target row.Source: A. ISAC Measurements · p. 4
  • Framewise geometric solving requires at least three equations, equivalent to Ns[k] ≥ 2 visible scatterers; the IMU fusion addresses this constraint.Source: A. ISAC Measurements · p. 4

B. ISAC–IMU Fusion via Extended Kalman Filter

The EKF tracks target Doppler and TX motion by combining ISAC and IMU measurements over time. Its updates account for correlated ISAC rows and changing scatterer visibility.

B. ISAC–IMU Fusion via Extended Kalman Filter

A. Simulation Setup

The simulations use standard-compliant 5G NR uplink reference signals in a Python simulator, with modeled channel, reflector, and receiver-processing conditions.

A. Simulation Setup

  • The Python simulator uses standard-compliant 5G NR PUSCH DM-RSs generated with MATLAB 5G TOOLBOX, transmitting one DM-RS per slot.Source: A. Simulation Setup · p. 5
  • Reflectors are moving point targets with lognormal RCS, and the channel uses AWGN at −174 dBm/Hz with 200 mW TX power.Source: A. Simulation Setup · p. 5
  • The RX estimates channels by least squares, interpolates unused subcarriers, adds CFO and PO, and supplies path phases plus AoDs with Gaussian error; scatterers appear in bursts.Source: A. Simulation Setup · p. 5

B. Simulation Results

The simulations examine how AoD noise, node speeds, IMU grade, and frame period affect normalized Doppler error. Error increases with larger AoD noise and longer frame periods, while target-speed increases leave absolute Doppler error unchanged.

B. Simulation Results

1) Impact of the AoD noise:

  • At σα≤2°, median Doppler error stays below 0.5%, rising to 4.3% at 10° and 15% at 20°; the 5° default yields 1.1%.The angular information collapses path geometry onto TX orientation.Source: 1) Impact of the AoD noise · p. 5, Figure 3 · p. 5

2) Impact of the TX and Target speeds:

3) Impact of the IMU grade:

  • Across two decades of IMU grade, median Doppler, TX-speed, and orientation errors shift from 1.1% to 1.8%, 0.7% to 2.0%, and 0.05% to 0.17%, respectively.A smartphone-class IMU is sufficient for the proposed solution.Source: 3) Impact of the IMU grade · pp. 5–6, Figure 4 · p. 5
  • As frame period increases from 0.125 to 1 ms, median Doppler error rises from 1.2% to 13.6%.Longer intervals mean fewer phase updates and miss visibility bursts shorter than T, reducing scatterer rows that re-anchor IMU drift.Source: 4) Impact of the frame period · p. 6, Figure 5 · p. 6

4) Impact of the frame period:

The EKF remains usable when scatterers are intermittent or absent, while combining ISAC accuracy with an available IMU track. Simulations report median Doppler error below 1.2% under typical settings with a smartphone-grade IMU.

4) Impact of the frame period:

  • The visibility experiment varies scatterer presence from 0% to 100% and uses Ns = 2, the minimum required to solve the system in (9).The experiment adopts σω = 10−1 rad/s for the IMU.Source: 4) Impact of the frame period · p. 6
  • Median εfd falls from 0.7% at 0% visibility (IMU alone) to 0.4% at full visibility, with estimates available at every visibility level.Visibility below 100% yields no solution in the existing methods,.Source: 4) Impact of the frame period · p. 6

6) Comparison against the ISAC and IMU baseline:

  • The baseline comparison tests the proposed method against ISAC and IMU solutions over 2 s, with 50% scatterer visibility and unavailability periods of 50–500 ms.The IMU baseline is IMU-ISAC with no scatterers and no EKF integration.Source: 6) Comparison against the ISAC and IMU… · p. 6

5) Impact of scatterer visibility:

  • The proposed EKF continues estimating when scatterers are absent, unlike ISAC, while providing accurate estimates unlike the continuously drifting IMU track.The ISAC baseline provides no solution without scatterers; the IMU track drifts unless reset by an external source.Source: 5) Impact of scatterer visibility · p. 6

V. CONCLUSIONS

  • Below 1.2% median Doppler error is reported for typical settings with a smartphone-grade IMU and 5° angle-of-departure noise.The IMU has σω = 10−2 rad/s.Source: §V · p. 6
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