Direct Position Estimation (DPE) Overview

• Direct Position Estimation (DPE) is a method that estimates position, velocity, and time directly from raw sampled signals without using intermediary steps.
• It enhances localization accuracy by jointly optimizing a global cost function, thereby mitigating errors from multipath, interference, and non-line-of-sight effects.
• Recent advances extend DPE to GNSS, OFDM, and 5G systems, integrating robust statistics and multipath models to balance computational efficiency and performance.

Searching arXiv for recent and foundational papers on Direct Position Estimation to ground the article. Direct Position Estimation (DPE) is a one-step localization methodology in which position, and in many formulations position, velocity, and time (PVT), are inferred directly from received sampled signals without first estimating intermediate quantities such as code delay, Doppler shift, pseudorange, or time of arrival. In GNSS, DPE maximizes a global cost function derived from the raw sampled signal and parameterized jointly by user PVT instead of per-satellite delay and Doppler; in cellular OFDM and 5G NR, it is posed as a maximum-likelihood criterion over the received waveform; and across these settings its principal motivation is improved robustness in weak-signal, interference, multipath, and NLoS conditions (Li et al., 2023, Li et al., 4 Aug 2025, Li et al., 25 Feb 2025).

1. Core estimation principle

The canonical contrast is between DPE and conventional two-step positioning. In conventional GNSS positioning, each satellite’s signal is processed individually to estimate intermediate parameters such as code delay and Doppler shift, and those measurements are then used to solve for the receiver’s PVT. DPE replaces that decomposition with a one-step, joint approach that estimates PVT directly from the sampled signal without intermediate variables. The received baseband signal is written as

$$x[n] = \sum_{i=1}^M \alpha_i\, c_i\!\left(nT_s-\tau_i(\boldsymbol{\kappa})\right) e^{j\left(2\pi f_{d,i}(\boldsymbol{\kappa}) nT_s+\phi_i\right)} + \eta[n] + i[n],$$

where $\boldsymbol{\kappa}$ parameterizes the receiver PVT. The maximum-likelihood DPE estimate is obtained by maximizing

$$\hat{\boldsymbol{\kappa}} = \arg\max_{\boldsymbol{\kappa}} \left\{ \sum_{i=1}^M \left| \mathcal{C}_i(\boldsymbol{\kappa}) \right|^2 \right\},$$

with

$$\mathcal{C}_i(\boldsymbol{\kappa}) = \sum_{n=0}^{N-1} x[n]\, c_i\!\left(nT_s-\tau_i(\boldsymbol{\kappa})\right) e^{-j 2\pi f_{d,i}(\boldsymbol{\kappa}) nT_s}.$$

In this formulation, the cross-ambiguity function is parameterized jointly by user PVT instead of per-satellite delay and Doppler (Li et al., 2023).

The stated advantages are specific. DPE avoids error propagation from intermediate delay and Doppler estimates, does not process channels separately before the navigation solution is computed, performs a lower-dimensional search directly over PVT, offers simplified synchronization and easier inclusion of side information, and is more robust to interference since it fuses all satellite information jointly (Li et al., 2023). A related GNSS formulation used in a plug-in SDR module defines a candidate PVT vector $\mathbf{y} = [P_x,P_y,P_z,S_t]^T$ and solves

$$\mathbf{y}^{*} = \operatorname*{arg\,max}_{\mathbf{y}} \sum_{i=1}^{M} \left| \mathbf{x}^{H}\mathbf{c}_i(\mathbf{y}) \right|^2,$$

with locally generated replicas $\mathbf{c}_i(\mathbf{y})$ for each candidate PVT (Vicenzo et al., 2024).

2. Robustness to interference and multipath

A major research direction is the integration of Robust Interference Mitigation (RIM) into DPE. In this line of work, interference is treated as statistical outliers and mitigated using robust statistics without explicitly detecting or estimating the jammer waveform. The standard cross-ambiguity function is replaced by a robust CAF,

$$\mathcal{C}_{\rho,i}(\boldsymbol{\kappa}) = \sum_{n=0}^{N-1} \bar{x}[n]\, c_i\!\left(nT_s-\tau_i(\boldsymbol{\kappa})\right) e^{-j 2\pi f_{d,i}(\boldsymbol{\kappa}) nT_s},$$

and the estimator becomes

$$\hat{\boldsymbol{\kappa}} = \arg\max_{\boldsymbol{\kappa}} \left\{ \sum_{i=1}^{M} \left| \mathcal{C}_{\rho,i}(\boldsymbol{\kappa}) \right|^2 \right\}.$$

Time-domain, frequency-domain, and dual-domain robustification are considered, implemented via Zero Memory Non-Linearities such as Huber’s function, complex signum, and myriad. The reported findings are that the loss of efficiency is negligible when the robustification threshold is properly set; empirical and theoretical loss of efficiency match closely; for intentional CW jamming, frequency-domain RIM is most effective; and for DME interference, only dual-domain RIM, especially time-then-frequency processing, fully mitigates the effect while maintaining low RMSE across high interference powers (Li et al., 2023).

A separate multipath-oriented variant is MMT-DPE, introduced as a Direct Position Estimation plug-in module for conventional two-step MATLAB software-defined receivers. The module is programmed in MATLAB, can be incorporated with 2SP MATLAB SDRs, both vector tracking and scalar tracking with minimum changes, and is intended to make practical implementation easier to understand. MMT-DPE adds the MP components into the DPE signal model by integrating the MMT cost function into DPE. The abstracted result is not that DPE is immune to severe channel distortions, but that in MP-only conditions an MMT-integrated 2SP has similar performance with MMT-DPE, whereas MMT-DPE shows great superiority against NLOS, making it the preferable option for applications in urban environments (Vicenzo et al., 2024).

This also clarifies a common misconception. DPE is described as robust to multipath and weak signals, but severe multipath and NLOS conditions can still distort the autocorrelation function, and under deep multipath the highest ACF peak may diverge from the true LOS correlation. The motivation for MMT-DPE is precisely to backstop that failure mode (Vicenzo et al., 2024).

3. Geometric characterization of error propagation

Recent GNSS work separates the effects of thermal noise and multipath in explicitly geometric terms. Multipath and thermal noise are described as inducing estimation bias and variance respectively, and the paper develops a geometric portrait of how multipath error propagates from the CAF domain to the PVT solution (Huang et al., 24 Jul 2025).

For a satellite at elevation $\varphi_m$, a multipath code-delay bias $\boldsymbol{\kappa}$0 projects to a range bias

$\boldsymbol{\kappa}$1

and the corresponding range-rate bias is written analogously in terms of Doppler error. For two satellites with range biases $\boldsymbol{\kappa}$2 and azimuth separation $\boldsymbol{\kappa}$3, the PVT solution bias is

$\boldsymbol{\kappa}$4

When all satellites have the same bias $\boldsymbol{\kappa}$5, this reduces to

$\boldsymbol{\kappa}$6

These equations underpin the satellite circular multipath bias (SCMB) model, in which each satellite defines a circle around the true receiver position and tangent-line intersections represent possible DPE solutions (Huang et al., 24 Jul 2025).

Several consequences are stated explicitly. The maximum PVT bias depends on the largest multipath errors observed across various satellite channels. PVT bias increases with satellite elevation angles, influenced by the CAF multipath bias projection. As $\boldsymbol{\kappa}$7 or $\boldsymbol{\kappa}$8, the denominator tends to zero and the PVT error can theoretically diverge. The proposed geometric guidance is therefore to choose a balanced combination of high and low elevation angles and to maximize azimuthal spread, rather than relying on an all-high-elevation or nearly collinear satellite configuration (Huang et al., 24 Jul 2025).

The paper reports confirmation of this geometrical portrait through both Monte Carlo simulations and urban canyon tests. This suggests that DPE performance cannot be characterized solely by signal-level robustness; satellite geometry remains structurally important even in a direct estimator (Huang et al., 24 Jul 2025).

4. OFDM and 5G cellular formulations

DPE has been extended from GNSS to OFDM-based cellular positioning. In a multi-source SISO downlink OFDM system with multiple base stations transmitting known reference signals, the user equipment state is estimated directly from the raw received OFDM signals rather than from intermediate ToA and Doppler estimates. The maximum-likelihood problem is posed as

$\boldsymbol{\kappa}$9

and the corresponding Fisher Information Matrix and CRB are derived for the real-valued parameter vector containing channel coefficients, path parameters, and UE state (Li et al., 4 Aug 2025).

The conclusions of that CRB analysis are narrow but important: DPE consistently outperforms the two-step approach in OFDM systems under all evaluated conditions; a large bandwidth is crucial in both methods; increasing subcarrier spacing is more beneficial for a fixed bandwidth; and utilizing multiple OFDM symbols for positioning leads to substantial improvements in localization accuracy compared to relying on a single symbol, although further increasing the number of symbols yields marginal improvements while significantly increasing computational complexity (Li et al., 4 Aug 2025).

In 5G NR, DPE is applied to dense urban positioning under 3GPP tapped delay line propagation models. With the discrete signal model

$$\hat{\boldsymbol{\kappa}} = \arg\max_{\boldsymbol{\kappa}} \left\{ \sum_{i=1}^M \left| \mathcal{C}_i(\boldsymbol{\kappa}) \right|^2 \right\},$$0

the maximum-likelihood estimator becomes

$$\hat{\boldsymbol{\kappa}} = \arg\max_{\boldsymbol{\kappa}} \left\{ \sum_{i=1}^M \left| \mathcal{C}_i(\boldsymbol{\kappa}) \right|^2 \right\},$$1

The reported system-level simulation uses 26 BSs deployed over 227,360 m² in Hong Kong’s Tsim Sha Tsui area at 10 m height and 24 dBm power, a 100 MHz PRS downlink, and 5000 independent trials with LoS in 17% and NLoS in 83% of realizations. The results state that 5G DPE achieves satisfactory positioning accuracy in a 10 dB noisy channel, with an overall RMSE constrained within 6 m, and that it outperforms OTDoA by 95.24% in terms of positioning accuracy in an NLoS-dominated propagation environment. In the four-BS comparison scenario, 99% of DPE trials have RMSE below 7 m and 90% below 2 m, while OTDoA has 90% RMSE at 42 m (Li et al., 25 Feb 2025).

5. Algorithmic variants and related direct localization methods

In emitter localization, closely related work is often formulated as Direct Position Determination (DPD). These methods share the defining feature of direct estimation from jointly processed signal data rather than a two-stage measurement-then-solve pipeline.

Variant	Setting	Key point
One-Bit DPD	Narrowband Gaussian signals	Uses one-bit quantized measurements and second-order statistics
IS-based ML DPD	Multiple stationary emitters	Replaces multidimensional grid search by importance sampling
Classical DPD objective	Multistation emitter localization	Maximizes largest eigenvalue over candidate positions

One-Bit DPD addresses the communication burden created when raw signal data must be transferred to a common processor. The method quantizes each complex sample with a one-bit ADC, reconstructs second-order statistics of the unquantized signals using the arcsine law, forms beamformed matrices at hypothesized delays, and estimates position through

$$\hat{\boldsymbol{\kappa}} = \arg\max_{\boldsymbol{\kappa}} \left\{ \sum_{i=1}^M \left| \mathcal{C}_i(\boldsymbol{\kappa}) \right|^2 \right\},$$2

The stated theoretical results are that the model’s identifiability conditions rely only on second-order statistics, the estimator has appealing asymptotic properties, and much of the information regarding the unknown emitter position is preserved under this crude form of quantization (Weiss et al., 2020).

For multiple stationary emitters observed by moving receivers through angle and Doppler measurements, a computationally efficient maximum-likelihood DPD method uses Pincus’ theorem and importance sampling. The concentrated ML objective is transformed from an exhaustive multidimensional grid search into random-variable generation with multiple low-dimensional pseudo-probability density functions, and a circular mean is used for superior position estimation performance. The paper states that the computational complexity is modest, the off-grid problem is significantly alleviated, the method can be implemented in parallel separately, and with a reasonable parameter choice the estimator is very close to the Cramér-Rao lower bound even in adverse low-SNR conditions (Wang et al., 2021).

6. Practical implementation, computational burden, and current trajectory

The computational burden of DPE is a recurring practical issue. In the 5G and OFDM formulations, the maximum-likelihood search is explicit and the number of candidate states grows rapidly with search volume, bandwidth, and symbol count. The OFDM CRB study notes that using more OFDM symbols improves accuracy but eventually produces only marginal improvements while significantly increasing computational complexity, and it observes that the optimization by grid search is highly parallelizable and suited to GPU acceleration (Li et al., 4 Aug 2025). The SDR plug-in implementation similarly centers a configurable candidate grid around an initial estimate from a two-step receiver, pre-calculates code-phase correlations for efficiency, and then evaluates the DPE objective over that grid (Vicenzo et al., 2024).

Another practical constraint is distributed processing. One-Bit DPD is motivated by the fact that classical DPD requires raw signal data to be transferred to a common processor, creating a heavy communication load between base stations and the processor. The one-bit formulation is presented specifically as a way to alleviate the requirements on the communication links while preserving much of the position information (Weiss et al., 2020).

At the same time, GNSS positioning with DPE is described as mostly left unapplied commercially, and continuing research into DPE is described as having remained relatively stagnant over the past few years. The recent appearance of MATLAB plug-in modules for conventional SDRs, OFDM CRB analyses, 5G NR urban simulations, and geometric multipath studies suggests renewed methodological activity, but the enduring research tension remains the same: direct estimators can provide more robust and accurate PVT estimates in the presence of multipath, weak signals, interference, and NLoS, while demanding careful control of search complexity, signal modeling assumptions, and geometry (Vicenzo et al., 2024, Li et al., 4 Aug 2025, Huang et al., 24 Jul 2025).